Y. Cengiz Toklu, Gabriel Bekdaş (eds.)
METAHEURISTICS AND ENGINEERING Proceedings of the 15th EU/ME Workshop
14th Workshop of the EURO Working Group “EU/ME: The Metaheuristic Community” 24.03.2014 – 25.03.2014 Istanbul, Turkey
Y. Cengiz Toklu, Gabriel Bekdas (eds.)
METAHEURISTICS AND ENGINEERING Proceedings of the 15th EU/ME Workshop
15th Workshop of the EURO Working Group
''EU/ME: The Metaheuristic Community'' 24.03.2014 – 25.03.2014, Istanbul, Turkey
Y. Cengiz Toklu Civil Engineering Department, Faculty of Engineering, Bilecik S¸eyh Edebali University, Bilecik, Turkey (email:
[email protected]) Gabriel Bekda¸s Civil Engineering Department, Faculty of Engineering, Istanbul University, Istanbul, Turkey (email:
[email protected])
Bilecik S¸eyh Edebali University, 2014 ISBN 978-605-85313-0-7
Contents Preface.......................................................................................................................................................ii People.......................................................................................................................................................iii Sponsors..................................................................................................................................................vii
Contributed Articles Using Monocular Vision for Navigation of LEGO Robot Yasir Salih, Mohammed Simsim..................................................................................................................1 Modeling Interstice Loading Effect of Groups of Six Cylindrical Silos Using Artificial Neural Network S¨ uleyman Bahadir Y¨ uksel, M. Hakan Arslan...............................................................................................7 An Overview of Metaheuristic Algorithms Yusuf Cengiz Toklu....................................................................................................................................13 An Efficient Metaheuristic Approach for Solving a Class of Matrix Optimization Problems Petrica Pop, Oliviu Matei..........................................................................................................................17 Mathematical Programming Based Heuristics for the Capacitated Lot Sizing Problems Hacer G¨ uner G¨ oren, Semra Tunal.............................................................................................................27 An Adaptive Large Neighborhood Search Approach for the Electric Vehicle Routing Problem Merve Keskin, B¨ ulent C ¸ atay......................................................................................................................31 A Method of Composition of Services Based on QoS Makhlouf Derdour, Sourour Maalem, Ghoualmi Nacera ...........................................................................37 Analysis of plane stress problems as optimization problems ¨ ur Yaylı , Burhanettin Altan..................................................................45 Yusuf Cengiz Toklu, Mustafa Ozg¨ A Genetic Algorithm Application for Multi-objective Multi-project Resource Constrained Project Scheduling Problem Fikri K¨ uc¸u ¨ksayacigil, G¨ und¨ uz Ulusoy.......................................................................................................49 The Effect of Eccentricity for Optimum Compressively Loaded Reinforced Concrete Columns Gebrail Bekda¸s, Sinan Melih Ni˘gdeli........................................................................................................53 Fusion of Palm-Vein Finger-Vein for Personal Identification Using Principal Component Analysis Abdallah Meraoumia, Hakim Bendjenna, Salim Chitroub, Ahmed Bouridane ........................................57 Applications of Meta-heuristic Algorithms to Civil Engineering Problems, A Survey Ali Erdem C ¸ er¸cevik, Hasan Bozkurt, Yusuf Cengiz Toklu........................................................................63 Estimation of Fault Plane Parameters by Using Stochastic Optimization Methods ¨ Ozlem T¨ urk¸sen.........................................................................................................................................71 Remarks on Robust and Reliable Design Optimization Simon Gekeler, Rolf Steinbuch.................................................................................................................77 Modelling Uniform Temperature Effects of Symmetric Parabolic Haunched Beams Using Adaptive Neuro Fuzzy Inference Systems (ANFIS) S¨ uleyman Bahadir Y¨ uksel, Alpaslan Yarar...............................................................................................83
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Robustness of Optimum TMDs According to Change of the Stiffness of the Structure Sinan Melih Ni˘gdeli, Gebrail Bekda¸s........................................................................................................89 SME Clustering for Sustainable Collaborative Innovation Ay¸ca Altay, G¨ ulg¨ un Kayakutlu.................................................................................................................93 Neural Network-Based Metaheuristic: A Method to Prioritrizing Software Test Cases Negar Majma, Seyed Morteza Babamir....................................................................................................99 Particle Swarm Optimization for Unplanned AGV Routing in Kanban Systems ¨ Alper Ozpinar, Emel S ¸ eyma L¨ ok............................................................................................................107 Analysis of Structures with Unilateral Boundary Conditions Gebrail Bekda¸s, Rasim Tem¨ ur, Yusuf Cengiz Toklu...............................................................................113 Artificial Neural Network (ANN) Modelling of the Parabolic Haunched Beams Subjected to Uniform Temperature Change S¨ uleyman Bahadır Y¨ uksel, Alpaslan Yarar..............................................................................................117 A Variable Neighbourhood Metaheuristic for the Clustered Vehicle Routing Problem Christof Defryn, Kenneth S¨ orensen........................................................................................................123 User Interface for Testing Heuristic Algorithms ¨ Mehmet S¨ uleyman Yıldırım, Cihan Karakuzu, Ozlem Yıldırım..............................................................127 Metaheuristics in Applied Geophysics C ¸ a˘glayan Balkaya, G¨ okhan G¨ okt¨ urkler, Yunus Levent Ekinci, Se¸cil Turan.............................................133 Exploiting Genetic Algorithm to Path Coverage in Software Testing Shima Amirsadri, Seyed Morteza Babamir.............................................................................................141 On-line Path Planing for Mobile Robots Based on Basic Heuristic Guidance Cihan Karakuzu, Robert Babuska..........................................................................................................147 Behaviour of Zero Force Truss Members in Nonlinear Analysis Rasim Tem¨ ur, Gebrail Bekda¸s, Yusuf Sait T¨ urkan, Yusuf Cengiz Toklu.................................................153 The (city) Bike Request Scheduling Problem – A Novel Approach to Solve the City Bike Repositioning Problem Kenneth S¨ orensen, Darpana Dilip..........................................................................................................157 Transportation of Handicapped Persons Soto Maria, Marc Sevaux, Andre Rossi..................................................................................................163 Reinforcement Design of Axially Symmetric Cylindrical Walls Gebrail Bekda¸s.......................................................................................................................................167 Addressing Churn Prediction Problem with Meta-heuristic, Machine Learning, Neural Network and Data Mining Techniques: A Case Study of a Telecommunication Company A. Keramati, R. Jafari-Marandi, M. Aliannejadi, M. Mozzafari, U. Abbasi, I. Ahmadian.....................171 Shape Optimization of Steel Cross-Sections for Flexural Moment Sinan Melih Ni˘gdeli, Gebrail Bekda¸s......................................................................................................181 An Efficient Genetic Algorithm Method For Large Population Solutions Osman H¨ urol T¨ urkakın, Ekrem Manisali...............................................................................................185 Numerical Function Optimization by Migrating Birds Optimization Algorithm ˙ Ilker Elik¨ u¸cu ¨k, Ekrem Duman................................................................................................................189
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Preface It goes without saying that, meta-heuristic methods made a fantastic entrance to professional lives of scientists and engineers who are interested in solving real life problems which were very difficult and even impossible to solve with existing methods. Indeed, these methods which are in use since about half a century, are very efficient in solving optimization problems with all types of constraints, with no requirement on the existence of gradients, with variables of all types including those with any combinations of them, with single or multiple objectives, and even those with no well-defined formulations. The success of these new techniques can be traced in the number and efficiency of studies on problems being solved in a great variety of fields of science and engineering, and also in the continuously increasing types of algorithms themselves, based on nature, social life, politics, physics, music, metallurgy, games, etc. This volume is a collection of papers submitted and accepted to the scientific meeting, 15th Workshop of the EURO Working Group on Metaheuristics (EU/ME), on the intersection of metaheuristic algorithms and engineering. The title of the workshop, ’Metaheuristics and Engineering’, summarizes well the main theme of the meeting: advances in metaheuristic techniques and their applications on various field of engineering. The workshop is organized by Bilecik S¸eyh Edebali University and provided an international forum on the subject to about 40 participants with origins from very different countries. The editors would like to express their gratitude especially to the President of the Bilecik S¸eyh Ede¨ bali University, Professor Azmi OZCAN and the Dean of the Engineering Faculty, Professor Nurg¨ ul ¨ ¨ OZBAY, and the international advisors Andreas REINHOLZ, Marc SEVAUX, Kenneth SORENSEN, for their encouragements and advises at difficult moments. The workshop is made possible with the help of team members forming the Organization Committee and especially the young member Mr. Ali Erdem ˙ C ¸ ERC ¸ EVIK. We hope that the keynote speeches by Luca Maria GAMBARDELLA, Ali KAVEH, Patrick SIARRY, and Xin-She YANG will demonstrate the depth of the meta-heuristic algorithms horizon to the participants, and the presentations by the participants and the following discussions will lead to fruitful advances in engineering applications of these algorithms. Finally, we wish a fruitful and pleasant stay in Istanbul for the occasion to all participants and presenters and thank them for their contributions.
Y. Cengiz TOKLU Gabriel BEKDAS ¸
Istanbul, Turkey March 2014
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PEOPLE Honorary Chairs ¨ Azmi OZCAN, President, Bilecik S ¸ eyh Edebali University, Turkey ¨ Nurgul OZBAY, Dean of the Engineering Faculty, Bilecik S ¸ eyh Edebali University, Turkey
Local organizers Y. Cengiz TOKLU, Bilecik S ¸ eyh Edebali University (Workshop Coordinator) Cihan KARAKUZU, Bilecik S ¸ eyh Edebali University (Workshop Co-Chair) S¨ uheyla YEREL KANDEMR, Bilecik S ¸ eyh Edebali University (Workshop Co-Chair) Gebrail BEKDAS ¸ , Istanbul University (Workshop Co-Chair) ˘ ˙ Istanbul University (Workshop Co-Chair) Sinan Melih NI˙ GDEL I, ¨ ur YAYLI, Bilecik S Mustafa Ozg¨ ¸ eyh Edebali University ¨ Istanbul University Rasim TEMUR, Hasan BOZKURT, Bilecik S ¸ eyh Edebali University ˙ Bilecik S Ali Erdem C ¸ ERC ¸ EVIK, ¸ eyh Edebali University
International Advisory Board Andreas REINHOLZ, Techniche Universtat Dortmund, Germany Marc SEVAUX, Universit de Bretagne-Sud, France ¨ Kenneth SORENSEN, University of Antwerp, Belgium
Scientific Committee ABE, Akira (Asahikawa National College of Technology, JP) ALAVI, Amir H. (Michigan State University, USA) ALTAN, Burhanettin (Bayburt University, TR) AKAY, H. Umur (Atilim University, TR) ARFIADI, Yoyong (Atma Jaya Yogyakarta University, IN) AYDIN, Nizamettin (Yıldız Tecnical University, TR) BASMACI, Yakup (S ¸ ırnak University, TR) CEYLAN, Salim (Bilecik S ¸ eyh Edebali University, TR) ˙ IC ˙ ¸ IO ˙ GLU, ˘ C ¸ IV Pınar (Erciyes University, TR) COELLO COELLO, Carlos A. (Instituto Politcnico Nacional, MX) CSEBFALVI, Aniko (Pecs University, HU) ˘ DALOGLU, Ay¸se (Karadeniz Tecnical University, TR) DAVEY, Keith (The University of Manchester, UK) ˘ DOGAN, Erkan (Celal Bayar University, TR) ELC ¸ I, Atilla (Aksaray University, TR) ˙ Ibrahim ˙ EKSIN, (Istanbul Technical University, TR) ERBATUR, Fuat (Emeritus, TR) GANDOMI, Amir H. (The University of Akron, USA) GEEM, Z.W. (Gachon University, KP) GRECO, Marcelo (Federal University of Uberlandia, BR) GUNES, Mustafa (Gediz University, TR) HADI, Muhammad N. S. (Univ. of Wollongong, AU) HAJIRASOULIHA, Iman (University of Sheffield, UK) ˙ Oguzhan (Middle East Tecnical University, TR) HASANC ¸ EBI, ˘ KARABOGA, Dervis (Erciyes University, TR) KAVEH, Ali (Iran University of Science and Technology, IR) KESLER, Metin (Bilecik S ¸ eyh Edebali University, TR) KILIC ¸ , H¨ urevren (Gediz University, TR) KURBAN, Mehmet (Bilecik S ¸ eyh Edebali University, TR) LEUNG, Andrew (City University of Hong Kong, HK) MARANO, Giuseppe Carlo (Technical University of Bari, IT) MONTEMANNI, Roberto (Istituto Dalle Molle di Studi sull’Intelligenza Artificiale, CH) ¨ OZCAN, Sel¸cuk (Bilecik S ¸ eyh Edebali University, TR) ¨ OZDAMAR, Linet (Yeditepe University, TR) POP, Petrica (Technical University of Cluj-Napoca, RO) iii
STEINBUCH, Rolf H. (Reutlingen University, DE) TAKEWAKI, Izuru (Kyoto University, JP) TAPKIN, Serkan (Istanbul GeliSim University, TR) TOROPOV, Vassili (University of Leeds, UK) WEBER, G.-W. (Middle East Tecnical University, TR) YAMIK, Hasan (Bilecik S ¸ eyh Edebali University, TR) YANG, Xin-She (Middlesex University, UK) ¨ YUZGEC ¸ , U˘ gur (Bilecik S ¸ eyh Edebali University, TR)
Keynote Speakers GAMBARDELLA, Luca Maria, (Universit della Svizzera italiana, CH) KAVEH, Ali (Iran University of Science and Technology, IR) SIARRY, Patrick (Universit de Paris 12, F) YANG, Xin-She (Middlesex University, UK)
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Using Monocular Vision for Navigation of LEGO Robot Yasir Salih and M.T Simsim∗ Abstract This paper presents vision based navigation of LEGO Mindstorms robot using a single camera. This robot is equipped with a camera of known pose (height and pitch angle). The aim of the project is to establish a vision based navigation on a small robotic platform such as LEGO Mindstorms robot. While navigating, the robot detects predefined targets in the image and then computes its location with respect to robot. The target is detected based on its color properties which are previously defined to the robot. The 3D coordinates of the target is computed using triangulation with a known pose camera. The implemented depth computation algorithm has very low computational requirement and it can easily be adopted to achieve real time 3D navigation on small robots such as LEGO. Keywords: LEGO robot, color detection, depth estimation, objects tracking.
1
Introduction
LEGO Mindstorms robot is a widely used robotic platform for teaching robotic, embedded systems and programming courses. This kit contains small hardware components that can be customized to any application such as wheeled robot, humanoid robot as well as task oriented robot [13]. In many education institutions, LEGO is the most appropriate robotic kit to help lecturers deliver the basic knowledge about robotics, mechanics and programming to freshmen students [1]. Moreover, LEGO can be integrated with various types of sensors such as GPS, accelerometer, touch sensor, ultrasound sensor as well as cameras. This makes the LEGO Mindtorms suitable for wide range of applications. In addition to that and because of the large number of people using it, LEGO has been adapted to various programming tools such as Matlab, LabVIEW, ROS, Python and many other software tools [7]. Moreover, LEGO Mindstorms robots are widely used for teaching robotics courses for degree students. Faculty members of Georgia Techs School developed an introduction to ECE design based on LEGO Mindstorms robot to provide students with system level design of ECE disciplines at an early ∗ Yasir Salih is with Science and Technology Unit, Umm Al-Qura University, Makkah, Saudi Arabia (email:
[email protected]) Mohammed T. Simsim is with Electrical Engineering Department, Umm Al-Qura University, Makkah, Saudi Arabia (email:
[email protected])
1
stage of their academic life [16]. The course content introduces students to different types of sensors and actuators. In RWTH Aachen University, LEGO Mindstorms robot is used for teaching engineering course to freshman students [1]. In Malaga University, LEGO Mindstorms robot is integrated with Lab VIEW for delivering the laboratory work of the mechatronics course [10]. The course content teaches students robot navigation, fuzzy logic control, line following robots and reactive robotic navigation. The ability of a mobile device to navigate is an important step in build a fully autonomous system [15]. Navigation requires the scene of perception so that the robots see and understand other objects around it [4]. When using vision based navigation firstly, the target of interest is identified in the image using suitable visual cue such as color, shape or motion [2]. In this paper, we describe a vision based navigation scheme on LEGO Mindstorms robot with four wheels and NXT camera connected to the LEGO brick where all the processing is performed. The remaining of this paper has been organized as follows. Section 2 describes related works on LEGO Mindstorms. Section 3 describes how the components of LEGO Mindstorms robot and the image processing are used for detecting obstacles. Section 4 describes the experiment setup and the mace used for navigating the robot. Finally Section 5 provides a brief conclusion about this work and provides some future directions in improving this work.
2
Related Works
LEGO Mindstorms robot is very common in the robotics society and many applications have been presented based on it. Kim and Jeon [9] presented a study on how to program LEGO robot using visual programming environment based on LabVIEW and Microsoft Robotic Studio (MSRS). This robot was used for implementing inter-university project between several universities from US and Europe. The project involves collaborative works with multiple robots at distant universities by sharing the project resources and performing complimentary tasks at each institute [11]. Hsu and Tsai [6] built a home security system based on LEGO Mindstorms robot. They used touch, light, ultrasound and sound sensors as inputs. These sensors are used as a part of school project to protect a safe box by detecting any encroachment to the box. Trung et al. [12] used LEGO Mindstorms robot equipped with a we-
bcam for recognizing road signs. They used webcam to captures images and send the images to be processed on a remote computer instantaneously. The webcam recognized the location of the road sign and its types while an ultrasound is used to gauge the distance between the robot and the road sign. Alfaro and Riff [3] developed a real-time collision detection algorithm for navigating LEGO Mindstorms robot. Their algorithm uses a light sensor for navigation and three touch sensors for sensing the possibility of collision at the front, left and right sides of the robot. The robot uses the touch sensors information to plan the next move then uses the light sensor to navigate in that direction until a new obstacle is detected. Lee [5] developed a real time face detection and recognition system using LEGO Mindstorms robot and wireless camera. In this implementation, all the face detection and recognition tasks are implemented on a host PC which communicates with the robot using Bluetooth. Keskin and Uyar [8] presented a multiple robot navigation and control to avoid collision between these robots. The robots are monitored by an overhead camera which detects the location of each robot and controls its navigation. Brigandi et al. [14] implemented triangular swarm intelligence algorithm for navigation of four robots using light and ultrasound sensors.
3
LEGO Robot Navigation
This section describes the basic components and functions of the LEGO Mindstorms robot. Then this section describes the image processing module of the navigation algorithm and how path planning is achieved. Lastly this section describes how to compute depth and geometry form single image using triangulation of a camera with a known pose.
3.1
LEGO Mindstorms Robot
LEGO Mindstormss robot was introduced at MIT Media Lab and then it became one of the famous robotic platforms. LEGO mind also known as LEGO brick is equipped with 32-bit ARM7 processor and 250 MHz speed, 64KB RAM and 256 KB of flash memory [5]. The LEGO brick also contains Atmel AVR microcontroller that runs at 4MHz speed and it has a RMA of 512 Byte. It has 100x64 pixel LCD matrix display. The brick can communicate using USB and Bluetooth and it can connect to various types of sensors and actuators using dedicated I/O interface. Figure 1 shows a block diagram of the basic components of the LEGO brick.
Figure 1: Basic components of LEGO Mindstorms brick [9]
are captured from LEGO camera which is considered as a low resolution camera of 88144 pixels and renders 30 frames per second. The camera has a 3.6 mm lens with 920 diagonal aperture. The camera communicates with LEGO brick using I2C Bus. Initially, the robot camera is trained on the color of the objects to be detected and tracked in the mace. In this experiment, 8 color patterns have been stored prior to the navigation process. The user selects the patterns by setting the threshold of the RGB color components for each pattern (learning process). Then for every pattern, a color template is created by taking the mean and the variance of the color pattern. For every new frame, firstly the object with desired color is detected using a color pattern stored earlier. After that, object blobs are created by applying morphological operators to clear small blobs as well as apply closing process to cluster neighboring blobs in one larger object blob. Lastly, feature matrix is created for each blob in the blob image. The feature matrix contains the top left and bottom right points in the image as well as the average color of the blob. Figure 2 shows a flow chart of the image processing module for extracting, creating and detecting selected color patterns in the image captured by LEGO camera.
3.3
Depth and Geometry Computation
In this research, a new algorithm has been implemented for computing depth and geometry of the previously detected object. As a part of the detected object features, this algorithm extracted the ground location (bottom most location) of the object blob in the image assuming that the object is standing on a flat ground. Beside the object location in image coordinates, this algorithm as3.2 LEGO Image Processing Module sumes that the robot has a known camera pose which means the camera has been fixed at a known Navigating LEGO robot using camera inputs in- height on top of the robot and with a known vertivolves processing images to extract objects of in- cal angle. Figure 3 shows a model of a robot with terest (obstacles) so they can be avoided. Images a known camera pose where theta represents the
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Figure 4: An object location at pixel p(i,j) of a known pose camera
Distance = h ∗ tan(ψ)
Figure 2: Color pattern creation and extraction process
3.4 camera pitch angle and FOV is the camera field of view. Cam Height is the height of the camera from the ground in centimeters while Image height is the height of the image in pixels which is 144 pixels for NXT camera (NXT camera has image resolution of (88x144).
4.1
The geometry of any object in in the camera view can be computed using triangulation. Firstly when a blob is detected in the image, the robot will turn so that the central vertical axis of the blob is aligned with the middle vertical line of the image. Figure 4 shows a model at which an object is located at pixel p(i,j) in front of a known-pose camera. To compute the depth of obstacle, firstly the robot computes the vertical angle of the obstacle in the image using (1). Then the distance between the robot center and the obstacle is computed using (2) where H and W are image height and width respectively while h is the camera height. ψ = θ + ((H/2) − j) ∗ (F OV /H)
(1)
3
and
Path
LEGO robot uses the color detection algorithm to navigate its way. Once the pattern is detected in the image, the geometry computation algorithm computes the distance between the robot and the obstacle. After that, the robot plans the next move so that it avoids colliding with the obstacle while taking the shortest path forward.
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Figure 3: LEGO robot equipped with a known pose camera
Robot Navigation Planning
(2)
Experimental Results Experiment Setup
As explained earlier, in this paper NXT camera is the only perception sensor used for navigating the LEGO Mindstorms robot. Table 1 shows the intrinsic and extrinsic parameters of the used camera. The main task of the robot is to navigate in the mace shown in Figure 5 by detecting the landmarks which are specially colored objects and then plans the next motion according to lookup table which tells the turning direction after the detection of each one of these landmarks. The farthest distance shown between the robot and the object is 140cm which is relatively small but still allow the robot to makes correct navigation decisions. Table 1: Camera intrinsic and extrinsic parameters
P arameter camera height images size camera pitch angle camera field of view lens size
V alue 44cm 88×144 60o o 34.2 × 25.8o 3.6mm
firstly it matches the object color with the lookup table so that the object is recognized and the turning direction after that object is known. Then it measures the distance from it if the robot is far from the obstacle by some specified distance. Then the robot moves forward until it is close to the object and then it makes a turn according to the lookup table. The robot uses these two techniques to navigate its way in an unknown mace with 5 to 8 different obstacles. In most of the cases, the robot makes correct navigation decision however there were some errors due to miss-detection of the obstacle color or confusion with the background colors of the mace.
Figure 5: Mace for navigating LEGO robot
4.2
Table 2: Measuring distance between robot and the obstacles
Results and Analysis
Image
The developed robotic platform has been tested by navigating it in the mace given in Figure 5. In this task, the robot detected a previously known object (based on color) and measured the distance between the robot and the object using the algorithm described earlier. If this distance is greater than 20cm, the robot continues its way forward. Once the robot is close to the object with a distance less than 20cm, the robot takes a turning decision based on a given lookup table for each color. The lookup table is designed in advance based on how the obstacles are placed in the mace. The main navigation task is measuring the distance between robot and detected objects using triangulation methods with known camera pose. Table 2 shows results of measuring the distance between robot and obstacles. The first column shows view of the scene which includes the robot and the corresponding obstacle. The second column shows the blob image presented on the LEGO LCD screen. The third column shows the distance between robot and obstacle measured by the proposed method while the fourth column shows the actual distance. Last two columns show that the object has been accurately detected and the measured distance is close to the actual. In all measurements, the maximum error obtained is around 5cm which is only 3.5 of the maximum measurable distance. The last column shows how well the algorithm recognizes this obstacle by testing the decision the robot takes after it passes the object. The turn decision tests how accurately the robot recognizes the color of the object. In this experiment, the robot has been taught 8 different colors and it can clearly distinguish them in the scene. The last column tell how accurately the robot recognized the color of the object (the turning decision are stored in the lookup table according to the object colors). The robot uses the color recognition and distance measurement inputs to navigate its way through the mace. Prior to the navigation process the robot is provided with a lookup table that tells it what is the action to take after it recognizes an object. Thus when the robot detects an object;
4
5
Blob
Conclusions Works
Xmsr
Xact
Action
74cm
74cm
True
47cm
42cm
True
55cm
56cm
True
94cm
95cm
True
and
Future
In this research, we presented a vision based robot navigation technique built using LEGO Mindstorms robot and the NXT camera. The main contribution is by implementing the geometric computation algorithm on the LEGO robot as well as efficiently using it for navigation to achieve some tasks. As a future enhancement for this project, shape features can be used for detecting obstacles beside color which makes the algorithm more robust. In addition, background subtraction can be used to detect moving object in the scene such as another robot moving in the mace.
References [1] R. Schwann B. Neumann R. Schnitzler J. Balle T. Herold A. Telle T.G. Noll K. Hameyer T. Aach A. Behrens, L. Atorf. Matlab meets lego mindstorms a freshman introduction course into practical engineering. IEEE Transactions on Educations, 53(2):306–317, 2010.
[2] J. Driemeyer A. Saxena and A. Y. Ng. Robotic grasping of novel objects using vision. The International Journal of Robotics Research, 27(2):157–173, 2008. [3] T. Alfaro and M.-C. Riff. An on-the-fly evolutionary algorithm for robot motion planning. Lecture Notes in Computer Science (Evolutionary systems: from biology to hardware), 3637:119–130, 2005. [4] F. Bonin-font and A. Ortiz. Visual navigation for mobile robots: a survey. Journal of Intelligent and Robotic Systems: Theory and Applications, 53(3):264–296, 2008. [5] T. hoon Lee. Real-time face detection and recognition on lego mindstorms nxt robot. Lecture Notes in Computer Science (Advances in boimetrics), 4642:1006– 1015, 2007. [6] K.-K. Hsu and D.-R. Tsai. Build a home security surveillance system using lego mindstorms nxt. International Conference on Intelligent Information Hiding and Multimedia Signal Processing, pages 254–257, 2009. [7] J. Fernndez-lozano J. M. Gmez-de gabriel, A. Mandow and A. J. Garca-cerezo. Using lego nxt mobile robots with labview for undergraduate courses on mechatronics. IEEE Transactions on Educations, 54(1):41–47, 2011. [8] O. Keskin and E. Uyar. A framework for multi robot guidance control. International Conference on Industrial Applications of Holonic and Multi-Agent Systems, pages 315–323, 2009. [9] S. H. Kim and J. W. Jeon. Programming lego mindstorms nxt with visual programming. International Conference on Control, Automation and Systems, pages 2468–2472, 2007. [10] A. P. Moreira M. Pinto and A. Matos. Localization of mobile robots using an extended kalman filter in a lego nxt. IEEE Transactions on Educations, 55(1):135–144, 2012. [11] J. M. Thiriet W. Grega P. Adam, A. J. Kornecki and O. Rysavy. Inter-university project based on lego nxt. IEEE International Conference on Control Applications, pages 1248–1253, 2009. [12] N. Afzulpurkar P. Trung and D. Bodhale. Development of vision service in microsoft robotics studio for road signs recognition and control of lego mindstorms robot. IEEE International Conference on Robotics and Biomeimetics, pages 1176–1181, 2009. [13] A. Gasparetto R. Vidoni, F. Garca-Snchez and R. Martnez-Bja. An intelligent framework to manage robotic autonomous agents. Expert Systems with Applications, 38(6):7430–7439, 2011. [14] J. Field S. Brigandi and Y. Wang. A lego mindstorms nxt based multirobot system. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pages 135–139, 2010. [15] Y. Salih and A. S. Malik. Comparison of stochastic filtering methods for 3d tracking. Pattern Recognition, 44(10-11):2711–2737, 2011. [16] D. B. Williams. A freshmen introduction to ece design course based on the lego mindostorm nxt. IEEE Conference on Digital Signal Processing Education, pages 435–439, 2010.
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Modelling Interstice Loading Effect of Groups of Six Cylindrical Silos Using Artificial Neural Network S. Bahadır YÜKSEL*, M. Hakan Arslan Abstract The determination of the design forces for the reinforced concrete groups of six cylindrical silos (GSCS) requires significant computational effort due to structural continuity and the force transfer between adjacent silos. In this study, the efficiency of Artificial Neural Network (ANN) method in predicting the design forces and moments of GSCS due to interstice loadings was investigated. Previously obtained finite element (FE) analyses results in the litrature were used to train and test the ANN models. Each parameter (silo wall thickness, intersection wall thickness and the central angle spanning the intersection walls of the GSCS) affecting design forces and moments was set to be an input vector. The outputs of the ANN models would be the bending moments, hoop forces and shear forces at the supports of the interstice walls due to interstice loadings. All the outputs of the ANN models were trained and tested using 11 three-layered different back-propagation methods widely used in the literature. The obtained results presented that all the back-propagation methods were capable of predicting the design forces and design moments at the interstice walls of the GSCS.
The typical geometrical parameters of the groups of six cylindrical silos is shown in Figure 1. GSCS has two interstice cells, the interstice loading case will include two interstice loading combinations to determine the worst-case interstice loading cases. Yuksel [4] analyzed the GSCS subjected to interstice loadings by FE method using eight node isoparametric solid elements and calculated the design forces at the prescribed sections of the interstice walls having different silo wall thicknesses, intersection wall thicknesses and the intersection wall lengths. Based on the results of his finite element analyses (FEA), new design formulas and estimation coefficients were proposed for the calculation of the design forces without necessitating any FEA for the GSCS subjected to interstice loadings.
Keywords: Silos, concrete silos, granular material, grouped silos, artificial neural networks, backpropagation methods.
1
Introduction
Figure 1. Geometrical parameters of the typical group of six cylindrical silos
Reinforced concrete grouped silos may be constructed in circular, rectangular and hexagonal configurations with various geometries. Of these configurations, the simplest and the most common forms used for the storage of the granular materials are the grouped cylindrical silos that are widely used in the world. The computation of the design forces for the reinforced concrete GSCS requires significant computational effort due to the wall continuity between the adjacent silos. The general behavior of grouped silos due to stored materials has been studied for many years [1,2,3]. Very few researchers have investigated the behavior of the GSCS under internal and interstice loadings [4,5]. *S .
B a h a d ı r Y Ü K S E L is with the Department of C i v i l E n gi n e e r i n g , Selcuk University, Konya, , Turkey (email: s b y u k s e l @ s e l c u k . e d u . t r )
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The objective of this research is to investigate the usability of the ANN models for the estimation of the design forces of the GSCS due to interstice stored material pressures. Design forces at the prescribed sections of interstice walls were computed by using the design formulas and the estimator coefficients proposed by Yuksel [4]. In the light of these obtained results, 11 different ANN approaches were performed to estimate the design forces and the design moments due to interstice and internal loadings of the GSCS [5]. The FE analyses results obtained by Yuksel [4] were compared with those of 11 different back-propagation models. Training error, test error, training time and correlation coefficient (R2) that indicate the initial performance evaluation of different back-propagation models were also compared for each of the 11 ANN algorithms.
Two critical loading conditions should be evaluated for the design parameters of a GSCS as demonstrated in Figures 2(a) and 2(b) under the conditions of interstice loadings. CASE1 and CASE2 expressions were used to define the condition of filling one interstice cell or two The typical geometric parameters of the reinforced interstice cells with material, respectively. concrete GSCS of same diameters are shown in Figure 2 where “the intersection wall” is the overlapping part Data Base between two adjacent silos, and "the interstice walls" 3 are the walls of the interstice cells. The "supports" and The data considered here was obtained from the existing "crowns" are the boundaries and the mid-spans of the database of Yuksel [4] which was entirely based on interstice walls, respectively. The silo walls except the FEA results. The concrete compressive strength, the interstice and the intersection walls are called as the modulus of elasticity (E) and the Poisson’s ratio (ν) "external walls", and the silo diameter, silo radius and were respectively taken as 25 MPa, 3×107 kN/m2 and silo wall thickness are denoted by letters D, r and t, 0.2 in all the analyses. Concrete compressive strength is respectively, and α is the central angle spanning the given to determine the modulus of elasticity. Linear intersection walls. The thickness at the mid-section of elastic FEA was performed to be able to investigate the the intersection walls and the intersection wall length behavior of the GSCS silos under the interstice loading are respectively symbolized with tIW and LIW. GSCS has conditions. The silo diameter (D) of 12.50 m and the 2 two interstice cells, the interstice loading case will pressure of 110 kN/m applied by the stored materials include two interstice loading combinations to (p) were directly used, while the other values were varied to achieve the values of the parameters. In determine the worst-case interstice loading cases. particular, the following values were considered; t = 0.20 m, 0.25 m, 0.30 m, 0.35 m and 0.40 m (having D/t diameter-to-wall thickness ratio of 62.5, 50.0, 41.7, 35.7 and 31.3); tIW = 1.25×t and 1.50×t; α = 30°, 35°, 40°, 45° and 50°.
2 Geometric Parameters and Loading Cases for the GSCS
The bending moments (MSUPPORT), hoop forces (NSUPPORT) and shear forces (VSUPPORT) at the supports of interstice walls were calculated considering both of the interstice cells filled with material (CASE 2). The values are presented for the variations in the values of bending moments, hoop forces and shear forces as the functions of the diameter-to-wall thickness ratios (D/t of 31.3, 35.7, 41.7, 50.0, 62.5) for different values of α (30°, 35°, 40°, 45°, 50°) and tIW (1.25×t and 1.50×t).
(a)
The criteria used to establish the database for this study were; (1) diameter-to-wall thickness ratios (D/t) (2) thickness at the midsection of the intersection walls (tIW), (3) central angle spanning the intersection walls (α). The outputs of this study are; (1) bending moments (MSUPPORT), (2) hoop forces (NSUPPORT), (3) shear forces (VSUPPORT) at the supports of interstice walls due to interstice loadings due to interstice loadings.
3 Fundamental Aspects of Artificial Neural Networks (ANNs) (b) Figure 2. Interstice loading conditions for the group of six cylindrical silos; (a) One interstice cell is filled with material (CASE1). (b) Two interstice cells are filled with material (CASE2).
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ANN is a type of artificial intelligence application implemented by engineers to carry out specialized design tasks so far. Neural networks thus have been a powerful tool for the solution of various structural engineering problems [3-12].
3 Comparison of ANN Model Results In this study, 3:HN:1 ANN structures were used to compute reasonable values for the critical design forces of GSCS by using the input values of D/t, tIW , α and the output values of MSUPPORT, NSUPPORT and VSUPPORT.
The neural network model chosen in the present study is a multilayered feed-forward network with neurons in all the layers fully connected in feed-forward manner. A three-layer feed-forward ANN was used and trained with the error back propagation method. The ANN architecture of feed-forward multilayer network is given in Figure 3 where the general structure of the neural network consists of an input layer, one or more hidden layer(s) and an output layer that are fully interconnected, as shown by lines. The input data is introduced with ANN at the input layer and processed in a forward direction through the hidden layer(s), and the output of ANN is computed at the output layer. This process is known as the “feed-forward mechanism” in which the flow of information is from left to right. In engineering problems, the number of input and output parameters is generally determined by the design requirements. Since there is no general rule for selecting the number of neurons in a hidden layer, the number of hidden layer neurons (HN) is selected by the user. The training phase of ANN is performed by using an error back-propagation algorithm. The simplest implementation of back-propagation learning updates the network weights and biases in the direction in which the performance function most rapidly decreases to the negative of the gradient. The back-propagation computation is derived using the chain rule of calculus that various back propagation training algorithms proposed by researchers have been used in the application so far. Mostly used 11 algorithms can be divided into two main categories; the first one developed from an analysis of the performance of the standard steepest descent algorithm uses the heuristic techniques, variable learning rate back-propagation (GDA, GDM and GDX) and resilient back-propagation (RP), and the second one uses the standard numerical optimization techniques (CGF, CGB, CGP, SCG,BFG, OSS, LM).
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The comparisons of GSCS design forces computed by FEA and estimated with ANN are plotted in Figures 4 to 6 where SCG algorithm’s data for MSUPPORT, CGP’s data for NSUPPORT, BFG’s data for VSUPPORT were used due to their superior estimation performances than those of other algorithms. The CGP algorithm completed the classification process in a smaller period of time than the other algorithms did for MSUPPORT, VSUPPORT, and NSUPPORT. 650
R² = 0.969 600 550 500
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Figure 3. Feed forward multilayer network consisting of an input layer, a hidden layer and an output layer
The performance of the back-propagation methods for MSUPPORT is given where it is obvious that the performances of all the configurations are very close concerning the correlation coefficients (R2). The SCG algorithm offered better estimates than the other 10 ANN approaches even though the training time was quite long due to the training cycles. Furthermore, the CGP algorithm estimated the values of NSUPPORT better than the other methods in accordance with the correlation coefficients (R2). In addition, when compared to the other ANN methods, quasi – Newton back propagation approach BFG provided stronger relations with the FEA results in terms of computing the VSUPPORT values. All the back-propagation methods were carried out with the average accuracy rate (100 % - error %) of 85.68 % and 99.39 % for the testing phase of the neural network and the average accuracy rate (100 % error %) of 92.47 % and 99.76 % for the training phase of the neural network.
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Figure 4. Comparison of FEA and ANN approaches for MSUPPORT
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Figure 5. Comparison of FEA and ANN approaches for NSUPPORT
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However, although the estimation capability of the Quasi-Newton learning algorithm (BFG) is higher than that of the other 10 algorithms, having considerably longer iteration periods can be evaluated as a disadvantage of BFG. It was evident that the results obtained by ANN would change related to the size and variety of the selected data set. Additionally, changing the parameters (momentum coefficient, learning rate, error tolerance, etc.) used for training ANN will also change the obtained results. However, in literature, various algorithms different from 11 back-propagation algorithms that were used in this study have been also used for the estimation processes with ANN. Testing the FEA results by using the aforementioned algorithms may cause to have more different results. All the details about this study can be found elsewhere [5].
R² = 0.992
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Figure 6. Comparison of FEA and ANN approaches for VSUPPORT
In this way, a general investigation was performed on the success of the training algorithms and the following conclusions are made. Different number of nodes between 2 and 10 were selected for the hidden layer and the optimum number of hidden nodes was determined by applying separate solutions for each node. Besides the estimation of the number of the hidden layers requires many trials, having less number of nodes used at the hidden layer expresses the appropriateness of the data and causes to have greater performance for the analysis. Obtaining highly accurate results with an average number of 6 HN at the hidden node layer is especially another fact that proves the success of the study. The most appropriate results of HNs selected between 2-10 for each algorithm were determined as “4” for MSUPPORT, VSUPPORT, and “6” for NSUPPORT. When the iteration number and the training period were considered, the Conjugate Gradient Algorithms (CGB, CGF and CGP) reached the results of FE method faster than the other 9 ANN algorithms. Since this study was not a “real time” application, the completion of the training period should not be considered as a significant performance property. CGB, CGF and CGP algorithms are accepted as the most appropriate selections, only if the training time will be compared.
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This study presents the application of ANN methods for estimating the design forces of GSCS that were compared with the results previously determined in the literature by using FEA. Mostly applied 11 ANN algorithms in the literature were used to estimate the design forces of GSCSs and the performance of each algorithm was investigated by considering many various viewpoints. After comparing the obtained ANN results with the design forces computed with FEA, both of the results were found to be closer to each other. The correlation coefficient values (R2) varying between 86.12% and 99.27% proved that the estimation performances of 11 algorithms used for the estimation of different design forces were rather good. However, when the algorithms of the study were compared with each other, some of the algorithms were superior to the others in terms of their estimation performances and analysis completion periods. The superior algorithms in terms of estimation accuracy were SCG algorithm for MSUPPORT, BFG algorithm for VSUPPORT, CGP algorithm for NSUPPORT. Especially the estimation performances of the algorithms (GDA, GDM, GDX and RP) in the 1st category were found to be extremely lower than those of the other algorithms. In terms of the training period, CGF, CGB and CGP algorithms of the 2nd category performed great success when compared to the others. Since the appropriateness between the algorithm and the data set used in the training phase directly affects the accuracy and the speed of the test results, the selection of the algorithm appropriate to the data set is a significant parameter for the solution of the problem. As a result, the use of ANN provides an alternative way to estimate the design forces for GSCS.
References [1] C. Balkaya, E. Kalkan, S.B. Yuksel. FE analysis and practical modeling of RC multi-bin circular silos. ACI Structural journal, 103(2): 365-371, 2006. [2] S.B. Yuksel, S. Arikan. A new set of design aids for the groups of four cylindrical silos due to interstice and internal loadings. Structural Design of Tall Special Buildings, 18(2): 149-169, 2009. [3] S.B. Yuksel, M.H. Arslan. Design Force Estimation Using Artificial Neural Network for Groups of Four Cylindrical Silos. Advances in Structural Engineering, 13(4): 681-693, 2010. [4] S. B. Yuksel. Design Formulas for the Groups of Six Cylindrical Silos Due to Interstice Loadings. Advances in Structural Engineering, 14(2), 265-280, 2011. [5] S. B. Yuksel, M. H. Arslan. Design Forces For Groups Of Six Cylindrical Silos by Artificial Neural Network Modeling. Structures and Buildings, 165(10): 567 - 580, 2012. [6] M.M. Kose. Prediction of transfer length of prestressing strands using neural networks. ACI Structural journal, 105,:162–169, 2007. [7] M. Inel. Modelling ultimate deformation capacity of RC columns using artificial neural Networks. Engineering Structures, 29(3): 329-335, 2007.
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[8] A. Tashakori, H. Adeli. Optimum design of cold-formed steel space structures using neural dynamics model. Journal of Constructional Steel Research, 55: 1545– 1566, 2002. [9] R. Chandak, A. Upadhyay, P. Bhargava. Shear lag prediction in symmetrical laminated composite box beams using artificial network. Structural Engineering and Mechanics, 29(1), 77-89, 2008. [10] V. Giri, A. Upadhyay. ANN based prediction of moment coefficients in slabs subjected to patch load. Structural Engineering and Mechanics, 29(1), 77-89, 2006. [11] S. Rajasekaran, R. Amalraj. Predictions of design parameters in civil engineering problems using SLNN with a single hidden RBF neuron. Computers & Structures, 80, 2495–2505, 2002. [12] G.R. Consolazio. Iterative equation solver for bridge analysis using neural networks. Computer-Aided Civil Infrastructure Engineering, 15(2): 107-119, 2000.
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An Overview of Metaheuristic Algorithms Y. C. Toklu∗ Abstract In this paper it is intended to present a general look to metaheuristic algorithms. It is seen that metaheuristic methods can be considered to be in concordance with a general flow chart. Several techniques are analyzed as to show their common characteristics in obeying this flow chart. The advantages and disadvantages of metaheuristic algorithms over classical method are discussed. Keywords: Metaheuristic algorithms, engineering, global solutions, multiple solutions, TPO/MA, FEM.
1
Introduction
2
Definitions on brief history
MAs
and
Algorithms known as Random Search and Local Search, which were being used long before the formal MAs, are perhaps the first examples of this class due to use of heuristic rules in choosing step sizes, stopping criteria, determination of starting points and new solution candidates. Actually, MAs are defined as stochastic optimization methods inspired by observations from various sources like nature, physics, mathematics, music, animal sociology, and politics. The first techniques that deserve the right of being called as MA formally are Genetic Algorithms and Simulated Annealing which are both forwarded before 1980. The former is based on the theory of evolution of living organisms and the principle of the survival of the fittest. The latter has a metallurgical process in its origin. Both phenomena have countless stochastic decisions in their processes, and this property is effectively reflected in the corresponding MAs. Following these two examples, many other algorithms like Tabu Search in 1989, Ant Colony Optimization in 1992, Particle Swarm Optimization in 1995, Harmony Search and Big-Bang Big-Crunch Optimization in 2001, Viral Systems in 2007, Cuckoo Search in 2009, Multiobjective Flower Algorithm in 2013 are forwarded and this activity does not seem to have come to an end, lest the contrary [1]. Besides solo applications of MAs in solving problems, there are also many hybrid applications where MAs are combined with each other or with some conventional techniques. MAs are applicable to problems with discrete variables or continuous variables, or to both with some modifications. Some of these algorithms are based on improving one single candidate solution, while in most of them the solutions are searched by improvements in a bunch of candidate vectors.
Mathematical approaches in dealing with analysis and design problems in science and engineering mainly end up with two types of formulations. The first type is root finding, i.e. search for x such that a function of x will assume a certain value, f(A, x)=b, x=?. The second type is optimization, i.e. search for x optimizing a function of x, opt f(A, x), x=?. In these formulations A is to represent the properties of the system under consideration. In some problems A is independent of x, in other problems which form a much broader set, A is a function of x. If A depends on x the problem becomes much more complicated. Both root finding and optimization problems may have, in addition, constraints on x which also increase the level of difficulty of the problems. Metaheuristic algorithms (MAs) are forwarded for the solution of optimization problems. They have made their official introduction in the last quarter of the 20th century, and from that day on, they have increased enormously in number and in capacity. Currently there are more than 50 such algorithms and they have found applications in almost all sciences and engineering fields. It can further be said that, their success have led researchers to find ways of applying them even to root finding problems using alternate formulations. In the 3 Common characteristics of present presentation, the next section will deal with MAs the definition of MAs and with their history. The following section will be dealing with characteristics Common characteristics of metaheuristic algocommon to MAs. Their applications and comparrithms are that they can deal with scientific and enisons with other optimization techniques will be the gineering problems without necessitating complex subject of the next two sections. mathematical expressions, constraints can be handled with an amazing ease as compared to classi∗ Y. Cengiz Toklu is with Civil Engineering Department, Faculty of Engineering, Bilecik Seyh Edebali University, Bile- cal techniques and that they all intend to favorize cik, Turkey. (email:
[email protected]) the search for the global optimal solution instead
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Figure 1: General flow chart for metaheuristic methods [2]
of local solutions. That is why engineers and scientists are recurring to meta-heuristic methods in solving their problems which can be formulated as numerical optimization problems for the purpose of reaching to the optimal solution or at least to a near-optimal solution. A general look to metaheuristic methods indicates that they roughly obey to the flow chart shown in Fig.1 of course with different expansions of certain boxes. The basic steps in this flow chart are Step 1 - Creation of base vector(s). Step 2 - Evaluation of base vector(s), i.e. computation of objective function for each vector, checking the satisfaction of constraints for each vector, and finally assigning an evaluation value to each vector taking into account the objective function and constraint satisfaction. Step 3 - Create a new set of vectors, candidates, according to the rules of the algorithm. This new set may be completely different than the base vectors, or some of them may have changed, depending on the rules of the algorithm. Step 4 - Evaluation of candidate vector(s) as it has been done for base vectors in Step 2. The difference in Step 4 and Step 2 is that, in Step 4 only
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new vectors are evaluated. Step 5 - Comparison of base vectors and candidate vectors, i.e. deciding on which set is better looking at the results of Steps 2 and 4. Step 6 - Re-defining the step size in search area depending on the trend of cycles as seen from comparison in Step 5. The general rule here is that if the candidate vectors are better than the base vectors, then the step size is enlarged, otherwise diminished. The relevant change is applied with very small percentages at each cycle, or more generally, after some number of cycles, like 100, with bigger percentages. It is to be noted that, the step size change mentioned here is sometimes performed with change of parameters defined in Step 8 below. Step 7 - Deciding on ending the computations based on the number of cycles run or the satisfaction of convergence criteria. There may be several criteria used separately or in parallel for this purpose. • Number of cycles. If the number of cycles reaches a predetermined number, generally large, the computation process gets stopped. This case, except for very special situations, corresponds to non-convergence state.
• Stabilization of best evaluation value. This is a rather common criteria used in normal applications. It is applied for instance by putting the rule as a percentage of the best evaluation value in the last, say, 100 iterations. • Reaching to a point where the search area cannot be significantly diminished. This criterion can be understood remembering the operations in Step 6. Assuming that an optimum value is reached, all the following iterations will necessitate diminishing of the search space, until reaching at a preset minimum limit, thus ending further search for better values. Step 8 - Redefining base vectors and rearranging rules and parameters of application. This step, although carrying a number largest in the flow chart, in fact can be considered to be the starting point of the next generation. At this step, according to the rules of the algorithm being applied, the new base vectors are defined, some rules and parameters are changed looking at the results of the previous cycle(s). The meanings of these steps can better be understood by considering specific application in some algorithms. In the examples given in the coming paragraphs, some details of operations performed in these Steps are explained for a number of algorithms. It is to be noted that in the steps mentioned above, the first one is the same for all algorithms, save the number of vectors. Steps 4, 5, and 7 do not present any change from algorithm to algorithm. On the other hand, steps 3, 6, and 8 are algorithm specific; they are specially defined for each algorithm.
3.1
Simulated Annealing (SA)
In SA applications only one vector is taken into account and the process is based on improving that vector. So in Step 1, one vector is randomly created in the search space. That vector is evaluated in Step 2. In Step 3, a new vector is created within the predetermined neighborhood of the base vector and it is called the candidate vector. Candidate vector is evaluated in Step 4. In Step 5, the fitness functions of the base vector and the candidate vector are compared to each other, and a decision is given as to which one is better. If the candidate vector is better than the base vector, then in Step 6 the step size is decreased a little amount or that fact is noted to be applied later if repeated multiple times. For the cases where the candidate vector is worse, reverse operation will be applied to step size. In Step 7, decision will be given for stopping, of course in later cycles. In Step 8 the new base vector will be chosen between the two vectors at hand, according to the rules of SA:
• If candidate vector is not better than the base vector, then, in most of the cases, the old vector will continue to be the new base vector for the next cycle, and for the remaining very small cases, the two vectors will be swapped, i.e., the candidate vector will be the new base vector although its being worse than the old base vector. • In this Step, parameters of the process will be revised so that the probability level mentioned will be diminished a little so that the acceptance of worse vectors gets more difficult as cycles continue.
3.2
Genetic Algorithms (GAs)
For these algorithms, a number of vectors are created randomly in the search space in accordance with Step 1. These base vectors are evaluated in Step 3. In Step 3, same numbers of vectors are created from base vectors applying the operators of GAs, selection, mating, cross-over, mutation, etc. to form the candidate vectors. These vectors are evaluated in Step 4. In step 5 the two sets are compared to each other and best fitness function is kept in the memory. No operations are performed in accordance with Step 6, although the change in mutation rate, considered in Step 8, could well be considered here. In Step 7, the stopping criterion is checked and applied if necessary. In step 8, the candidate vectors are taken to be the next base vectors, sometimes applying elitism, i.e. creating the new base vectors set from candidate vectors, replacing some of them with the best base vectors. Another operation performed here is the diminishing of the magnitude of mutation operator, so that as the cycles continue, search will be made more closely to the old vectors. In some applications of GAs, there is a concept called island which roughly corresponds to performing the above operations independently a number of times, on so called islands, and then making interchanges between islands from time to time for the purpose of sharing the best vector(s) in all islands [3]. This, of course, does not mean the violence of the common flow chart given in Fig. 1, but it corresponds its being used several times in parallel and interchanging data from time to time between these parallel applications.
3.3
Harmony Search (HS)
HS also starts with a bunch of vectors in Step 1. Step 2 is applied as in other algorithms. In Step 3, first of all a single vector is created according to the rules of HS, based on the components of the old vectors, small variations of them, or not based upon them, but considering the whole range of search space. For doing so, HS makes use of • If candidate vector is better than the base vec- three parameters. Then, in Step 4, this new vector, then it will be the new base vector, tor only is evaluated. In Step 5, the new vector is
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compared to the worst of the base vectors. No operations are performed in Step 6. If cycles continue after decision given in Step 7, two operations are performed in Step 8. Firstly, new base vectors are defined as the old base vectors, with the difference that, the worst of them being replaced with the new candidate vector, if the latter is better. The other operations consist playing with the parameters of HS for the purpose of diminishing the probability of creating new vectors far from the old ones. The examples of algorithms obeying the flow chart in Fig. 1 can be extended as to wish, especially giveng details on the operations on Steps 3, 6, and, 8, as stated above.
sor time for the former will be much shorter. But this does not form an important disadvantage for MAs considering that they are especially successful in cases where classical methods are inapplicable or insufficient.
The success of MAs comes from the fact that they have seen to be applicable to almost all types of optimization problems, with continuous and/or discrete variables, with no requirements about differentiability of the functions considered, with all types of constraints, for linear or non-linear formulations. This is not the case for conventional methods, which are generally designed for some welldefined problems with strict limits, and become of no use for other problems. To give an example, linear programming, for instance, is applicable only to linear problems with continuous variables with linear constraints and it cannot be applied to other problems is there is any non-linearity somewhere in the formulation. When the function to be optimized becomes quadratic, then one can apply the technique named quadratic programming which is designed only for those problems. If the variables are integers, then one has to apply a specially prepared algorithm. Thus, one can say that the biggest advantage of MAs is their versatility, i.e. their applicability to almost all type of problems. As far as the speed of computations, one has to state that, in general, if a problem can be solved both by a conventional method and by a MA, the central proces-
[3] Y. C. Toklu. Application of Genetic Algorithms to Construction Scheduling With or Without Resource Constraints. Can. J. Civ. Eng./Rev. Can. Gnie Civ., 29(3):421-429, 2002.
6
Conclusions
Metaheuristic methods are strongly entering into lives of engineers and scientists in solving problems which were difficult or even impossible to handle with conventional techniques. The tests performed on several MA applications have shown that they are robust and sufficiently accurate. It is not difficult to foresee that they will increase their impor4 Typical problems solved by tance in the coming years parallel to advances in computer technology both in hardware and software MAs senses. An obvious conclusion coming out these considerations is that MAs have to find their ways Since engineering is very closely related to find opin the curricula of universities, at introductory level timal solutions to various real life problems, startbefore graduation, and in a more elaborate level at ing with their emergence, metaheuristic algorithms the graduate level. have found many ways of being applied to problems in almost all fields of science and engineering [2]. Kicinger et al. [4] gave a review of applications References on structural design. Yang et al. [5] have analyzed applications on hydraulics, geotechnical, and [1] J. I. Fister, X.-S. Yang, I. Fister, J. Brest and transport engineering. Vasant [6] have studied apD. Fister. A Brief Review of Nature-Inspired plications on engineering, business, economics, and Algorithms for Optimization. Elektrotehniski finance. Cercevik et al. [7] give a more recent asVestnik English Edition, 80(3):17, 2013. sessment of applications in civil engineering. [2] Y. C. Toklu and N.E. Toklu. Analysis of structures by Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA). 5 Comparison of MAs to other In Siarry, P. ed., Heuristics : Theory and optimization methods Applications Nova Science, 16:345-374, 2013.
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[4] R. Kicinger, T. Arciszewski, K. DeJong. Evolutionary computation and structural design: A survey of the state-of-the-art. Computers and Structures, 83:1943-1978, 2005. [5] X.-S. Yang, A. H. Gandomi, S. Talatahari, A. H. Alavi. Metaheuristics in Water, Geotechnical and Transport Engineering, Elsevier, 2012. [6] P. Vasant. Meta-Heuristics Optimization Algorithms in Engineering, Business, Economics, and Finance. IGI Global, doi:10.4018/978-1-4666-2086-5, 2013. [7] A. E. Cercevik, H. Bozkurt, Y. C. Toklu. Applications of Meta-heuristic algorithms to civil engineering problems, A survey. EU/ME 15th Workshop, Metaheuristics and Engineering, Istanbul 24-25 March 2014.
An Efficient Metaheuristic Approach for Solving a Class of Matrix Optimization Problems Petric˘a Pop ∗Oliviu Matei
†
Abstract In this paper we present an improved genetic algorithm based heuristic for solving a class of matrix optimization problems consisting in finding permutations of rows and columns of a matrix such that a certain cost function is optimized, e.g. minimization of the bandwidth, maximization of the sum of the super-diagonal entries, etc. Computational results are reported in the case of matrix bandwidth minimization problem (MBMP), linear ordering problem (LOP) and antibandwidth minimization problem (ABMP) for an often used set of benchmark instances. The obtained results show that our genetic algorithm based heuristic outperforms the other existing heuristics in terms of quality of the provided solutions and has reasonable computing-time requirements.
columns of a given matrix such that a certain cost function is optimized. The paper is organized as follows: Section 2 contains the class of matrix optimization problems we are concerned with, followed by a briefly description of the matrix bandwidth minimization problem (MBMP), linear ordering problem (LOP) and antibandwidth maximization problem (ABMP), Section 3 outlines the general genetic algorithm, followed by a description of its components, Section 4 describes the computational results obtained in the case of MBMP, LOP and ABMP and finally Section 5 concludes the paper with a discussion of the advantages of our proposed GA and possible enhancements of the algorithm which would improve its computational performance.
Keywords: matrix optimization problems, metaheuristics, genetic algorithms.
2
Matrix optimization problems
For the class of matrix optimization problems considered in this paper, we are looking for finding permutations of the rows and columns of a given matrix Matrix optimization problems have been subject of such that a certain cost function is optimized. Deresearch for at least 54 years, beginning with the pending on the cost function to be used, different solution described in 1958 by Chenry and Watanmatrix optimization problems can be defined: abe [8] in the case of the linear ordering problem and the Cuthill-McKee algorithm [11] developed in • The matrix bandwidth minimization problem, 1969 in the case of matrix bandwidth minimization denoted MBMP, with the aim to keep the nonproblem. zero elements in a band as close as possible to Since then, due to their interesting theoretical the main diagonal. properties and important real-world applications, the matrix optimization problems have been inten• The average bandwidth minimization problem sively studied over the years. proposed by Mafteiu [31] that has the advanFor matrix optimization problems, very differtage of leading to a more uniform distribution ent approaches have been suggested in the past. of non-zero elements around the main diagonal. In principle, they can be classified into exact algo• The matrix profile minimization problem that rithms, approximation algorithms, relaxation methconsists in minimizing the number of elements ods, heuristic approaches and hybrid algorithms. in the envelope of a square matrix (i.e. the set The aim of this paper is to describe an efficient of index pairs that lie between the first nonzero genetic algorithm based heuristic that can be apelement in each row and the diagonal) plus the plied for solving a class of matrix optimization probnumber of elements on the diagonal, see [19]. lems consisting in finding permutations of rows and
1
Introduction
∗ Petric˘ a
Pop is with the Department of of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Str. Victoriei, No. 76, Baia Mare, Romania (email:
[email protected]) † Oliviu Matei is with the Department of Electrical Engineering, Technical University of Cluj-Napoca, North University Center at Baia Mare, Str. V. Babes, No. 62/A, Baia Mare, Romania (email:
[email protected])
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• The bandwidth and profile minimization problem of sparse matrices, see [22]. • The linear ordering problem, denoted by LOP and introduced by Chenry and Watanabe [8] in 1958, whose objective is to maximize the sum of the entries in the upper triangle. The LOP
appeared in the literature under various names: The graph and the matrix versions of the bandthe maximum acyclic subdigraph problem, the width problem are equivalent [40]. The equivalence maximum consistent arc set, or the median or- is clear if we replace the nonzero entries of the madering problem. trix by 1’s and interpret the result as the adjacency matrix of a graph. • The linear ordering problem with cumulative It has been proven that the bandwidth minimizacosts is a variant of the LOP introduced by tion problem is NP-hard [36], even for some special Bertacco et al. [4] in which there is considered cases and as well is NP-hard to approximate within a cumulative non-linear propagation of the sum any constant. of the arc weights. On graphs the BMP arises on more subtle ways and finds several applications: circuit design, data • The minimum edge product linear ordering mining, VLSI design, network survivability, data problem introduced by Lindstrom [30] in which storage, industrial electromagnetics, etc. a new layout measure called edge product is Due to its practical applications, the MBMP has considered. generated a considerable interest over the years be• The antibandwidth problem (ABP) was intro- ing proposed several exact and heuristic algorithms. duced by Leung et al. [26] and is also known Corso and Manzini [10] proposed two exact algoin the literature as separation number problem rithms that solved problems for randomly generor dual bandwidth problem. Its objective is ated graphs with nodes up to 100. The first heuristo maximize the distance of any nonzero entry tic algorithm for solving the MBMP was proposed from the center diagonal. by Cuthill-McKee [11]. The difficulty of obtaining optimum solutions for the MBMP has led to The methodology that we are going to describe the development of several metaheuristics. The in this paper can be applied to any matrix optifirst such algorithms were the spectral analysis apmization problems falling into the class of problems proach proposed by Bernard et al. [3], the heurisdescribed in this section. In the remaining of the tic algorithm described by Dueck and Jeffs [15], paper we will apply it in the case of the the matrix the parallel heuristic algorithms introduced by Esbandwidth minimization problem, antibandwidth posito and Tarricone [16], the Tabu Search (TS) maximization problem and linear ordering problem. heuristic proposed by Marti et al. [32], the Greedy In what it follows we will define and describe Randomized Adaptive Search Procedure (GRASP) these matrix optimization problems. combined with a Path Relinking (PR) method described by Pinana et al. [37], the genetic algo2.1 Matrix bandwidth minimization rithm (GA) suggested by Lim et al. [29], the ant colony algorithm combined with hill climbing proproblem posed by Lim et al. [27], the particle swarm optiThe matrix bandwidth minimization problem mization combined with hill climbing described by (MBMP) consists in finding a permutation of the Lim et al. [28] and a hybrid ant colony optimizarows and columns of a matrix that keeps all the tion metaheuristic suggested by Pintea et al. [38]. non-zero elements in a band that is as close as posMore recently, Rodriguez-Tello et al. [43] proposed sible to the main diagonal. an improved Simulated Annealing (SA) heuristic, Formally, the MBMP can be stated as follows: Koohestani and Poli [23] described the first genetic given a sparse matrix A = [aij ]n×n , we are inprogramming approach, the same authors proposed terested in finding a permutation of the rows and a hyper-heuristic algorithm based on genetic procolumns that minimizes the distance b of any nongramming [24], a different genetic programming apzero entry from the center diagonal. The MBMB proach was developed by Pop and Matei [40] and plays an important role in solving large linear sysfinally, Mladenovic et al. [35] elaborated a variable tems because Gaussian elimination method can be neighbourhood search (VNS) based heuristic for reperformed in O(nb2 ) on matrices of bandwidth b, ducing the bandwidth of a matrix. while in the general case the algorithm is performed in O(n3 ). In the context of graphs, the MBMP can be de- 2.2 Antibandwidth problem fined as follows: let G = (V, E) be a finite graph The antibandwidth problem was introduced by Lewith |V | = n and f : V → {1, ..., n} a labeling of its ung et al. [26] and is also known in the literature vertices, then the bandwidth of G under f is defined as separation number problem or dual bandwidth as: problem. The problem was introduced originally as a dual variation of the well-known bandwidth minimizaBf (G) = max{|f (vi ) − f (vj )| : (vi , vj ) ∈ E} (1) tion problem. Even though it was not so intenand the bandwidth minimization problem (BMP) sively studied as the bandwidth minimization probconsists in finding a labeling f which minimizes lem, the antibandwidth problem finds many pracBf (G). tical applications: multiprocessor scheduling prob-
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lem, radio frequency assignment problem [20], obnoxious facility location problem [42], obnoxious center problem, tournament scheduling, etc. Given a finite graph G = (V, E) with |V | = n and f : V → {1, ..., n} a labeling of its vertices then the antibandwidth of the graph G under the labeling f is defined as: ABf (G) = min{ABf (v) : v ∈ V } where ABf (v) = min{|f (u) − f (v)| : u ∈ N (v)} is the antibandwidth of the vertex v and by N (v) we denoted the set of adjacent vertices of the vertex v. Then the antibandwidth problem consists in finding a labeling f which maximizes ABf (G): AB(G) = max ABf (G). f ∈πn
where by πn we denoted the set of all permutations of {1, 2, ..., n}. In the context of the matrices the antibandwidth problem can be stated as follows: given a sparse matrix A = [aij ]n×n , we are interested in finding permutations of the rows and columns that maximizes the distance of any non-zero entry from the center diagonal. Leung et al. [26] proved that the antibandwidth problem is NP-hard, but there exist efficient polynomial algorithms for finding the antibandwidth parameter in complements of interval graphs, treshold graphs and arborescent comparability graphs [13]. At the beginning the researches focused on theoretical aspect of the antibandwidth problem: Leung et al. [29] proved the NP-completeness of the problem and gave as well some polynomial time algorithms for some special classes of graphs, Yixun and Jinjiang [46] derived several upper bounds for AB(G), Raspaud et al. [42] solved the problem in the case of the following special classes of graphs: two dimensional meshes, tori and hypercubes and Dobrev et al. [12] proposed tight upper bounds for AB(G) in the case of general Hamming graphs and provided optimal solutions for a special class of these graphs. Recently, some heuristic approaches have been proposed in order to obtain high-quality solutions for the antibandwidth problem on general graphs: Duarte et al. [14] developed some heuristics based on GRASP and evolutionary path relinking and Bansal and Srivastava [2] elaborated a memetic algorithm.
2.3
Formally, the LOP can be stated as follows: given a square matrix A = [aij ]n×n , we are interested in finding a permutation of the rows and columns such that the sum of the entries in the upper triangle is maximized. The problem plays an important role due to the large number of applications in various areas including economics, scheduling, social sciences, electrical engineering, machine learning, ranking in sports tournaments, etc. For more information on the problem and its applications we refer to [7, 33]. Garey and Johnson [18] proved that the linear ordering problem is NP-hard and therefore the problem cannot be solved exactly in realistic time for practical problem instances. The difficulty of obtaining optimal solutions for practical problem instances has led to the development of several heuristic and metaheuristic algorithms: the first solution methods have been proposed by Chenry and Watanabe [8], a multi-start method was described by Chanas and Kobylanski [6] is based on an insertion mechanism that searches for the best position to insert a sector in the partial ordering under construction, a Tabu Search introduced by Laguna et al. [25] that includes an intensification phase using short-term memory based on a tabu search criterion, a diversification process through a long-term memory and an additional intensification process that applies a path relinking strategy based on elite solutions. Campos et al. [5] developed a heuristic approach based on scatter search, Schiavinotto and Stutzle [45] proposed a memetic algorithm obtained by combining a genetic algorithm with a single local search on an insertion neighborhood and Garcia et al. [17] described a heuristic algorithm based on variable neighborhood search (VNS) and as well a hybrid method that combines the VNS with a short-term tabu search for improved outcomes. Pintea et al. [39] proposed a hybrid heuristic based on ant algorithms in order to solve the triangulation problem for Input-Output tables and Chira et al. [9] investigated ant models for solving LOP. Pop and Matei [41] developed a genetic programming approach for solving the LOP and presented some preliminary computational experiments. The memetic algorithm described by Schiavinotto and Stutzle [45] is the state-of-the-art heuristic for solving LOP. A benchmark library and a comprehensive survey on heuristic algorithms for solving the linear ordering problem was given by Marti et al. [33, 34].
3
Linear ordering problem
The linear ordering problem (LOP) is a classical combinatorial optimization problem which appeared in the literature under various names: the maximum acyclic subdigraph problem, the maximum consistent arc set, or the median ordering problem.
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The genetic algorithm
The Genetic Algorithms (GAs) were introduced by Holland [21] in the early 1970s, and were inspired by Darwin’s theory of evolution. The idea behind GA is to model the natural evolution by using genetic inheritance together with Darwin’s theory of evolution.
In GAs, in order to find the solution of an optimization problem it is used a population of potential solutions which evolutes through iterative application of genetic operators. A potential solution to an optimization problem is represented as a set of parameters known as a gene. These parameters are joined together to form a string of values known as a chromosome. Each chromosome represents a possible solution to the optimization problem. Attached to each chromosome is defined a fitness value, which defines how good a solution that chromosome represents. Genetic operators of GAs are similar to those in the natural world and usually are selection, crossover and mutation. A crossover operator plays the role of reproduction and a mutation operator is assigned to make random changes in the solutions. A selection procedure, simulating the natural selection, selects a certain number of parent solutions, which the crossover uses to generate new solutions, also called offspring. At the end of each iteration the offspring together with the solutions from the previous generation form a new generation, after undergoing a selection process to keep a constant population size. By using crossover, mutation and selection, the population will converge to one containing only chromosomes with a good fitness. The solutions are evaluated in terms of their fitness values identical to the fitness of individuals.
3.2
The Representation Structure
It is known that a good representation scheme is important for the performance of the GA and it should define noteworthy crossover, mutation and other specific genetic operators to the problem in order to minimize the computational effort within these procedures. In order to meet this requirement, an individual is represented as a list of interchanges of lines or columns: I = (Mi < ksi , kdi >)i=1,m
(2)
where Mi ∈ L, C (L means an interchange of lines, and C is an interchange of columns) and ksi respectively kdi are the two lines/columns to be interchanged. The permutations are applied successively, in order.
3.3
Initial population
The construction of the initial population is of great importance to the performance and ability of the GA. In our algorithm the initial population is generated randomly, having the advantage that it is representative from any area of the search space. The length of each individual is chosen at random, up to twice the number of rows (columns) of the Genetic algorithms have proven to be a power- square matrix. ful and successful problem-solving strategy, demonstrating the power of evolutionary principles. 3.4 The fitness value Next we present our proposed genetic algorithm for solving the matrix optimization problems de- Every solution has a fitness value assigned to it, scribed in the previous section, followed by a de- which measures its quality. In our case, the fitness value is given by the bandwidth of the matrix for scription of its components. the MBMP, the antibandwidth of the matrix for the ABMP, respectively the sum of of the entries in the upper triangle for LOP, resulted after the interchanges of lines and columns have been applied 3.1 The proposed methodology to the original matrix. The genetic algorithm starts with building an initial population consisting of a number of randomly gen- 3.5 Genetic operators erated individuals (see Subsection 3.3). The pseudo code of our algorithm showing the overall program We consider three genetic operators for maintaining genetic diversity and variation in our genetic algostructure is presented in Algorithm 1. Steps 1 to 9 of this pseudo code covers the main rithm: crossover, mutation and pruning. The most functional block of the genetic algorithm and con- important one is the crossover operation. In the sists of selection, reproduction: crossover (steps 10 crossover operation, two solutions are combined to to 27), mutation (steps 28 to 38) and pruning (steps form two new solutions, called offspring. 39 to 44). For the selection process we used tournament selection with groups of 7 (see Subsection 3.6). The selected solutions participate now in the reproduction process (see Subsection 3.5). At each generation a bestMatrixRequirement is achieved. The process stops when there are no improvements of the bestMatrixRequirement over a given number of successive generations (15 in our case) or in the specified number maxNumberOfEpochs of generations.
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3.5.1
Crossover
Two parents are selected from the population by the tournament method and they can undergo two types of crossover with the same probability: onecut crossover or a concatenation. One-cut crossover operator In this case, offspring are produced from two parent solutions using the following crossover procedure described by Holland [21]: it creates offspring which preserve the order and position of symbols
ALGORITHM 1: The Genetic Algorithm - pseudo code showing the overall program structure Input: Population = generateRandomInitialPopulation(); currentEpoch = 0; previousBandwidth = ∞ Output: bestBandwidth = getBestBandwidth(Population) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
while (currentEpoch ≤ maxNumberOfEpochs) and (bestBandwidth < previousBandwidth) do previousBandwidth = getBestBandwidth(Population); newPopulation = recombine(Population); mutate(newPopulation); prune(newPopulation); Population = select(Population, newPopulation); bestBandwidth = getBestBandwidth(Population); currentEpoch = currentEpoch + 1 end procedure recombine(population) ; newPopulation = ∅ ; parentP opulation = select λ individuals randomly; for ind1 and ind2 ∈ parentP opulation do choose randomly a recombination operator ρ: crossover or concatenation; if ρ = crossover then choose a random cutting point ; create two offspring by preserving the ordering position of symbols in the corresponding sequences of the parents ; add the two offspring to the newPopulation; else if ρ = concatenation then generate one offspring from the concatenation of ind1 and ind2 ; add of f to the newPopulation end end end end end procedure procedure mutate(newPopulation); for ind ∈ newPopulation do for allele ∈ ind do choose a random number r ∈ [0, 1); if r < mutationProbability then choose a random integer number rm ∈ [0, numberP ossibleM utations] ; mutate allele depending on the type of mutation chosen by rm end end end end procedure procedure prune(newPopulation) for ind ∈ newPopulation do if exist shorter sequences of allele with better fitness then add the found sequence as a new individual to the population end end end procedure
21
in a subsequence of one parent while preserving the relative order of the remaining symbols from the other parent. It is implemented by selecting a random cut point. The first offspring is made of the first part of the first parent and the second part of the second parent. The other offspring is made of the first sequence of the second parent and the second sequence of the first parent. Given the two parents: P1 P2
= (M11 M21 |M31 M41 M51 ), = (M12 M22 |M32 M42 ),
(3) (4)
where the superior index represents the parent (first or second), the number of elements of the parent represent the number of permutations (interchanges of lines or columns) and ”|” defines the cutting point, then the offspring are:
2. removal of a move: a move is chosen randomly and removed from the individual. This way, the length of the individual decreases. 3. exchange of two moves: two alleles randomly selected are swapped. 4. replacement of the item which undergoes the move: a column is replaced by a line or the other way around: e.g. L < 1, 4 > is replaced by C < 1, 4 >. 5. replacement of the position of the items which undergo the move: e.g. L < 2, 3 > by L < 1, 5 >. 6. replacement of the entire move: a randomly selected allele is replaced by a new one, yet generated randomly.
The choice of which of the operators described (5) above should be used to create an offspring is proba(6) bilistic. Their probabilities of application are called operator rates. Typically, crossover is applied with Concatenation operator highest probability, the crossover rate being 90% or The concatenation operator concatenates two in- higher. On the contrary, the mutation rate is much dividuals. The first offspring is formed by adding smaller, typically being in the region of 10%. the second parent at the end of the first one. The other offspring is made of the second parent followed 3.5.3 Pruning by the first one. It is often the case that longer individuals contain Given the same two parents: shorter sequences of moves which lead to better reP1 = (M11 M21 M31 M41 M51 ), (7) sults. This is the reason for introducing a new opP2 = (M12 M22 M32 M42 ), (8) erator, called pruning. Given an individual: the offspring are: P = M1 M2 M3 ...Mk Mk+1 ...Mn , (11) O1 O2
P1 P2
= (M11 M21 |M32 M42 ), = (M12 M22 |M31 M41 M51 ).
= (M11 M21 M31 M41 M51 |M12 M22 M32 M42 ) (9) = (M12 M22 M32 M42 |M11 M21 M31 M41 M51 )(10)
the pruning operator generates a new individual:
P = M1 M2 M3 ...Mk The concatenation operator is of great importance because it is the most important way of evolv- holding the following condition: ing individuals to longer ones (with more moves). g([M1 M2 M3 ...Mk ]) = min g([M1 ...Mi ]), −→ i=1, n 3.5.2 Mutation Mutation is another important feature of genetic algorithms since it diversifies the search directions and avoids convergence to local optima. If at the beginning the evolutionary algorithms used only one mutation operator in producing the next generation, it was shown that each optimization problem may require different mutation operators in order to obtain best results, for more details we refer to [19]. In our GA based on preliminary experiments, we used simultaneously six random mutation strategies, chosen with the same probability, in order to produce the new generation:
(12)
(13)
where g([M1 ...Mi ]) is the fitness value of the sequence of moves [M1 ...Mi ]. The pruning operator is deterministic and it is applied for all individuals.
3.6
Selection
Two of the most commonly used methods of selecting individuals for parents to crossover are fitnessproportional selection (also known as roulette-wheel selection) and tournament selection [1]. In the former, individuals are selected with probability proportional to their fitnesses. In the latter, groups of 1. addition of a move: an allele (position in an 3 or 7 individuals are randomly selected and the inindividual) is chosen at random and a new ran- dividual with the highest fitness in each group is sedom move is inserted in that place. This way, lected. In either case, the selection process repeats the length of the individual increases. a number of times equal to the population size to
22
obtain the parents for the new generation. Notice that several copies of the individuals with highest fitness are likely to be added to the parent pool whereas the lowest ranking individuals will have a lower chance at breeding. In our algorithm we used tournament selection with groups of 7. The reasons for choosing the tournament selection are: it is easier to implement, easier to parallelize and it is more likely to select for breeding the individuals with the highest fitness values.
4
Computational results
a set of 10 random connected graphs (RCG) from RND/BUP with the edge densities between 2.52% and 5.77%. Table 2: Comparison of GA heuristic with MA for RCGs instances from RND/BUP collection Graphs ug1 ug2 ug3 ug4 ug5 ug1 ug2 ug3 ug4 ug5
In this section, we present the performance of our genetic algorithm based heuristic approach on a set of benchmark instances in the case of the considered matrix optimization problems. The testing machine was an Intel i7, 2,6 GHz and 4 GB RAM. with Windows XP Professional as operating system. The algorithm was developed in 4.3 Java, JDK 1.6.
4.1
Results of GA Mean Best Time 18.2 20 37.8 17.8 20 21,6 17.8 18 25,3 18.6 19 36,4 20.5 21 50,1 22.6 24 70.1 23.8 25 17.4 22.6 23 70.1 21.4 22 131.1 22.6 23 39.3
Computational results in the case of LOP
In Table 3 we compare the solution qualities and
Computational results in the running times of our genetic algorithm based heuriscase of MBMP tic with some of the best algorithms from the lit-
In table 1 we compare the solution qualities (i.e. the minimum bandwidth obtained) of our genetic algorithm based heuristic with other five best algorithms from the literature: Variable Neighborhood Search (VNS) [35], Simulated Annealing (SA) [43], Genetic Algorithm (GA) [29]and Tabu Search (TS) [32] in the case of the medium instances. In our experiments we performed 10 independent runs for each instance. Table 1: Computational results for the 10 medium instances from the Harwell-Boeing Sparse Matrix Collection Instance arc130 ash85 bcspwr01 bcspwr02 bcspwr03 bcsstk01 bcsstk04 bcsstk05 bcsstk22 can 144 can 161 curtis54
4.2
50 50 50 50 50 60 60 60 60 60
Results of MA Mean Best Time 17.4 18 65.2 16.8 18 33.5 16.8 17 52.0 18.4 19 59.5 19.8 20 83.4 20.2 21 155.9 21.8 23 21.8 20.2 22 116.1 21.2 22 235.2 20.8 21 70.2
n 130 85 39 49 118 119 132 153 110 144 161 54
our GA 63 9 5 7 9 16 37 20 10 13 18 10
VNS 63 9 5 7 10 16 37 20 10 13 18 10
SA 63 9 5 7 10 16 37 20 11 13 18 10
GA 63 9 5 7 12 16 37 21 11 15 19 10
TS 64 9 5 7 11 17 38 20 11 14 19 10
Computational results in the case of ABMP
In the Table 2 we present the computational results obtained with our genetic algorithm heuristic in comparison with those obtained by Bansal and Srivastava [3] using their memetic algorithm for
23
erature: the Chanas and Kobylanski heuristic algorithm (CK) [6], the local search heuristics proposed by Schiavinotto and Stutzle [44] that consists of the following neighborhoods: insert neighborhood (NI ), interchange neighborhood (NX ) and the concatenations of NI with NX (NI + NX ), NX with NI (NX +NI ), NI with CK (NI +CK), CK with NI (CK +NI ), the memetic algorithm (MA) described by Schiavinotto and Stutzle [45], Tabu Search [25] (T S) and the scatter search (SS) developed by Campos et al. [5]. For the results of obtained using our genetic algorithm GA algorithm, we report the average deviation computed over all the results obtained for 100 runs in the case of LOLIB set of instances. Table 3: Comparison of our GA algorithm to other algorithms from the literature LOLIB instances
LOLIB
Heuristic algorithms CK TS SS NI NI + CK CK + NI MA GA
Average deviation 0.2403 0.04 0.01 0.1842 0.1819 0.236 0.00 0.24
# optima 38 30 42 42 44 40 49 49
Running time (s) 0.0205 0.33 3.82 0.1802 0.1881 0.042 0.00176 7.62
Analyzing the computational results reported on Tables 1-3, we observe that our genetic algorithm based heuristic provides high quality solutions, improving in the case of some instances even the existing state-of-the-art approaches.
5
Conclusions
In this paper, a genetic algorithm has been developed in order to solve a class matrix optimization problems consisting in finding a permutation of rows and columns of a matrix such that a certain cost function is optimized. Two important key features that have a great impact on the efficiency of our proposed method are: • the new representation of the candidate solutions as a list of of interchanges of lines and columns; • the multitude of the developed genetic operators: two crossover operators: the one-cut crossover operator and the concatenation operator, six different mutation operators and a problem specific operator called pruning. The considered genetic operators establish a balance between the exploration and exploitation of the search space of the considered matrix optimization problems: MBMP, ABMP and LOP. Extensively computational experiments on a set of medium and large instances used in the literature, show that our approach outperforms the best existing metaheuristics proposed in the literature in terms of solution quality and therefore it may be considered as a new state-of-the-art heuristic. For future work we plan to improve the running times of our heuristic by developing a parallel implementation strategy of the algorithm.
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Acknowledgments This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS - UEFISCDI, project number PN-II-RU-TE2011-3-0113.
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[29] A. Lim, B. Rodrigues, and F. Xiao. Heuristics for matrix bandwidth reduction. European Journal of Operational Research, 174(1):69–91, 2006. [30] P. Lindstrom. The minimum edge product linear ordering problem. Technical Report LLNL-JRNL-496076, LLNL technical report, 2011. [31] L.O. Mafteiu-Scai. Bandwidth reduction on sparse matrix. West University of Timisoara Annals, XLVIII:163–173, 2010. Timisoara, Romania. [32] R. Marti, M. Laguna, F. Glover, and V. Campos. Reducing the bandwidth of a sparse matrix with tabu search. European Journal of Operational Research, 135(2):211–220, 2001. [33] R. Marti and G. Reinelt. The Linear Ordering Problem. Exact and Heuristic Methods in Combinatorial Optimization, volume 175. Springer, 2011. [34] R. Marti, G. Reinelt, and A. Duarte. A benchmark library and a comparison of heuristic methods for the linear ordering problem. Computational Optimization and Applications, 51:1297–1317, 2012. [35] N. Mladenovic, D. Urosevic, D. Perez-Brito, and C.G. Garcia-Gonzalez. Variable neighbourhood search for bandwidth reduction. European Journal of Operational Research, 200(1):14–27, 2010. [36] C. H. Papadimitriou. The N P-completeness of the bandwidth minimization problem. Computing, 16(3):263–270, 1976. [37] E. Pinana, I. Plana, V. Campos, and R. Marti. Grasp and path relinking for the matrix bandwidth minimization. European Journal of Operational Research, 153(1):200–210, 2004. [38] C.-M. Pintea, G.-C. Cri¸san, and C. Chira. A hybrid aco approach to the matrix bandwidth minimization problem. In Proceedings of HAIS 2010, volume 6076 of Lecture Notes in Computer Science, pages 405–412, 2010. [39] C.M. Pintea, G.C. Crisan, C. Chira, and D. Dumitrescu. A hybrid ant-based approach to the economic triangulation problem for input-output tables. In Proc. of HAIS 2009, LNCS 5572, Lecture Notes in Computer Science, pages 376–383, 2009. [40] P.C. Pop and O. Matei. An improved heuristic for the bandwidth minimization based on genetic programming. In Proceedings of HAIS 2011, volume 6079 of Lecture Notes in Artificial Intelligence, pages 67–74. Springer, 2011. [41] P.C. Pop and O. Matei. A genetic programming approach for solving the linear ordering problem. In Proc. of HAIS 2012, Lecture Notes in Computer Science, pages 331–338. Springer, 2012. [42] A. Raspaud, H. Schroder, O. Sykora, and Vrto I. Torok, L. Antibandwidth and cyclic antibandwidth of meshes and hypercubes. Discrete Mathematics, 309:3541–3552, 2009. [43] E. Rodriguez-Tello, J.-K. Hao, and J. Torres-Jimenez. An improved simulated annealing algorithm for bandwidth minimization. European Journal of Operational Research, 185(3):1319–1335, 2008. [44] T. Schiavinotto and T. Stutzle. Search space analysis of the linear ordering problem. In Applications of Evolutionary Computing, volume 2611 of Lecture Notes in Computer Science, pages 322–333. Springer Verlag, 2003.
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Carryover.combines the properties of big and small bucket models.. Due to its computational complexity, most of the earlier studies deal with this problem using heuristic approaches (Sox and Gao (1999); Gopalakrishnan et al. (2001); Suerie and Stadtler (2003); Gupta and Magnusson (2005); Almada-Lobo et al. (2007). By hybridizing GAs with Fix-and-Optimize heuristic, in a previous work,(Goren et al. (2012)) we also proposed a heuristic approach to solve this problem. Unlike our previous study where Fix-and-Optimize heuristic is embedded into the GA and it is used to refine the solutions obtained by GA, in the current study we propose two heuristic approaches involving sequential hybridization. The first approach consists of GAs and Fix-and-Optimize heuristic. It is a well known fact that pure GAs can quickly identify promising areas in the search space, however they are not good at reaching the optimum in large complex search spaces. In this study, the performance of the pure GAs is further improved by a mathematical programming based heuristic. The idea is to run the GA for a predetermined number of generations and then employ Fix-andOptimize heuristic to further improve the solution quality. The second one is to combine two Mixed Integer Programming (MIP) based heuristics (i.e. Relax-and-Fix heuristic with the Fix-and-Optimize heuristic). The idea is the same with the first approach as the Relax-and-Fix approach maintains the initial solution which is used by the Fix-andOptimize approach. The solution is further improved by the Fix-and-Optimize approach.
Mathematical Programming Based Heuristics for the Capacitated Lot Sizing Problems Hacer Güner Gören1 Semra Tunalı2 Abstract In this paper, two hybrid approaches are proposed to solve the capacitated lot sizing problems with setup carryover. The first one consists of Genetic Algorithms (GAs) and Fix-andOptimize heuristic whereas the second one consists of the Relax-and-Fix heuristic and Fix-andOptimize heuristic. The performances of these heuristics are compared to pure GAs as well as a state of the art commercial solver. Computational experiments show the efficiency and effectiveness of the heuristics in solving this problem. Keywords: Capacitated lot sizing problem with setup carryover, fix-and-optimize, relax-and-fix, genetic algorithms.
1. Introduction Lot sizing deals with timing and quantity of production runs of either for a single or multiple products. It is one of the most important and also one of the most widely studied problem in production planning. Various forms of lot sizing problems have been studied by many researchers over the years. Among these problems Capacitated Lot Sizing Problem (CLSP) is the most well known. CLSP consists of determining the production quantity and timing for several items on a single facility over a finite number of periods so that the demand and capacity constraints can be satisfied at a minimum cost. A variety of approaches have been proposed so far to solve this problem with different extensions such as set-up times, set-up carryover, backordering, etc. This study focuses on Capacitated Lot Sizing Problem with Setup Carryover which allows producing more than one product per period and also carrying a setup of at most one product from one period to the other. Capacitated Lot Sizing Problem with Setup
The rest of the paper is organized as follows. In the following section, the capacitated lot sizing problem with setup carryover is defined. The proposed hybrid approaches are defined in section three. The fourth section summarizes the computational results. The findings of the study are summarized in the last section and some future research directions are presented.
2. The Capacitated Lot Sizing Problem with Setup Carryover The CLSP with setup carryover determines the timing and sizing of the production along with the semi-sequencing of the products in a period. In this study, the model proposed by Suerie and Stadtler (2003) has been employed under the following assumptions to solve the CLSP with setup carryover: The planning horizon P is fixed and divided into time buckets (1,….., P). There is one resource available. Several products requiring a unique set-up state can be produced on the resource in each period (property of a big bucket model).
1
Hacer Güner Gören is with the Department of Industrial Engineering, Pamukkale University, Denizli, TURKEY (email:
[email protected])
2
Semra Tunalı is with the Department of Business Administration, Izmir University of Economics, Izmir, TURKEY (email:
[email protected])
27
X jt M (Yjt Wjt ) j K; t {1,...., P}(8)
The resource consumption to produce one unit of product j is fixed. Setups incur setup costs and consume setup time. Setup costs and setup times are sequence independent. At most one setup state can be carried over from one period to the next on the resource. Single item production is possible (i.e. the conservation of one setup state for the same product over two consecutive bucket boundaries). A setup state is not lost if there is no production on the resource within a bucket.
Qt 0 t {1,...., P 1}
Wjt 0,1 (Wj1 0) , Yjt {0,1} j K; t P (10)
X jt , I jt 0
items j K {1, 2,3,...K } ; periods t P {1, 2,3,...P} . setup cost for item j; unit holding cost for item j in period t; amount of capacity available in period t; time to process one unit of item j; setup time of item j; a large number; demand for item j in period t. Inventory level for item j at the end of period t, Xjt: Production amount of item j in period t, Y jt : Binary setup variable (=1, if a setup for item j
3. Mathematical Programming Based Heuristics
resource is occupied solely by item i in period t (=1) or not (=0).
This section explains the properties of the proposed hybrid approaches. The hybridization scheme used in the proposed approaches is the sequentail hybridization in which both GAs and the Relax-and-Fix heuristic are followed by Fix-andOptimize heuristic.
P
(1)
j 1 t 1
s.t.
I j ,t 1 X jt I jt d jt
(a X jK
W jK
j
jt
jt
1
j K ; t P (2)
st jY jt ) Ct t P t {2,...., P}
Relax-and-Fix is a MIP based heuristic in which the integer variable set is divided into disjunctive sets. In each iteration, the variables of only one of these sets are defined as integers, while the others are relaxed. The resulting model is solved. The following iteration starts with fixing a sub-set of integer variables at their current values and the process is repeated for all remaining sets (Ferreira et al., 2010).
(3)
(4)
Wjt Yjt 1 Wjt 1 j K , t {2,...., P} (5)
W jt 1 W jt 1 Qt
The Fix-and-Optimize heuristic is another MIP based heuristic in which a sequence of MIPs is solved over all real-valued decision variables and a subset of the binary variables. The numerical effort required to solve the MIP model presented in Section 2 is mostly affected by the number of
t {1,...., P 1} (6)
Y jt Qt 1 t {1,...., P 1}
(11)
only possible if there is no setup in this period (7). Constraints (8) are the upper bounds on the production quantities. Finally, variables are restricted to be nonnegative or binary, respectively, (9) to (11). It is assumed that there are no setup carryovers in the first period as stated in constraints (10). More details on this formulation can be found in Suerie and Stadtler (2003).
is performed in period t, =0 otherwise), Wjt: Binary linkage variable which indicates whether a setup state for item j is carried from period (t-1) to (t) (=1) or not (=0), Qt : Single item variable which indicates that the
Min ( sc jY jt h j I jt )
j K ; t P
The objective function (1) aims at the minimization of inventory holding and setup costs. Constraints (2) are the inventory balance equations. The capacity constraints are placed in Constraints (3). Constraints (4) ensure that at most one setup state can be preserved from one period to the next on the resource. Constraints (5) guarantee that a setup can be carried over to period t only if either item j is setup in period t-1 or the setup state is already carried over from period t-2 to t-1. A setup state can only be preserved over two bucket boundaries, if Qt 1 in constraints (6), which is
j: t: scj: hjt: Ct: aj: stj: M: djt: Ijt:
K
(9)
(7)
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binary setup and setup carryover variables rather than the number of real-valued variables. The idea in the Fix-and-Optimize heuristic is to solve a series of smaller problems that are derived from the model stated in Section 2 in a systematic manner. In each iteration of the algorithm, one problem is solved by setting most of the binary setup and carryover variables to fixed values. This reduction leads to a limited number of non-fixed binary variables which are optimized in a given problem. Then the problem is solved using a standard MIP solver. In the next iteration, there is a new problem with a different subset of fixed binary variables and the rest of the binary variables are optimized. However, in each problem the complete set of real-valued decision variables is considered. (Sahling et al. 2009). The Fix-and-Optimize heuristic is originally implemented in Sahling et al. (2009) for solving the multi-level CLSP with setup carryover. Later, in another study (Helber and Sahling (2010)) Fix-andOptimize heuristic is employed to solve the multilevel capacitated lot sizing problem. The reader can refer to Pochet and Wolsey (2003) for more information about these heuristics.
instances were used to analyze different problem characteristics, and in phase three, 540 problem instances were generated to test the algorithm. In this study, the problem instances generated in phase two and three (i.e. total of 681 instances) were used to evaluate the performance of the proposed approaches. The classification of these instances is given in Table 1. Based on the number of binary variables (number of periods*number of products) which is considered as a measure of the problem complexity, these problem classes have been placed into three groups, small, medium and large (see Table 1). All computations were carried out on a PC with Dual Core, 2 GHz microprocessor and 2 GB RAM. The pure and hybrid GAs were coded in Visual C++ 2008 Express Edition and all sub-problems were solved using Concert Technology of Cplex 11.2. As a result of some preliminary tests the computational time to solve each problem using MIP based heuristics was limited to 2 seconds. Some pilot experiments were carried out to select an efficient parameter setting for each problem size and selected values are given in Table 2.
In the search space, GAs search for the setup and setup carryover variables, which are binary. If the setup and carryover variables are fixed to specific values based on the chromosome values, the result is a Linear Programming (LP) which consists of determining the optimal production and inventory decision variables. Therefore, each chromosome in the population of the GA corresponds to a LP and the objective value of a LP is used to determine the fitness of the chromosome during the search (Goren et al., 2012). After the evaluation of each chromosome, selection, crossover and mutation take place. Appropriate operators are used to repair the infeasibilities that occur after these operators. GAs are run for a predetermined number of generations and the best solution is used as an initial solution for the Fixand-Optimize heuristic. In this study, time decomposition scheme is used in both Fix-andOptimize and Relax-and-Fix heuristics.
Table 1: Classification of TTM
Class
#
Phase II #
#
Problem
Items
Periods
Instances
Size
6
15
116
Small
2
6
30
5
Small
3
12
15
5
Small
4
12
30
5
Medium
5
24
15
5
Medium
6
24
30
5
Large
7
Phase III 10 20
180
Small
8
20
20
180
Large
9
30
20
180
Large
1
Table 2: GA parameter setting
4. Computational Experiments The performance of the proposed hybrid approaches are compared to the recent results reported in literature. The test instances generated by Trigiero et al. (1989) are used to evaluate the performance of the proposed approaches. These instances were used by Trigiero et al. (1989) to test the performance of their algorithm (TTM algorithm) in order to solve the CLSP. The authors generated test instances in three phases in which phase one involved 70 problem instances which were used for fine-tuning of the parameters of the TTM algorithm. In phase two, 141 problem
Small
Medium
Large
P/G
20/500
20/500
100/100
%C
0.9
0.5
0.7
%M
0.011
0.003
0.001
The general conclusion which can be drawn from this comparative experimental study is that hybridizing the pure GAs with the Fix-and-
29
Optimize heuristic significantly improves its performance in solving the CLSP with setup carryover. The performance of the relax-and-fix approach is also improved by the Fix-and-Optimize heuristic. In a future research, different 1.
3.
5.
6.
decomposition strategies will be used in MIP based heuristics.
5. References
Almada-Lobo B., Klabjan D., Carravilla M.A., Oliveira J.F., 2007. Single machine multiproduct capacitated lot sizing with sequencedependent setups. International Journal of Production Research, 45 (20), 4873-4894. Helber S., Sahling F., 2010. A fix-and-optimize approach for the multi-level capacitated lot sizing problem. International Journal of Production Economics, 123 (2), 247-256.
2.
Ferreria D., Morabito R., Rangle S. (2010). Relax and fix heuristics to solve one-stage onemachine lot-scheduling models for small-scale soft drink plants. Computers & Operations Research, 37, 684691.
4.
Goren Guner H., Tunali, S., Jans, R., 2012. A Hybrid Approach for the Capacitated Lot Sizing Problem with Setup Carryover. International Journal of Production Research, 50 (6), 1582-1597. Sox C.R. and Gao Y., 1999. The Capacitated Lot-Sizing Problem with Set-up Carryover. IIE Transcations, 31 (2), 173-181. Suerie C., Stadtler H., 2003. The Capacitated Lot-sizing problem with Linked Lot sizes. Management Science, 49 (8), 1039-1054. Trigeiro W., Thomas L.J., McClain J.O., 1989. Capacitated Lot Sizing with setup times. Management Science, 35 (3), 353-366, 1989.
7.
Gupta D. and Magnusson T., 2005. The capacitated lot sizing and scheduling problem with sequence-dependent set-up costs and setup times. Computers & Operations Research, 32 (4), 727-747. Sahling F., Buschkühl L., Tempelmeier H., Helber S., 2009. Solving a multi-level capacitated lot sizing problem with multiperiod setup carry-over via a fix-and-optimize heuristic. Computers and Operations Research, 36 (9), 2546-2553.
8.
9.
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An Adaptive Large Neighborhood Search Approach for the Electric Vehicle Routing Problem Merve Keskin* and Bülent Çatay* Abstract
introduced by Erdogan and Miller-Hooks (2012). In this study, the recharging durations are assumed constant and the objective is to minimize the total distance traveled. The problem is solved using two heuristic approaches. Schneider et al. (2013) address this problem using the hierarchical objective approach where the primary objective is to minimize the number of vehicles whereas the secondary objective is to minimize the total distance. They model the problem assuming variable recharging times and propose a Variable Neighborhood Search approach to solve it. Other articles studying similar problems include Wang and Shen (2007), Conrad and Figliozzi (2011), Omidvar and Tavakkoli-Moghaddam (2012), and Wang and Cheu (2012).
The Electric Vehicle Routing Problem with Time Windows is a new variant of the classical Vehicle Routing Problem with Time Windows where the vehicles are routed to service a set of customers under recharging constraints. In this study, we propose an Adaptive Large Neighborhood Search method to solve this problem. Our initial results show the proposed method is effective in finding good solutions. Keywords: Vehicle routing, recharging, metaheuristics, large neighborhood search.
1 Introduction The use of electric vehicles has recently become very popular due to the new regulations related to reducing the greenhouse gas emissions. The electric vehicles do not only meet the emission standards but they may also reduce the energy costs. However, it brings additional constraints to the well-known Vehicle Routing Problem with Time Windows (VRPTW) because the vehicles may need to visit recharging stations to have their batteries charged in order to continue their route. Electric Vehicle Routing Problem with Time Windows (E-VRPTW) is an extension of classical VRPTW with recharging stations. The problem was first
In this study we propose an Adaptive Large Neighborhood Search (ALNS) approach to solve the EVRPTW modeled by Schneider et al (2013). Our approach combines the ALNS scheme of Pisinger and Ropke (2005, 2007) and Ropke and Pisinger (2006a) with problem-specific algorithms. Different from Schneider et al (2013) our objective is to minimize the total distance.
* Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, 34956 Istanbul, Turkey (e-mails: {mervekeskin, catay}@sabanciuniv.edu)
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2 Problem Description
3.1 Initialization
Similar to the classical VRPTW, there are customers that have time windows, service times, and demands. On the other hand, we have a fleet consisting of electric vehicles which have a load capacity and charge capacity. While the vehicle is traveling, its charge level decreases proportionally with the distance traversed. So, the vehicle may need to have its battery recharged at certain points in time in order to be able to continue servicing customers along its route. The number of stations is usually small and the stations are dispersed in distant locations, which increases the difficulty of the problem. Recharging may take place at any battery level and after the recharging the battery is assumed to be full. Similar to classical VRPTW, all vehicles have to return to the depot before the due date of the depot. The reader is referred to Schneider et al (2013) for the mathematical model of the problem and its details.
We use the savings-based algorithm of Solomon (1987) to construct the initial solution. We insert the customer which increases total distance the least while satisfying time and charge constraints. If any customer cannot be inserted because of low battery level, then the candidate customer is inserted along with a recharging station. If no customer can be added to the current route due to capacity or time-window constraints, then we open a new route and continue same procedure until all customers are serviced.
3 ALNS Solution Method
Random, Worst-Distance, Worst-Time, Shaw, Proximity Based, Demand Based, Time Based, and Zone Removal algorithms are used for the removal of customers as described in Demir et al. (2012). The new algorithms that we introduce are as follows:
3.2 Removal Algorithms 3.2.1 Customer Removal In the first step of the algorithm, the current solution is destroyed by removing 𝑞 customers from the solution according to different rules and adding them in a removal list ℒ. 𝑞 is determined randomly using a uniform distribution.
The ALNS heuristic is based on the ruinand-recreate framework proposed by Schrimpf et. al. (2000) and improved by Pisinger and Ropke (2005). The current feasible solution is destroyed by removing some customers from their routes and then repaired by inserting the removed customers to the solution in an intelligent way. Several removal and insertion algorithms are applied and they are selected dynamically and adaptively based on their past performances. The new solution is accepted if it satisfies some criteria defined by the local search framework. In this study we use the simulated annealing mechanism at the outer level.
Multiple Random Route Removal: This operator randomly selects 𝑟 routes and removes the customers in those routes. 𝑟 is determined randomly depending on the number of routes in the current solution. Multiple Greedy Route Removal: This operator uses a greedy removal heuristic. The number of customers in all routes is identified and then the route which has the least number of customers is removed
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from the solution. This continues until 𝑟 routes are removed. This operator helps distribute the customers in shorter routes into other routes in an attempt to reduce the total distance traveled.
3.2.2 Station Removal Recharging stations are the crucial part of this problem. Hence, changing their positions in the visit sequence of a route may also improve the solution. After a predetermined number of iterations, a station removal and insertion procedure is applied. The number of stations to be removed 𝑛𝑠 is determined in a similar fashion as q.
In the current feasible solution, a vehicle may visit a recharging station before or after servicing a customer. The successor or predecessor station may also be removed along with a customer using the following procedures which are also selected adaptively.
Random Station Removal: This algorithm simply removes 𝑛𝑠 stations randomly from the current solution.
Remove Customers Only: This algorithm removes the customers in the removal list from their routes and the corresponding arrival time, arrival charge, capacity, departure time, and departure charge level are updated along with the stations in the route according to the new sequence. In case of infeasibilities due to the battery level, the Best Station Insertion mechanism (to be described below) is used to make the route feasible.
Worst Distance Station Removal: The mechanism is the same as Worst Distance Customer Removal with customers replaced with stations. Worst Charge Usage Station Removal: We make sure that a vehicle visits a recharging station when the battery needs recharging. In other words, we should make use of the battery as long as possible and go to a station when it is impossible to move to a customer without being recharged. Hence, we remove the stations visited by vehicles with higher battery levels.
Remove Customers and Predecessor Station: This algorithm removes not only the customer in the removal list but also the station visited right before the removed customer is serviced in the current feasible solution. If the route becomes infeasible with respect to the battery level then Best Station Insertion algorithm is called to make it feasible.
3.3 Insertion Algorithms 3.3.1 Customer Insertion After destroying the current solution, we must repair it by inserting the customers in the removal list back into the routes. We use four insertion mechanisms: Greedy, Regret, and Zone Insertion algorithms are adapted from Demir et al. (2012) where Regret-2 Insertion is a variant of that of Pisinger and Ropke (2007). If the route become charge infeasible with an insertion then a station is inserted into the route using the Greedy Station Insertion algorithm.
Remove Customers and Successor Station: This algorithm removes customer in the removal list and the station visited right after the removed customer is serviced in the current feasible solution. If the route becomes infeasible with respect to the battery level then Best Station Insertion algorithm is called to make it feasible.
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incurs the least distance increase is kept. Then the same procedure is repeated for the previous position in the route and the best station is found for that position. The insertion which has less distance increase is performed. If any station cannot be found for the position just before the negative charged node, then the best station for previous position is inserted. Again if the route has not become feasible, then the procedure is repeated for the new negative node.
3.3.2 Station Insertion After removing some stations, current feasible solution may become charge infeasible. In order to repair the solution, some stations must be inserted to the infeasible routes. We make an infeasible route feasible by identifying the first node which has negative battery charge level at the arrival to a customer in a route and make its arrival charge level positive by inserting a station before that customer. This procedure is repeated until all routes become feasible.
4 Computational Study The algorithm is coded on Java and run on a computer with 2.13 Ghz preprocessor, 2.00 GB RAM and 32-bit operating system. To tune the parameters we used a strategy similar to that of Ropke and Pisinger (2006a) on six E-VRPTW benchmark instances with 100 customers.
Greedy Station Insertion: This algorithm inserts the first station in the station list which makes the arrival charge of the first negative charged node positive. After an insertion is performed, the whole route may be still infeasible. Then the same procedure is repeated for the new negative arrival charged node until all arrival charge are positive.
We used all 92 instances of Schneider et al. (2013) to test the performance of our algorithm. Those instances were created based on the well-known VRPTW instances of Solomon. 56 are large size instances with 100 customers whereas the remaining 36 are grouped into 3 classes of 12 instances with 5, 10, and 15 customers.
Best Station Insertion: This algorithm tries all the stations in the station list for the position just before the first negative charged node and records the distance increase in the route if the insertion is feasible. The insertion which incurs the least distance increase is performed. If any station cannot be found for the position just before the negative charged node, then the previous positions are tried. Again if the route has not become feasible, then the procedure is repeated for the new negative node.
For small problems, the optimal solutions are obtained using CPLEX. We observe that ALNS is able to find the optimal solution in all of these instances. Noting that our objective is different from that of Schneider et al (2013), Table 1 shows our solutions on large instances with a comparison to the solutions reported by Schneider et al (2013).
Best Station Insertion (with Comparison): This algorithm tries all the stations in the station list for the position just before the first negative charged node and records the distance increase in the route if the insertion is feasible. The station which
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Erdogan, S. and Miller-Hooks, E. (2012). A green vehicle routing problem, Transportation Research Part E: Logistics and Transportation Review 48(1): 100–114.
Table 1. Summary of results Problem Type
ALNS TD
Schneider et al.
# Veh
TD
# Veh
C1
1019.92
11.67
1048.12
10.67
C2
642.91
4.00
642.92
4.00
R1
1242.07
14.25
1259.81
12.83
R2
867.83
5.09
915.41
2.64
RC1
1425.67
14.13
1409.67
13.13
RC2
1061.30
6.50
1224.06
3.17
Omidvar, A. and Tavakkoli-Moghaddam, R. (2012). Sustainable vehicle routing: Strategies for congestion management and refueling scheduling. In Energy Conference and Exhibition (ENERGYCON), 2012 IEEE International, pages 1089–1094, Florence, Italy. Pisinger, D. and Ropke, S. (2007). A general heuristic for vehicle routing problems. Comput. Oper. Res., 34 (8), 2403–2435.
Each column shows the average value of the best solutions found for the corresponding problem type where TD is the total distance and #Veh is the number of vehicles. As expected, ALNS shows a better or the same performance with respect to the average distance values, however, the average number of vehicles are higher. Only in type RC1 instances, ALNS is outperformed by the VNS of Schneider et al (2013).
Ropke, S. and Pisinger, D. (2006a). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, 40 (4), 455–472. Ropke, S. and Pisinger, D. (2006b). A unified heuristic for a large class of vehicle routing problems with backhauls. European Journal of Operational Research, 171 (3), 750–775. Schneider, M., Stenger, A. , Goeke, D. (2013). The electric vehicle routing problem with time windows and recharging stations, Technical Report. Schrimpf, G. et al. (2000). Record Breaking Optimization Results Using the Ruin and Recreate Principle, Journal of Computational Physics 159, 139-171.
5 Conclusion In this paper, we described an ALNS algorithm to solve E-VRPTW. We propose some problem specific mechanisms and combined them with some existing algorithms from the literature. For future work, we will focus on improving our algorithms to further enhance the solution quality. We will also introduce new algorithms to reduce the number of routes with a hierarchical objective framework similar to that of Schneider et al. (2013).
Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming. Springer, New York, 417–431. Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time windows. Operations Research, 35:254-265. Wang, H. and Cheu, R. L. (2012). Operations of a taxi fleet for advance reservations using electric vehicles and charging stations, In TRB 2013 Annual Meeting.
6 References Wang, H. and Shen, J. (2007). Heuristic approaches for solving transit vehicle scheduling problem with route and fueling time constraints, Applied Mathematics and Computation 190(2): 1237–1249.
Conrad, R. G. and Figliozzi, M. A. (2011). The recharging vehicle routing problem. In Proceedings of the 2011 Industrial Engineering Research Conference. Demir, E., Bektas, T., and Laporte, G. (2012). An adaptive large neighborhood search heuristic for the pollution-routing problem. European Journal of Operational Research, 223, 346-359.
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A Method of Composition of services based on QoS Makhlouf Derdour a,*, Sourour Maalemb, Ghoualmi Nacerac a
1
University of Tebessa, Faculty of SESNV, Mathematics and Computer Department, Tebessa, Algeria b ENS Constantine, Computer Department, Algeria. c University of Annaba, Computer Department, Algeria.
Abstract
The advent of smart mobile devices has significantly changed the ratio of human to computers. The mobile terminal is regarded as a new component of the architecture of information systems, and the new conditions of use induced form the basis of pervasive information systems. The primary objective of a pervasive system is to meet the need of the user wherever they are and at any time. The hallmarks of pervasive systems: context awareness, smartness, scalability, invisibility and pro-action. All these keywords underlie adaptation procedures. Contextawareness can provide information pulsing quality of adaptation services. The high quality of QoS information plays a vital role in the adaptation of a system rapidly changing. In this paper, we quantify the quality of service parameters and characteristics of data to be presented in a suitable form for use with pervasive applications. We also present a mechanism to adapt the quality of service according to application needs, and then evaluate these parameters. The enrichment of QoS information with the quality of service settings and context information increase the capacity of system to adapt to new situations in pervasive environments. We also present a QoS process based for the selection and choice of composite services dedicated to the ubiquitous applications adaptation. Keywords: adaptation, composition, service, choquet integral, heuristic.
1 Introduction In the multimedia community the researches goals are to improve ubiquitous access to content [2] in order to offer services anywhere, anytime and one any device. The QoS networks parameters vary with the available bandwidth (from low to very-speed broadband), the loss rate (more important in wireless networks) or delays (spanning a dozen minutes to seconds). The device capabilities are also very heterogeneous, since a mobile terminal with limited display size, memory and CPU may be required to maintain a service initially offered by a workstation. To handle these limitations, we can firstly adapt the content to be displayed on terminals. E-mail addresses:
[email protected] (Author 1),
[email protected] (Author 2),
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Secondly, adapt the distribution or access methods. The development of pervasive applications presents a number of challenges for software engineering. In particular, the adaptation of context-aware applications: adaptation to the environment (location, time, condition ...), to the connectivity (debit, protocol ...), to the limitations of the device (screen size, media format, power ...) and even to the user (physical disability, capacity ...), or the physical environment (roisy, dark …) under these constraints require multimedia data adaptation mechanisms. The composition of service in pervasive applications is necessarily dynamic in order to answer to an evolving environment. Mechanisms of dynamic reconfiguration make possible the adequate reaction to the stimuli of the environment. In this context where the multimedia, the mobility of users and the ubiquity of applications become widespread, the suppliers of software want to provide adaptable applications (context sensitive). This adaptation can be done in two ways. The first one, requests a change of services, Consists in witching and rebidding services with the most adequate supplier at the reconfiguration moment (dynamic reconfiguration of application is considered here as dynamic rebinding service). The second, requests the integration of services, called adaptation, to solve the problem of heterogeneity related to the semantic data exchange and caused by the change of context. We notice that in both cases, we need mechanisms which offer the adequate services to solve the problem of heterogeneity or the problem of reconfiguration. These services can be primitive or composite. In the case of the primitive services, we need a method and an evaluation mechanism for selecting a service from those exists, while basing itself on the QoS. In the case of the composite services, we need a method for composing and selecting services. Pervasive computing has changed the role, the characteristics and the requirements of software supporting users in their daily life. Hence, the way software systems are designed and built must change accordingly. A specific feature to consider towards this purpose is Quality of Service (QoS). Indeed, pervasive computing brings new challenges and issues related to QoS. QoS-aware service composition is a key requirement in pervasive computing since it enables selecting services able to fulfill complex user tasks while meeting their QoS requirements. Nevertheless, the highly dynamic nature of pervasive environments raises several challenges regarding to QoS-aware service composition. To cope with these challenges we propose a process for
QoS-aware service selection and composition on the fly. In this paper we propose a definition of quality of service that can best respond to the changing context in ubiquitous applications. We also propose a complete process for the discovery of the available services, the evaluation computation of the QoS, and the selection of services using multi-criteria decision method.
2 Related Work The self-adaptation of a pervasive application refers to the capability of a system to adapt itself to user needs and operating conditions by exploiting knowledge about its composition and the context of its components [7, 8, 9, 10 and 11]. For content adaptation, several authors propose classifications [5] such as the elementary constituents of content (eg media) or the complete structure of the document are transformed, a media can be transcoded [2, 4] (eg reduction of the screen size, resolution or sampling frequency of a video) or converted to another modality [3] (audio to text or video to pictures) or even abstracted [6]. Lemlouma and Layaida [5] reviews in different techniques and tools for converting a complex multimedia presentation. These techniques are performed by primitive or composed services, and combine the adaptation of simple media and adaptation of the presentation structure (eg the structural and temporal relations between media). Several selection processes have been proposed to select service compositions with different composition structures and various QoS. Taxonomy of these solutions may be produced based on their objectives and the way they precede. According to this, a first class of approaches aims at determining the optimal service composition (i.e., composition with the highest QoS utility) using brute-force-like algorithms (e.g., Global Planning [13], BBLP, MCSP, WS-IP [12]). These solutions have high computational cost and they cannot provide a solution in a satisfying delay, more, they do not take into account all context information, thus they are inappropriate to be used in the context of dynamic service environments. To cope with this issue, other approaches propose heuristic-based solutions (e.g., WS-HEU and WFlow [12], Genetic algorithm [14, 15]) aiming to mind nearoptimal compositions, i.e., compositions that respect global QoS constraints and maximize a QoS utility function. Yu et al. [12] present two heurisics, WS-HEU and WFlow, for the service selection problem. WS-HEU is a specic heuristic applied to sequential workflows (i.e., workflows structured as a sequence of activities), whereas WFlow is designed for general workflow structures (i.e., sequential, conditional, parallel). The main idea of WFLow is to decompose workflows into multiple execution routes. WFlow considers a parameter for every route indicating its probability to be executed. Therefore, it focuses on the route with the highest probability, whereas in our approach we aim at giving feasible service compositions regardless of the way the
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workflow will be executed. Other approaches [16, 17] present heuristics based on a genetic algorithm. The application of such algorithm to the service selection problem presents two main drawbacks: first, the order in which service candidates are checked is randomly chosen, whereas in our approach we aim at checking services in an ordered way to optimize the timeliness and the optimality of our algorithm. Second, as the genetic algorithm can run endlessly, the users have to do a constant number of iterations fixed a priori. However, fixing a high number of iterations does not give any guarantee about the quality of the result. Therefore, the genetic algorithm is not useful for our purpose (i.e., selecting near-optimal compositions). More recently, Alrifai et al. [18] presented a novel approach that combines local and global optimization techniques. This approach starts from the global level and resolves the selection problem at the local level. It proceeds by decomposing global QoS constraints (i.e., imposed by the user on the whole composition) into a set of local constraints (i.e., for individual sub-tasks, part of the composition). To do so, it uses MILP (Mixed Integer Linear Programming) techniques to find the best decomposition of QoS constraints. The main drawback of this approach is that it represents a greedy selection method, since it selects services at the local level and does not ensure that the global QoS constraints are respected. In our approach, the selection of services is based on a calculation method for ensuring a better choice among those exists, so a better way to solve the problem of composed service. In the following we define a metamodel of service quality and its relationship to the multimedia data.
3 QoS Model The term "service" is one of the terms most used and most ambiguous in the software industry [19]. Usually, services are defined as features provided by a software system to other systems or to a human user [20]. In the context of SOA, services are provided by independent service providers that instantiate of software on their computers and publish the services which it provides using standardized mechanisms in order that they can be discovered and dynamically related to components that need. A service is a behavior defined by contract which can be realized and provided by any component in order to be used by any other on the base of contract [21]. The adaptation requires the detection of changes in context, but also the choice of an application configuration that maintains a satisfactory quality in the new context. It is therefore necessary to discover dynamically the adaptation services as soon as they are useful and their disappearance in order to ensure their replacement. The introduction of multimedia data in ubiquitous/pervasifs systems leads to manipulate various media types. The adaptation services are a solution to resolve the heterogeneity problem which
represents one of the major challenges of these applications. Depending on the type of service envisaged, the quality may be the bandwidth for (downloading or video streaming), time (for interactive applications or telephony), availability (access to a shared service), interoperability (semantic and technical compatibility of components) or the rate of packet loss (loss without influence for the voice or video, but critical for the download). The goal is to create the necessary flexibility to the organization. QoS is the ability of a service to answer the requirements of a context. The difficulty is to measure exactly this quality of service. It is thus necessary to distinguish the service expected (the needs of the system) and the service provided. The objective of the quality of service is to offer guarantees on the capacity of a service to provide with predictable results.
3.1 Metamodel for quality of adaptations service The expression «data adaptation» is composed of two significant terms:"Adaptation" and "data". The adaptation represents the service applied to the data; their quality introduces a concept of appreciation of objects indicated by the second term. The term "data" represent the output of adaptation service, i.e. the objects that will be appreciated. Sound *
Quality of output
Processing quality
Image * 1 Semantic Adaptation
Video
«uses»
QoS
Adaptation technique
Text
«uses»
Transcoding
Runtime environment
1
Screen
User preferences -satisfaction
Adaptation needs
*
*
Software
Hardware
Compression techniques -Mode: with or without loss of information
Context
User context
Transforming techniques -Mode: with or without semantic loss
-Resolution -Frequency
Transforming
Transmoding
Batter -Duration -Capacity
Memory -Taille
1 Sound Card -Speed -Power
CPU -Speed -Type
Graphics card -memory -Speed -Model
of adaptation service. QoS depends on the execution environment, that it is material like the memory, CPU, monitor, etc. or software like OS, platform, application, etc. QoS also depends on the context of use expressed by the preferences of users and applications needs (computing, display, detection, etc.).. The quality properties of the data relate to the type of media (text, image, sound, and video) and to the format (jpeg, bmp, wave, etc.).
3.2 Calculation and evaluation of QoS Data of application have a relationship among themselves and answer to the management rules implemented in the processes task. From this point of view, the quality of data is similar to the quality of a car (quality of transport service and comfort of travel): it does not depend exclusively on the quality of each component, but must take into account the quality of assembly (the data, the process and the assembly of adaptation services in case of complex adaptation). Generally, to make a measure, it requires having three elements: - A precise definition, and complete, of the object to be measured; - A definition of the criteria which are used to measure; - A reference system allows appreciating, for each criterion, the discrepancy between the measured object and the reference. To calculate the QoS we need two factors (α and β) that are provided by the decision maker (usually it is a designer). These two factors correspond to the context (environment, system, activity, etc.) giving preference to processing or data. For example, in the statistics applications of calculation of green zone percentage in a given surface, the preference will be attributed to the quality of data, since we need high quality images. Another example is that of the video broadcast of a football match; In this case we are very interested in treatment, since we try to increase the speed and to minimize the occupation of the bandwidth. We consider that QoS is a quality of service, QoD is a Quality Of output Data and QoP is Quality Of Processing. Supposing α and β are two coefficients attributed according respectively to the usage context and the execution environment to every adaptation service. The quality of service is defined as follows:
Figure 1: Metamodel for QoS of multimedia adaptations
Figure 1 shows the QoS metamodel for adaptation of multimedia data in pervasive environments. The evaluation of QoS is based on two axes, an evaluation of service provided by a component adaptation and an evaluation of output of this service. The first depends on the characteristic of services, such as flexibility, the setting, the run time, the resources, the portability, etc. The second is expressed by a set of characteristics such as resolution and size for the image, speed and sampling for video, etc. The quality of data depends on the quality
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0 < α, β < 1 α+β = 1 / We propose that both factors are lower than 1, in order to have a quality between 0 and 1. o According to the data descriptor, the data can have several measures, e.g. for an image: size, resolution, colors, compression, etc. For each measure is associated a factor which depends on its importance
regarding to the application. For example an application α β β M7 of extraction of information or statistics from an image, S4 M11 S8 the most important factor is the resolution (for the data) α α β α and level of compression (for processing). M-Input M3 M7 β α o The service parameters allow an adequate S5 M8 S2 α S9 manipulation of the running results of this service. A M4 α M12 service is good when it offers more flexibility to the α M1 β β user for the definition of parameters values. For S M5 E α α β S6 example: a data compression service can have the β M13 M9 M2 S10 compression ratio like parameter. Other measures can S3 β α exist such as the runtime, the occupation memory, etc. α The necessity of every measure determines its S7 M-Output M10 M6 coefficient which also depends on the context. o The QoS calculated from QoD and QoP allows Figure 2: Graph of adaptation services the comparison between similar services, which allow classifying the services in a table according to its QoS Each node in the graph represents an adaptation service and type of service. This table will be used to select the "Si", whereas the edge represents the provided/required best service for each type or to select alternative service data "Mi". The nodes and the edges are labeled by the for possible changes. values of α and β provided by the decision maker according to the usage context and execution environment. The inputs and outputs represent the 4 Composition Model of adaptation exchanged media flow. In this example, there are three possible paths: ES2S5S9S, ES2S6S10S and ES3S7S10S services each path represents a possible adaptation. After construction of adaptation graph, we need to The service composition process consists of three optimize this graph by deleting the useless paths and the phases: The planning phase provides an adaptation services that we do not need. graph constituted of the available adaption services and the links between them. The optimization phase allows 4.2. Optimization of adaptation graph to delete the useless paths in the adaptation graph and to calculate the QoS of each service. And finally, the After the construction of adaptation graph, the selection phase provides the most appropriate adaptation optimization phase involves several steps: path. In the following, we try to detail the role of these o Optimization of graph: an adaptation can three phases. correspond to several paths providing the desired adaptation. This phase allows deleting the useless paths 4.1. Definition of adaptation graph that do not connect the M-input to the M-output (e.g. S4, S8). Then, the deletion of the cycles that can exist, After specifying of requested adaptation, the adaptation as well as the deletion of the isolated nodes (node that is system consults the adaptation services available from not connected by its input or its output by another node). the register of service (web service). Then, it builds a Let G the set of vertices, E and S respectively represent graph containing all necessary adaptation services. Each the initial vertex and the terminal vertex of adaptation service is represented by all functional characteristics graph. and its Input/Output (data type and format). Function deletion of isolated node While it exist A є {G-S} and A is isolated Do Input data
Adaptation service
Output data
Delete A; End While
An adaptation service accepts a single input media and provides a single output media. The assembly of adaptation services produced an adaptation graph; the services constitute the nodes and the input/output the edges. e.g. the service S1 can be connected to the service S2 if S1 provides data required by S2 (same type and format).
A cycle is a circuit in which no vertex except the first (which is also the last) appears more than once. A cycle can be defined as a closed path. The first vertex is called DS that produced a cycle from the initial E. Function delete-cycle While it exist cycle in G Do Delete DS ; Delete-vertex-isolated ( ) ; End While
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Example: Consider the following graph: there is a cycle starting with E, which is E2541, and one isolated vertex that is 9. This graph contains also 3 adaptation paths that are: Path 1=E257S, Path 2 = E367S, Path 3 = E368S.
Path 3
3
Sound.wav 6 e
3
Path 2
Text.txt Image.pdf
E Sound.m p3
Path 1 Text.txt
Cycle
S
3 Vertex isolated
Image.bm 4 p 3
Image.jpeg Sound.Wave
1
4
Figure 5: Different paths of transcoding from the Mp3 sound to the Pdf image
9
Video.mp4 Texte.txt
Text.txt
2
E
5
Video.mp4
Sound.wave
7
S Image.pdf
Text.txt
Image.pdf
8
Son.wave Video.mp4
Sound.mp3
3
6
Sound.wave
Image.bmp
8
Figure 3: Transcoding graph from the Mp3 sound to the Pdf image
Each node in the graph represents an adaptation service; the value at each node represents the number of existing services (after consulting of service registers) for ensured adaptation by this node. The first step consists in calculating the QoS for each service at each node in order to choose the best service representing the node. Then, to classify them in a table as follows: Adaptation service
Exists services E
2 Video.mp4
5 Sound.wave
7 Text.txt
Son.wave Video.mp4
3
Sound.mp3
6
Image.pdf
8 Sound.wav e
8
Mp3 To Wave
Mp3 To Text
Wave To Text
….
Num
QoS
Num
QoS
Num
QoS
Num
QoS
S1 S2 S3
… … …
S1 S2 S3
… … …
S1 S2 S3 S4 S5 S6
… … … … … …
S1 S2 S3
… … …
S
Image.pdf
Image.bmp
Figure 4: Transcoding graph after deleting of isolated nodes and the cycles
o Calculation of the weights vectors of edges and nodes : This phase is ensured by the QoS Manager that calculate the weight vector of processing "QoP" and the weight vector of data "QoD" from a set of criteria that depend on process (compression ratio, execution time, reliability, flexibility, etc.) and data (size, resolution, etc.).
To choose a service at each node, we need to use multicriteria method to calculate the QoD and the QoP and finally the QoS. In order to calculate the QoS at each node (process + data), we use average weighted of QoD and QoP, where α and β correspond to their respective weights. For QoD and QoP we used the integral of Choquet. The decision defines the criteria for each service, each data and each coefficient depending to the context. It then applies the Choquet integral on these coefficients and the values of these criteria. The weighted average is the average of a number of values affected at the coefficients. In statistics, considering a set of data,
4.3. Choice of adaption path In order to choose the path of adaptation which is constituted of a set of services, the quality of service must be calculated for each service at each node, in order to find the best service for each node. Then each adaptation path will be evaluated according to the QoS of adaptation services.
Calcul de QdS et choix de service d’adaptation : For a better understanding, we are going to work on the
and the corresponding non-negative weights, the weighted average the formula:
Is calculated according to
, quotient of the weighted sum of xi by the sum of the weights;
following example: The Choquet integral can be used to construct a
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preference model aggregated by adaptation service.
y , y ,....., y ,......., y y i21 , y i22 ,......, y ii2 ,......., y in2 .................................... y p , y p ,......., y p ,......, y p ii in i1 i 2 1 i1
p
∏ ai
1 i2
1 ii
1 in
= Using the Choquet integral as aggregation operator preferences, each service builds its vector of preferences aggregate.
∏
-
Calculation of adaptation path quality : After calculating the quality of each service, we choose a service for each node in the graph, and we pass to the calculation of adaptation paths in order to compare and choose the best adaptation path. To calculate the adaptation path the most appropriate among those who exist, we apply a multi-criteria aggregation using the weighted average. Its application allows having the best path between existing ones, in terms of quality, compared to all compounds services (adaptation path) that can perform the requested adaptation.
= (Xij) comme suit :
ai
Xij
∑(y
= 1≤ k ≤ p
k ij
− y ijk +1 ) µ ( E k ) = C µ ( y ij1 ,......, y ijp )
5 Conclusion
The objective of this paper has been to address services' selection and composition in the context of adaptation ∀ai , a j ∈ A, ∀y ijk middleware for dynamic service environments. For this est un élément de purpose, we have proposed an efficient QoS-based p selection process. The importance of our process is threefold. Firstly, it introduces a novel approach using y ijp +1 = 0 multi-criteria method of decision support. Applying ai (i,j=1,......n)(k=1,......p) avec such techniques for services' selection brings new ideas E E E in this research area. Secondly, by producing not a - k ⊆ D, tel que : | 1 |=1,..., | p |=p. but multiple service compositions satisfying the µ ( E k ) is the measure of power or the weight single QoS constraints, our process underpins the concept of defined by the designer for a subset of criteria. To dynamic services binding. It allows finding solutions face the changing conditions in dynamic environments. apply the Choquet integral, each service Si Thirdly and most importantly, our process shows a performs a ranking of preference values from each criterion. It builds a nest and their preferences for satisfying efficiency in terms of timeliness and optimality, which makes it appropriate for service each of the services. composition in dynamic service environments. Generally the method used to choose the appropriate The quality of service is calculated using the formula: adaptation path is the weighted average. But, in our / case, the criteria have not the same importance and their combination is a degree of importance. Grabisch [22] The QoD and QoP are calculated from the capacity and and Marichal [1] proved the incapacity of the weighted weights table by applying the Choquet integral: average in multi-criteria decision support and proved QoD / QoP = (C ijk −C ijk +1 ) µ ( E k ) that the Choquet integral is more efficient. That is why 1≤ k ≤ p we selected this candidate method to select the best adaptation path. To calculate the most appropriate adaptation path among those existing, we applied a multi-criteria aggregation according to the Choquet integral. Its application provides an adaptation service wellbalanced, in terms of QoS, compared to all criteria Service C1 C2 C3 … … … constituting the adaptation service. The second (Processing) advantage of the Choquet integral compared to the P1 P2 P3 … … … Coefficients weighted average is the resolution of conflicts in case of equality of the values. Indeed, it solves this problem with the use of preferential information that allows the establishment of a priority between adaptation services. The presented work makes part of our ongoing research addressing QoS in adaptation middleware for pervasive environments. Our next steps concern further Data C1 C2 C3 … … … investigating clustering techniques for improving our (Output) QoS process, and considering in our QoS model Coefficients P1 P2 P3 … … … network-level for service compositions.
∏
∑
energy
Colour
Compression
…
flexibility
Resolution
…
Runtime
Size
Charge
Compression ratio
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References [1] Marichal, J.-L. & Roubens, M. , ‘Determination of weights of interacting criteria from a reference set’, European Journal of Operational Research 124, 641–650. 2000. [2] Margaritis Margaritidis and George C. Polyzos. Adaptation Techniques for Ubiquitous Internet Multimedia. Wireless Communications and Mobile Computing, 1(2) :141–163, 2001. [3] Mariam Kimiaei Asadi. Multimedia Content Adaptation with MPEG-21. PhD thesis, ENST Paris, 2005. [4] Tayeb Lemlouma and Nabil Layaida. Encoding Multimedia Presentation for User Preferences and Limited Environments. In IEEE ICME, pages 165–168, July 2003. [5] T. Lemlouma and N. Layaida. Media Resources Adaptation for Limited Devices. In International Conference on Electronic Publishing, pages 209–218, June 2003. [6] A. Divakaran, K. A. Peker, R. Radhakrishnan, Z. Xiong, and R. Cabasson. Video Summarization Using MPEG-7 Motion Activity and Audio Descriptors in Video Mining. Kluwer, 2003. [7] Rouvoy, R., et al., Composing Components and Services using a Planning-based Adaptation Middleware. In: Pautasso, C., Tanter, É. (eds.) SC 2008. LNCS, vol. 4954, pp. 52–67. Springer, Heidelberg (2008). [8] Geihs, K., et al., A comprehensive solution for application-level adaptation. Software: Practice and Experience (2008). [9] Brataas, G., et al.: Scalability of Decision Models for Dynamic Product Lines. In: Int. Work. on Dynamic Software Product Line, DSPL (2007). [10] Floch, J., et al.: Using Architecture Models for Runtime Adaptability. IEEE Software 23(2) (2006). [11] Lundesgaard, S.A., et al.: Construction and Execution of Adaptable Applications Using an Aspect-Oriented and Model Driven Approach. In: Indulska, J., Raymond, K. (eds.) DAIS 2007. LNCS, vol. 4531, pp. 76–89. Springer, Heidelberg (2007). [12] Tao Yu, Yue Zhang, and Kwei-Jay Lin. E_cient Algorithms for Web Services Selection with End-to-End QoS Constraints. ACM Trans. Web, 1(1):6, 2007. [13] Liangzhao Zeng, Boualem Benatallah, Anne H.H. Ngu, Marlon Dumas, Jayant Kalagnanam, and Henry Chang. QoS-Aware Middleware for Web Services Composition. IEEE Trans. Softw. Eng., 30(5):311{327, 2004. [14] Ziad Kobti andWang Zhiyang. An Adaptive Approach for QoSAware Web Service Composition Using Cultural Algorithms. In Mehmet A. Orgun and John Thornton, editors, Australian Conference on Artificial Intelligence, volume 4830 of Lecture Notes in Computer Science, pages 140{149. Springer, 2007. [15] Lei Cao, Minglu Li, and Jian Cao. Using genetic algorithm to implement cost-driven web service selection. Multiagent Grid Syst., 3(1):9{17, 2007. [16] Chunming Gao, Meiling Cai, and Huowang Chen. QoS-aware Service Composition Based on Tree-Coded Genetic Algorithm. In COMPSAC '07, Washington, DC, USA, 2007. IEEE Computer Society. [17] Yves Vanrompay, Peter Rigole, and Yolande Berbers. Genetic algorithm-based optimization of service composition and deployment. In SIPE '08:, pages 13{18, New York, NY, USA, 2008. ACM. [18] Mohammad Alrifai, Thomas Risse, Peter Dolog, and Wolfgang Nejdl. A Scalable Approach for QoS-based Web Service Selection. In QoSCSOA'08 in conjunction with ICSOC 2008, Sydney, December 2008. [19] Baida, Z., et al.: A shared service terminology for online service provisioning. In: 6th Int. Conf. on Electronic commerce, 2004. [20] Sassen, A., Macmillan, C.: The service engineering area: An overview of its current state and a vision of its future. European Commission. Network and Communication Technologies, Software Technologies, 2005. [21] Zoran Stojanovic , Ajantha Dahanayake, « Service-Oriented Software System Engineering: Challenges and Practices », IDEA Group, 2005, ISBN 1-59140-426-6. [22] M. Grabisch, L'utilisation de l'intégrale de Choquet en aide multicritère à la décision. Newsletter of European Working Group "Multicriteria Aid for Decisions", Vol 3 No 14, Fall 2006, 5-10.
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Analysis of plane stress problems as optimization problems ¨ ur Yayli†Burhanettin Altan‡ Yusuf Cengiz Toklu∗Mustafa Ozg¨ including physical parameters such as cross sections and size [1], [4], [5], [6]. Metaheuristic methods such as genetic algorithm method [3], [2] have been introduced for solving optimization problems. Recently, a method called Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) has been introduced for analysis of structures and applied succesfully to linear and nonlinear trusses [7], [8]. In this paper, the application area of TPO/MA is extended to plane stress problems. For this purpose, total potential energy of an arbitrary plane triangular element has Keywords: Metaheuristic algorithms, plane been derived. This procedure can certainly be genstress, structural analysis, internal strain en- eralized for more general types of structures. ergy, TPO/MA Abstract Metaheuristic algorithms (TPO/MA) for engineering mechanics have attracted considerable attention in recent years. This study emphasizes on the combined application of plane stress elasticity and genetic algorithms to design and optimize the two dimensional structural analysis. In order to apply the optimization method, which basically depends on the external potential and internal strain energy, a plane stress formulation is used to evaluate the nodal deflections.
1
2
Introduction
The transverse deflection of plates subjected to edge loadings is an area of plane stress elasticity which had received a great deal of attention in the last century. It is defined to be a state of stress in which the shear stress and the normal stresses directed perpendicular to the plane are assumed to be zero. Most of the studies has dealt with plates having distributed in plane uniform loads since the governing equations have constant coefficients. Numerical methods have been applied to calculate the deflections of plates for a long time. In plane stress especially, finite element method has been utilized for the solution of a wide variety of plate problems. Although finite element method may perform well in many practical cases, It may fail in more complex structures. In particular, nonlinear problems the number of problem parameters can be very large, and their influence on the value to be optimized can be very complicated. Such plane stress problems can not be handled by finite element method. In recent years, in the newly emerging branch of genetic algorithms have drawn special attention in the areas of structural mechanics. Genetic algorithms include a class of search techniquies for solving complex elasticity problems [9]. A large number of studies address the optimization of different structures, ∗ Yusuf
Cengiz Toklu is with the Department of Civil Engineering, Bilecik Seyh Edebali University, Bilecik, Turkey (email:
[email protected]) † Mustafa Ozg¨ ¨ ur Yayli is with the Department of Civil Engineering, Bilecik Seyh Edebali University, Bilecik, Turkey (email:
[email protected]) ‡ Burhanettin Altan is with the Department of Mechanical Engineering, Bayburt University, Bayburt, Turkey (email:
[email protected])
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Two dimensional model
For any triangular element of plane stress structure is plotted in Fig. (1). It is assumed that plane stress occurs in the x, y plane. This assumption means that the displacement fields are approximated by u(x, y) = ui + C1 x + C2 y
(1)
v(x, y) = vi + C3 x + C4 y
(2)
Where u(x, y) and v(x, y) are the displacement functions in x and y directions at any point x, y in the element. ui and vi are the x and y translations of node i. C1 , C2 , C3 and C4 are constants. Then, the strains can be calculated in classical elasticity as follows: ∂u = C1 (3) x = ∂x ∂v y = = C4 (4) ∂y γ=
∂u ∂v + = C2 + C3 ∂y ∂x
(5)
The nodal displacements as shown in Figure (1), as follows: u(0, 0) = ui
v(0, 0) = vi
(6)
u(aj , bj ) = uj
v(aj , bj ) = vj
(7)
u(ak , bk ) = uk
v(ak , bk ) = vk
(8)
Where ui , vi , uj , vj , uk and vk represent the nodes i, j and k displacement components in x and y directions. Computation of these six displacements at nodes i, j and k using Eq. (1) and (2) yields the six equations given below: u(0, 0) = ui
(9)
v(0, 0) = vi
uk = ui + C1 ak + C2 bk
(10) Inserting Eqs. (16)-(19) in Eqs. (24)-(25) leads to following stress equations: (11) E × (27) σx = 2 (12) (ν − 1)(ak bj − aj bk ) (13) υ (ak (vi − vj ) + aj (vk − vi ))
vk = vi + C3 ak + C4 bk
(14)
uj = ui + C1 aj + C2 bj vj = vi + C3 aj + C4 bj
+ (υ − 1)bk (ui − uj ) − (υ − 1)bj (ui − uk )
The last four of these nodal equations may be written in matrix form as follows: C1 ui aj bj 0 0 uj vj 0 0 aj bj C2 vi uk = ak bk 0 0 C3 + ui C4 vi 0 0 ak bk vk (15) From above linear equations, C1 to C4 can be calculated as C1 =
bk (uj − ui ) bj (uk − ui ) + aj bk − ak bj ak bj − aj bk
(16)
C2 =
ak (uj − ui ) aj (uk − ui ) + ak bj − aj bk aj bk − ak bj
(17)
C3 =
bj (vk − vi ) bk (vj − vi ) + aj bk − ak bj ak bj − aj bk
(18)
C4 =
ak (vj − vi ) aj (vk − vi ) + ak bj − aj bk aj bk − ak bj
(19)
σy =
E × (ν 2 − 1)(ak bj − aj bk )
(28)
ak (vi − vj ) + aj (vk − vi ) + υbk (uj − ui ) + υbj (ui − uk ) E × (1 − ν 2 )(ak bj − aj bk ) (1 − ν) ( ak (uj − ui ) + aj (ui − uk ) 2 + bk (vi − vj ) + bj (vk − vi )) τ=
(29)
With the aid of Eq. (20), strain energy density can be calculated as follows: e=
E 4(1 −
υ 2 )(ak bj
− aj bk )2
×
(30)
(−(υ − 1)(ak (uj − ui ) + aj (ui − uk ) + bk (vi − vj ) + bj (vk − vi ))2 + 2(ak (vj − vi ) + aj (vi − vk ))(υ(ak (vj − vi ) + aj (vi − vk )) + bk (ui − uj ) + bj (uk − ui )) + 2(ak (vj − vi ) + aj (vi − vk ))(ak (vj − vi ) + aj (vi − vk ) + υbk (ui − uj ) + υbj (uk − ui )))
In a two dimensional linear elastic body, the strain energy stored in the structure due to deformation is: Z 1 e= σd = (σx x + σy y + τ γ) (20) 2 =0 The total potential energy defined as: By using Eqs. (3)-(5) strains can be calculated as follows, bk (uj − ui ) bj (uk − ui ) x = + aj bk − ak bj ak bj − aj bk y =
γ=
ak (vj − vi ) aj (vk − vi ) + ak bj − aj bk aj bk − ak bj
Πp = U − Γ
(31)
where U is the sum of the internal strain energy and (21) Γ is the potential energy of the external forces: Z U= edV (32) V (22) Z Γ = h (Fx u + Fy v)ds (33) s
1 × ak bj − aj bk
(23) where h is the thickness of element, F and F are x y the components of applied forces in the x and y di(ak (uj − ui ) + aj (ui − uk ) rection. The principle of minimum total potential + bk (vi − vj ) + bj (vk − vi )) energy means that the two dimensional body is in equilibrium position when the energy has a miniFor two dimensional plane stress, stress strain rela- mum value. In order to define the potential energy tionships are (Γ) of the external forces, we have to define the external force in Eq. (33). In this work, a uniform E σx = ( + ν ) (24) traction q on the element edge defined by nodes j x y 1 − ν2 and k is assumed (see Fig. 2). The external potential of the element then becomes: E σy = (y + νx ) (25) 2 1−ν Z L (1 − ν) E e Γ = −h (u(s)q cos θ + v(s)q sin θ)ds (34) τ= ( γ) (26) 1 − ν2 2 0
46
Note that q sin θ is the component of q in the y direction and q cos θ is the component of q in the x direction. The minimum of the potential energy for the plane stress structure requires that total potential energy functional in Eq. (31) should be minimum. Objective of present paper is to formulate plane stress problems in order to apply an optimization method for their analysis. Once the formulations are identified, they will be implemented in the TPO/MA framework using a metaheuristic algorithm like genetic algorithms, harmony search, swarm optimization and the like.
2.1
Figures
y ak k
bk
j
References
bj i
[2] D. E. Goldberg. Genetic algorithms in search, optimization and machine learning. Addison Wesley;, 1989.
x
aj
[1] H. Adeli and N. T. Cheng. Concurrent genetic algorithms for optimization of large structures. Journal of Aerospace Engineering, 7(3):276–296, 1994.
Figure 1: Plane stress triangular element
[3] J. H. Holland. Adaptation in natural and artificial systems. ann arbor mi. University of Michigan Press;, 1975. [4] W. M. Jenkins. On the application of natural algorithms to structural design optimization. Engineering Structures, 19(4):302–308, 1997. [5] S. Rajeev and C. S. Krishnamoorty. Discrete optimization of structures using genetic algorithms. Journal of Structural Engineering, 118(5):1233–1250, 1992. [6] G. Syswerda. Uniform crossover in genetic algorithms. In Proceedings of the Third International Conference on Genetic Algorithms, pages 2–9, 1989. [7] Y. C. Toklu. Nonlinear analysis of trusses through energy minimisation. Computers and Structures, 82(2021):1581–1589, 2004. [8] Y. C. Toklu, G. Bekda¸s, and R Tem¨ ur. Analysis of trusses by total potential optimization method coupled with harmony search. Structural Engineering Mechanics, An International Journal, 45(2):183–199, 2013. [9] H. Wataba and N. Okino. A study on genetic shape design. In Proceedings of the Fifth International Conference on Genetic Algorithms, pages 445–450, 1993. y
k
L
q s
Θ j x i
Figure 2: A uniform traction q on the element edge
47
48
A Genetic Algorithm Application for Multi-objective Multi-project Resource Constrained Project Scheduling Problem Fikri K¨ uc¸u ¨ksayacıgil and G¨ und¨ uz Ulusoy Abstract Resource Constrained Project Scheduling Problem (RCPSP) has been studied extensively by researchers by considering limited renewable and nonrenewable resources. Several exact and heuristic methods have been proposed. Some important extensions of RCPSP such as multi-mode RCPSP, multi-objective RCPSP and multi-project RCPSP have also been focused. In this study, we consider multi-project and multi-objective resource constrained project scheduling problem. As a solution method, non-dominated sorting genetic algorithm (NSGA-II) is adopted. By experimenting with different crossover and parent selection mechanisms, a detailed fine-tuning process is conducted, in which response surface optimization method is employed. In order to improve the solution quality, backward-forward pass (BFP) procedure is proposed as both post-processing as well as for new population generation. The performance of the algorithm and CPU times are reported. The results show that backward-forward pass procedure is successful to improve the solution quality.
∗
the objectives. There are further relevant objectives such as, for example, minimization of the maximum outflow, i.e., the maximum cumulative cash outflow throughout the project duration. In the following, first the solution methodology is explained in some detail and then an extensive computational study is presented. The computational results reveal that BFP procedure proposed here as an improvement routine works well.
2
Solution Methodology
In this study, genetic algorithm (GA) approach for the study of multi-objective multi-project RCPSP is studied. NSGA-II is preferred as the solution method, since it represents the current state-ofthe-art among GA approaches to this problem [2]. The parameters of NSGA-II, which are population size, generation number, crossover rate and mutation rate are determined with a detailed fine-tuning experiment. In addition to classical GA operators some additional operators are included in NSGAII, such as non-dominated sorting procedure and crowding distance operator. In this study, NSGA-II Keywords: RCPSP, Genetic Algorithms, is further extended through some improvement proMulti-objective RCPSP; Multi-project RCPSP, cedures and divergence applications are proposed. backward-forward scheduling BFP procedure ([5], [6]) is applied as an improvement routine on the solutions.
1
Introduction
2.1
RCPSP has been extensively studied in the literature. There are several extensions of this problem such as multi-mode RCPSP, multi-objective RCPSP and multi-project RCPSP. As the number of project-based organizations increases, the importance of multi-project RCPSP increases as a management tool. In the last decades, projects become increasingly more preferred way of doing business. Projects have by their nature a number of stakeholders. For example, there can be a client and a contractor who negotiate the due date and the cost of the project. This decision environment can then be represented as a bi-objective RCPSP with the minimization of the makespan (Cmax) and the maximization of the net present value (NPV) being ∗ Fikri K¨ uc¸u ¨ksayacıgil and G¨ und¨ uz Ulusoy is with Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla, Istabul, Turkey (email:
[email protected],
[email protected])
49
Individual Representation
An individual is represented by a double list including precedence feasible activity list and mode assignment list. In precedence activity list, activities are replaced into the genes so that the predecessors of an activity are before that activity. By doing so, precedence relations between the activities are satisfied. In the second list, modes assigned to each activity from their mode sets exist.
2.2
Initial Population Generation
In this study, two different initial population generation techniques are applied. The first oneis called the random initial population generation technique, where the precedence feasible activity list is formed by selecting the next activity from the eligible set randomly. In other words, the activities existing in the eligible have equal probability of selection. Another type of random sampling applied here is the
regret based-biased random sampling, where the selection probabilities are derived from the latest finishing time of the activities and assigned to corresponding activities. It has to be noted that both of them are implemented, but random sampling is generally preferred because of undesired complexity of regret based-biased random sampling. After completing the precedence feasible activity list, modes are assigned to each activity randomly. In the second method called the feasible initial population generation technique, the precedence feasible activity list is formed with random sampling. However, mode assignment methods vary because of the observation that random mode assignment sometimes causes infeasible individuals with respect to non-renewable resource capacities. Thus, several mode assignment techniques are proposed in order to use them along with random mode assignment.
2.3
Scheduling the Activities
In order to schedule the activities, serial schedule generation scheme is used ([3], [4]). During assigning a starting and finishing time for an activity, precedence relations and renewable resource capacities are taken into account. In addition, it is also considered that an activity can not start earlier than the activities existing in the previous positions of precedence feasible activity list.
2.4
Chromosome Evaluation
In NSGA-II, an individual is assigned a rank value instead of fitness value, which is used in classical GAs so as to evaluate the quality of an individual. Rank value is assigned by using the domination principle. An individual dominates another individual if all objective values are better than those of the second individual and at least one objective value is strictly better than that of the second individual. For maintaining the diversity of the algorithm, crowding distance operator is developed by [2]. Crowding distance of an individual represents how far that individual is from the neighboring individuals on the same front.
2.5
Forming the Next Generation
Three different crossover techniques proposed in the literature are used in this study:One-point crossover, two-point crossover and multi-component uniform order-based crossover. As for mutation operator, it tries to change every activity pair iand i+1,if the precedence relations and mutation rate are satisfied. In addition, mutation operator tries to change the mode of every activity if the mutation rate is satisfied. Parent selection is applied with two different methods. In roulette wheel selection, selection probabilities of the individuals are determined by
50
using rank values so that the individuals whose rank values are the best are assigned the highest selection probabilities. In binary tournament selection, the winner is determined by using the rank values and crowding distance values. Population reduction is succeeded with a simple method that the best individuals with respect to rank value are left in the population and the worst individuals are removed from the population. If a tie occurs among the rank values, then the individuals whose crowding distance values are the highest are selected for the next generation.
3
Fine-Tuning of the Parameters
The parameters of the algorithm, which are population size, generation number, crossover rate and mutation rate, are determined with response surface optimization. It is a statistical method in order to optimize the multiple output variables in the existence of multiple input variables. In our case, input variables are parameters of the algorithm. As for the output variables, performance measurespreferredarehypervolume, maximum spread and the number of non-dominated individuals. For applying response surface optimization, 10activity, 20-activity and 30-activity instances are selected. An instance is solved five times using a parameter and operator combination (that is, the combinations of crossover and parent selection mechanisms). In each replication, three performance measures are calculated. Average performance measures for a parameter combination are obtained after taking the average values of the performance measures per five replications. Thus, at the end, each instance has several average performance measures each of which pertains to a parameter combination. Using the performance measures, response surface optimization calculates a desirability value, which represents the quality of the parameter combination. For each instance, the parameter combination is selected, whose desirability value is the most. For selecting a unique parameter combination for each 10-activity, 20-activity and 30activity instance sets, the parameter combination, whose difference of its parameter values from the parameters of other parameter combinations is the least, is selected. In order to select the best operator combination, each instance is solved with the determined parameter combination. After evaluating the solution qualities of each operator combination, one-point crossover and roulette wheel selection mechanism are determined to be the best combination. For larger size of projects, the same fine-tuning process is repeated with some differences. In the current experiment, crossover and parent selection mechanism are not experimented and one-point selection and roulette wheel selection mechanism are
used. In addition, crossover rate and mutation rate are not experimented, rather the crossover rate and mutation rate that are determined as the best for 30-activity instances in the previous experiment are used. Moreover, population size and generation number are the functions of the number of the activities existing in the project network. At the end of the current experiment, the best population size and generation number coefficients are determined for each objective combination.
number of projects and seven levels are set for the number of activities. In problem set C, a multiproject environment that is heterogeneous in terms of project sizes, is emphasized by grouping projects consisting of different number of activities resulting in 27 instances. The objectives studied are minCMAX/maxNPV. First, NSGA-II is employed to solve these sets of test problems. BFP is applied in two different modalities. In one modality, it is applied on the archive of non-dominated set of solutions obtained at the end of NSGA-II andis designated asBFP in 4 Extensions of NSGA-II the final stage.As an improvement routine, BFPis also applied in the intermediate stages, which is desIn this study, several divergence application and lo- ignated as BFP in the intermediate stages. cal searches are developed. However, we will report here on the results obtained employingBFP proceTable 1: Results for Set A - BFP in the Final Stage dure. BFP procedure applies backward pass and pass Without BFP in the Final Stage With BFP in the Final Stage INSSUB sequentially. Before applying, the individual is inACMAX ACMAX ANPV ANS ANPV ANS A11 43,72 27448,15 1,33 61,39 8452,00 4,33 serted into an empty individual list. Backward pass A12 39,50 30205,81 2,22 29,67 65177,23 1,56 shifts all the activities to the right by considering A13 38,33 35943,40 1,89 28,00 77852,86 1,00 A21 106,09 -3786,42 19,56 89,70 1313,29 13,67 the precedence relations and renewable resource caA22 41,76 42472,89 1,67 31,50 91857,04 1,22 A23 39,06 46336,24 2,00 30,83 94562,36 1,11 pacities after sorting the activities in decreasing orA31 168,01 -9566,67 27,33 161,28 -9956,69 28,78 der of finishing times. In contrast, forward pass A32 45,52 31616,04 1,44 35,56 82375,22 1,00 A33 43,50 54445,20 2,22 31,70 125864,36 1,56 shifts all activities to the left by considering the same conditions after sorting the activities in increasing order of starting times. After each backward pass, if the starting time of the first activity in the precedence feasible activity list is larger than Table 2: Results for Set A - BFP in the Intermediate zero, then finishing and starting time of all activities Stages are decreased bythat difference. At this phase, the resulting individual is inserted into the individual Without BFP in the Final Stage With BFP in the Final Stage INSSUB ACMAX ANPV ANS ACMAX ANPV ANS list. After each forward pass, the resulting individA11 50,16 26130,72 3,78 43,39 27585,80 2,11 A12 29,05 68494,32 2,44 29,05 68494,32 2,44 ual is inserted into the individual list. This proceA13 28,30 77474,89 2,44 28,30 77474,89 2,44 dure constitutes an iteration in BFP procedure. AfA21 89,65 -694,03 12,56 88,49 -773,11 12,33 A22 29,55 97170,35 2,89 29,32 97863,80 2,67 ter each iteration, individual list is updated and the A23 29,66 100150,57 2,67 29,41 100415,73 2,33 individuals dominated are removed from the set. If A31 158,28 -9101,59 26,33 155,10 -9316,50 27,78 A32 35,81 85830,11 2,11 35,81 85884,65 2,11 the non-dominated solutions set can not renew itA33 29,02 135491,89 2,33 29,06 135579,90 2,44 self through 10 generations, then BFP procedure is terminated and the individuals existing in the non-dominated solutions set are presented as the Due to space limitations, the results will be reimproved version of the initial individual. stricted to the test instance set A. In Table 1, the
5
Computational Study and Results
The test instances generated [1] are used here. Three problem sets denoted by A,B,C are created to represent a variety of different environmental factors.Problem set A is formed to analyze the effect of resource based factors while fixing other factors. Set A includes multi-project cases with the same number of projects and the same number of activities but different resource requirements and resource availability levels. Each instance includes 14 projects consisting of 10 activities.Problem set B consisting of 84 instances focuses on the effects of different number of projects and activities. In these multi-project instances, three levels are set for the
51
average values of 5 replications are presented as average Cmax (ACMAX), average NPV (ANVP), and average number of non-dominated solutions (ANS). The columns under Without BFP in the Final Stage correspond to pure application of NSGA-II to the test problems. The columns under With BFP in the Final Stage correspond, on the other hand, to ACMAX, ANPV, and ANS obtained after BFP is applied to the archive of non-dominated solutions resulting from the application of NSGA-II. When comparing ACMAX and ANPV under these two different categories we observe that both objectives improve considerably. Another point to note is the reduction in ANS. In Table 2, similar analysis is performed but this time under BFP in the intermediate stages. When we compare BFP in the intermediate stages under the category Without BFP in the Final Stage with
the NSGA-II application reported in Table 1, we observe that both objectives improve considerably. When we compare both categories in Table 2, then we observe slight improvement, if at all. This observation implies that improvements introduced by BFP in the intermediate stages do not leave much room for further improvement through BFP in the final stage. Another observation concerns the comparison between the ACMAX and ANPV results under the category With BFP in the Final Stagein Table 1 and BFP in the intermediate stages under the category Without BFP in the Final Stage in Table 2. We observe no significant difference. All the above observations and results replicate themselves for the test instance sets B and C.
6
Conclusion
In this paper, we report on the results of the application of NSGA-II and the extension proposed here to a multi-objective multi-project RCPSP, where the objectives are the minimization of Cmax and the maximization of NPV. The extension proposed and tested is BFP in the final stage and BFP in the intermediate stages. Results reveal that BFP in the final stage shows significant improvement over the solution quality of pure NSGA-II. It is also revealed that BFP in the intermediate stages shows significant improvement over the solution quality of pure NSGA-II.Hence, the extension of NSGA-II through BFP has been successful. For future work, we intend to extend the work to cover further objectives such as minimization of the maximum outflow and minimization of average resource usage deviation; minimization of mean weighted tardiness of the projects in cases where due dates are assigned to projects; or minimization of mean flow time of the projects
References [1] A. Can and G. Ulusoy. Multi-project scheduling with 2-stage decomposition. 2010. [2] K. Deb. A fast and elitist multi-objective genetic algorithm: Nsga-ii. IEEE Transactions on Evolutionary Computation, 6(2):182–197, 2002. [3] R. Kolisch. Project Scheduling under Resource Constraints-Efficient Heuristics for Several Problem Classes, chapter A metaheuristic approach to fuzzy project scheduling. Physica-Verlag, Heidelberg, 1995. [4] R. Kolisch. Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation. European Journal of Operational Research, 90:320–333, 1996. [5] K.Y. Li and R. J. Willis. An iterative scheduling technique for resource-constrained project scheduling. European Journal of Operational Research, 56:370–379, 1992. [6] L. Ozdamar and G. Ulusoy. A note on an iterative forward / backward scheduling technique with reference to a procedure by li and willis. European Journal of Operational Research, 89:400–407, 1996.
52
The Effect of Eccentricity for Optimum Compressively Loaded Reinforced Concrete Columns Gebrail Bekdaş, Sinan Melih Nigdeli
Abstract In this study, the optimum design of reinforced concrete (RC) columns for minimum cost was investigated for different eccentricity of compressive force (N). Because of eccentricity, RC column is exposed with flexural moment. A random search technique is employed for iterative optimization process. The method is effective on finding optimum design of RC columns for different eccentricities for the defined ranges of design variables.
2
Methodology
A random search technique (RST) is used for optimization according to ACI 318- Building Code Requirements for Structural Concrete [18]. The optimization process can be explained in seven steps.
Step 1: In this step, ranges of design variables are defined. These design variable are cross-section Keywords: Reinforced concrete, optimization, random dimension (bw for breadth and h for height), number and search technique, eccentricity, compressive force, diameter of reinforcements (longitudinal and shear). The loading of the columns are also defined. These loads are columns. axial compressive force (N), flexural moment (M) resulting from eccentricity and shear force (V). Also, design constants such as clear cover (cc), maximum 1 Introduction aggregate diameter (Dmax), length of column (l), elasticity modulus of steel (Es) and specific gravity of Optimization is an important process of Reinforced steel (γs), yield strength of steel (fy), compressive Concrete (RC) structural design. The size of RC strength of concrete (f΄c) and costs of materials are members is a parameter which is chosen according to defined. experience of engineers. The aim of engineers is to find best secured design with minimum cost and maximum Step 2: Cross-section dimension are randomized within gain. For different cross-sectional sizes, the amount of the range. reinforced bar may vary and the cost of the design may not be known without using an optimization procedure. Step 3: Brittle fracture conditions given Eqs. (1-3) are By optimization, the design with minimum cost can be checked. Ac is the cross-sectional area in these automatically found for security measures and design equations. constraints given in design codes and architectural (1) design. Metaheuristic methods have been generally used V 0.2 f cAc for optimization of various RC members. V 5.5 Ac (2) One of these metaheuristic methods is genetic N 0.5 f cAc (3) algorithm. It has been employed for optimum design of beams [1], columns [2], deep beams [3], shape optimization [4], frames [5-6], T-shaped beams [7], If the brittle fracture conditions are not met, Step 2 is continuous beams [8] and together with another repeated. metaheuristic methods; simulated annealing for Step 4: Reinforcement design is done in this step. The continuous beams [9]. For the optimum design of RC clear distance between the bars are considered and bars retaining walls, several metaheuristic method such as may place in two lines if needed. simulated annealing [10], big bang-big crunch [11], harmony search [12] and charged system search [13] Step 5: The distance from extreme compression fiber to have been used. Harmony search algorithm was neutral axis (c) is iteratively scanned for the best M-N employed for T-shaped RC beams [14-15], RC frames combination. N is limited by design force and maximum [16] and continuous beams [17]. flexural moment capacity of the column is found. In this paper, biaxial RC columns are optimized for minimum material cost by using a random search technique. The effect of eccentricity was investigated for compressively loaded RC columns. ∗ Department of Civil Engineering, Istanbul University, 34320 Avcilar Istanbul/Turkey; E-mail:
[email protected];
[email protected];
53
Step 6: The total material cost is calculated. This cost is the objective function of the optimization. Step 7: The optimization procedure is repeated for iterative number entered by user. For each iteration, the design with the minimum cost is saved.
3 Numerical Example The optimum design of columns was investigated for 1000 kN and 2000 kN compressive forces. The ranges and properties used in the optimization are given in
Table 1. The eccentricity (ec) was investigated between 100 mm and 450 mm. For easy production, crosssection dimensions were assigned as multiples of 50 mm. For every 150 mm clear distance between upper and lower longitudinal reinforcements, a pair of web reinforcements were placed.
Table 1. Ranges and properties used in optimization Definition Symbol Unit Value Length of column l m 3 Range of web width bw mm 250-400 Range of height h mm 300-600 Clear cover cc mm 30 Range of reinforcement ϕ mm 16-30 Range of shear reinforcement ϕv mm 8-14 Max. aggregate diameter Dmax mm 16 Yield strength of steel fy MPa 420 Comp. strength of concrete f'c MPa 25 Elasticity modulus of steel Es MPa 200000 Specific gravity of steel γs t/m3 7.86 Cost of the concrete per m3 Cc $ 40 Cost of the steel per ton Cs $ 400 Shear force V kN 100
4 Conclusion The optimum design variables and material costs are given in Table 2 and 3 for 1000 kN and 2000 kN compressive force, respectively. As expected, the height of the column is getting bigger by the increase of the eccentricity in order to carry additional flexural moment. For 2000 kN compressive force
Eccentricity (mm) bw (mm) h (mm) Bars in each face Web reinforcement Shear reinforcement diameter (mm) Shear reinforcement distance (mm) Optimum cost ($)
100 300 300 1Φ18+ 1Φ16 -
Table 3. Optimum design of column (N=1000 kN) 150 200 250 300 350 300 250 250 300 250 350 450 500 500 600 1Φ20+ 1Φ22+ 1Φ26+ 2Φ16 2Φ18 1Φ18 1Φ18 1Φ16 2Φ16 2Φ16 2Φ16 4Φ16
400 250 600 1Φ22+ 1Φ20 4Φ16
450 250 600 2Φ26+ 1Φ16 4Φ16
Φ8
Φ8
Φ8
Φ8
Φ8
Φ8
Φ8
Φ8
120
150
190
220
220
270
270
270
22.70
26.48
28.05
31.54
37.10
42.35
47.49
52.23
Eccentricity (mm) bw (mm) h (mm)
100 400 400
Bars in each face
1Φ20+ 1Φ18
Web reinforcement Shear reinforcement diameter (mm) Shear rein. distance (mm) Optimum cost ($)
after 200 mm eccentricity, the optimum cross-section dimension were formed as the upper limits of the ranges. In this situation, only reinforcements are optimized and optimum cost results shows rapid increase by the increase of the eccentricity. Optimum results show that longitudinal reinforcements and height of the columns are the critical factor for eccentricity. The proposed method is effective on finding the best suitable RC design.
2Φ18
Table 4. Optimum design of column (N=2000 kN) 150 200 250 300 350 350 300 400 400 400 500 600 600 600 600 1Φ24+ 2Φ22+ 1Φ24+ 3Φ20+ 2Φ20 4Φ16 1Φ20+ 2Φ16 1Φ18+ 1Φ18 1Φ16 2Φ18 4Φ16 4Φ16 4Φ16 4Φ16
400 400 600 2Φ30+ 1Φ26+ 1Φ18+ 1Φ16 4Φ16
450 400 600 2Φ30+ 1Φ28+ 1Φ20 4Φ16
Φ8
Φ8
Φ8
Φ8
Φ8
Φ8
Φ8
Φ8
170
220
270
270
270
270
270
270
38.58
41.20
48.42
55.06
64.83
74.54
84.78
95.20
54
References [1] C. C. Coello, F. S. Hernandez, F. A. Ferrera, Optimal Design of Reinforced Concrete Beams Using Genetic Algorithms, Expert Syst. Appl., Vol. 12 (1997), pp. 101-108. [2] M. Y. Rafiq, C. Southcombe, Genetic algorithms in optimal design and detailing of reinforced concrete biaxial columns supported by a declarative approach for capacity checking, Comput. Struct., Vol. 69 (1998), pp. 443-457. [3] V. K. Koumousis, S. J. Arsenis, Genetic Algorithms in Optimal Detailed Design of Reinforced Concrete Members, Comput-Aided Civ. Inf., Vol. 13,(1998), pp. 43-52. [4] D. P. Rath, A. S. Ahlawat, A. Ramaswamy, Shape Optimization of RC Flexural Members, J Struct. Eng.-ASCE, Vol. 125 (1999), pp. 1439-1446. [5] C. V. Camp, S. Pezeshk, H. Hansson, H., Flexural Design of Reinforced Concrete Frames Using a Genetic Algorithm, J Struct. Eng.-ASCE., Vol. 129 (2003), pp. 105-11. [6] V. Govindaraj, J. V. Ramasamy, Optimum detailed design of reinforced concrete frames using genetic algorithms, Eng. Optimiz., Vol. 39(4) (2007), pp. 471–494. [7] F. Fedghouche, B. Tiliouine, Minimum cost design of reinforced concrete T-beams at ultimate loads using Eurocode2, Eng. Struct., Vol. 42 (2012), pp. 43–50. [8] V. Govindaraj, J. V. Ramasamy, Optimum detailed design of reinforced concrete continuous beams using Genetic Algorithms, Comput. Struct., Vol. 84 (2005), pp. 34–48. [9] M. Leps, M. Sejnoha, New approach to optimization of reinforced concrete beams, Comput. Struct., Vol. 81 (2003), pp. 1957–1966. [10] B. Ceranic, C. Freyer, R.W. Baines, An application of simulated annealing to the optimum design reinfroced concrete retaining structure, Computer and structures, Vol. 79 (2001), pp. 15691581. [11] C. V. Camp, A. Akin, Design of Retaining Walls Using Big Bang–Big Crunch Optimization, J Struct. Eng.-ASCE, Vol. 138(3) (2012), pp. 438– 448.
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[12] A. Kaveh, A.S.M. Abadi, Harmony search based algorithms for the optimum cost design of reinforced concrete cantilever retaining walls, International Journal of Civil Engineering, Vol. 9(1) (2011), pp.1-8. [13] S. Talatahari, R. Sheikholeslami, M. Shadfaran, M. Pourbaba, Optimum Design of Gravity Retaining Walls Using Charged System Search Algorithm, Mathematical Problems in Engineering, Vol. 2012, pp. 1-10. [14] G. Bekdaş, S. M. Nigdeli, Cost Optimization of T-shaped Reinforced Concrete Beams under Flexural Effect According to ACI 318, In: “3rd European Conference of Civil Engineering”, December 2-4 2012, Paris, France. [15] G. Bekdaş, S. M. Nigdeli, Optimization of Tshaped RC Flexural Members for Different Compressive Strengths of Concrete, International Journal of Mechanics, Vol. 7 (2013), pp. 109-119. [16] A. Akın, M. P. Saka, Optimum detailing design of Reinforced Concrete Plane Frames to ACI 318-05 Using harmony search Method, In: “Proc. the Eleventh International Conference on Computational Structures Technology", 4-7 September 2012, Dubrovnik, Crotia. [17] A. Akın, M. P. Saka, Optimum detailed design of RC continuous beams using harmony search algorithm, The Tenth International Conference on Computational Structures Technology, 14-17 September 2010, Valencia, Spain. [18] ACI 318M-05, Building code requirements for structural concrete and commentary, American Concrete Institute, Farmington Hills, MI, USA (2005).
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Fusion of Palm-Vein & Finger-Vein for Personal Identification Using Principal Component Analysis Abdallah Meraoumia1 , Hakim Bendjenna2 , Salim Chitroub3 and Ahmed Bouridane4 1 Universit´ ´ e Kasdi Merbah Ouargla, Laboratoire de G´enie Electrique. Facult´e des Sciences et de la Technologie et des Sciences de la Mati`ere, Ouargla, 30000, Alg´erie 2 University of Tebessa, Computer Science Department, Tebessa, Algeria 3 Signal and Image Processing Laboratory, Electronics and Computer Science Faculty, USTHB. P.O. box 32, El Alia, Bab Ezzouar, 16111, Algiers, Algeria 4 School of Computing, Engineering and Information Sciences, Northumbria University, Pandon Building, Newcastle upon Tyne, UK.
Email:
[email protected],
[email protected], S
[email protected],
[email protected]
Among several traits, which can be extracted from the hand, palm and finger are two biometrics that has been systematically used to make identification for last years. So far, majority of studies on palm and finger identification are mainly based on image captured under visible light [5,6]. However, infrared technology have been recently used to improve the performance of hand based identification because infrared image highlights specific features of the palm and/or finger, making it possible to provide other information, like veinnet (palm-vein and finger-vein are much harder to fake than palmprint and finger-knuckle-print), to improve the accuracy and anti-spoofing capability of hand based systems. In this technique, an acquisition device, to capture the palm and finger images under infrared light resulting into an vein-net image, is used.
Abstract—Biometrics technology has been attracting extensive attention due to the ever growing demand on access control, public security, forensics and e-banking. With the fast development of biometric data acquisition sensors and data processing algorithms, diverse biometric systems have been now widely used in various applications. Among these biometric technologies, the hand-based biometrics is most popular and has the largest shares in the biometrics market. The main objective of this paper consists of contributing in designing and developing efficiency hand based biometric algorithm for various applications. In this context, palm-vein and finger-vein are used jointly for elaborating an efficient multimodal biometric recognition system. So, a fusion process is proposed for fusing these modalities. At the features-extraction stage the features are generated by the method of Principal Component Analysis (PCA ). Thus, an euclidian distance score is employed to measure the similarity between templates during the matching phase. The proposed scheme is tested and evaluated using a database of 106 users. The results show that the accuracy of the proposed method can meet the requirements of an online biometric identification.
Unimodal biometric systems perform person recognition based on a single source of biometric information. Such systems are often affected by some problems such as noisy sensor data and non-universality. Thus, due to these practical problems, the error rates associated with unimodal biometric systems are quite high and consequently it makes them unacceptable for deployment in security critical applications. Some of these problems can be alleviated by using multimodal biometric systems [7]. However, in the proposed multimodal system design, Palm-Vein-Print (PVP ) and Finger-Vein-Print (FVP ) operate independently and their results are combined using score level fusion scheme. In our method, PVP and FVP identification system is based on features extracted by PCA technique. These features are extracted by projecting PVP (FVP ) images into the subspace obtained by the PCA transform, called eigenpalm (eigenfinger) features.
Index Terms—Biometrics, identification, Palm-Vein, FingerVein, Principal Component Analysis, Data Fusion.
I. I NTRODUCTION ERSONAL identification and verification both play a critical role in our society. Traditional knowledge based or token-based personal identification or verification systems are time-consuming, inefficient and expensive [1]. Biometrics offers a natural and reliable solution to the problem of identity determination by recognizing individuals based on some characteristics that are inherent to the person. Furthermore, biometrics technologies are becoming the foundation of an extensive array of highly secure identification and personal verification solutions [2]. Nowadays, hand feature is a one of the most reliable biometrically based technology in applications of personal identification or verification due to its highly stability and uniqueness [3]. Thus, there are several motivations for a hand biometric; firstly, the data acquisition is economical via commercial low-resolution cameras, and its processing is relatively simple. Secondly, hand based access systems are very suitable for several usages. Thirdly, the hand features are more stable over time and are not susceptible to major changes. Oftentimes, some features (characteristics) related to a human hand are relatively invariant and distinctive to an individual [4].
P
The rest of the paper is organized as follows: The proposed scheme of the unimodal biometric system is presented in section 2. Section 3 gives a brief description of the feature extraction technique. A section 4 is devoted to describe the matching and normalization method. The fusion technique used for fusing the information is detailed in section 5. In section 6, the experimental results, prior to fusion and after fusion, are given and commented. Finally, the conclusions and further works are presented in sections 7.
57
Preprocessing
Observation
Matching
Normalization
Decision
Enrollment
Preprocessing
Fig. 1.
Observation
Training
Database
Unimodal palm-vein identification system based on principal component analysis for modeling and classification.
II. P ROPOSED U NIMODAL S YSTEM
B. Observation Vector Generation
Fig. 1 shows the block-diagram of the proposed unimodal biometric identification system based on the palm-vein image. In the preprocessing module, the Region Of Interest (ROI ) is localized. For the enrollment phase, each ROI sub-image is mapped into one dimensional signal (Observation vector). After that, these vectors are concatenated into two dimensional signal. This vector is transformed by the PCA transform into feature space called eigenpalms space (Training module). For identification phase, the same feature vector is extracted from the test palm-vein image and projecting into corresponding subspace. Then euclidian distance is computed using all of the references in the system database (Matching module). Finally, after a normalization process, decision which person accepted or rejected is made.
The PCA applied to a set of images, can be used to find the subspace that is occupied by all of the images from the analyzed set. When the images are encoded into this subspace and then returned to the original space, the error between the reconstructed and the original images is minimized. To begin, we have a training set of N ROI sub-images. By reordering these ROI sub-images into one dimensional vector, xi , and concatenate all xi , with i = [1· · · N ], for obtaining a two dimensional vector, X = [x1 , x2 , x3 ,· · · , xN ]. The process of obtaining a single subspace consists of finding the covariance matrix C of the training set of ROI sub-images, X, and computing its eigenvectors. Each original ROI sub-image can be projected into this subspace. The eigenvectors spanning the palm-space can be represented as images with the same dimensionality as the palm ROI sub-images used to obtain these eigenvectors. These sub-images are called eigenpalms.
III. F EATURE E XTRACTION AND M ATCHING One challenging problem with the biometric technologies is the extraction of features from the biometric images. In this work, after a palmprint image is captured, a Region Of Interest (ROI ) has to be located from the original image before further feature extraction, using the methods described in [8] and [9] for PVP and FVP, respectively. In our method, the features are generated from the PVP and FVP images by PCA technique.
IV. M ATCHING & N ORMALIZATION PROCESS Given two sets of features originating from two modalities, the objective of the feature matching process is to determine whether or not the prints represent the same modality. However, each PVP (FVP ) is represented by a unique observation vector. The task of major concern was to appoint an unknown PVP (FVP ) to one of the possible classes. We will assume that a set of reference PVP (FVP ) are available to us and we have to decide which one of these reference patterns an unknown one (the test pattern) matches best. A reasonable first step to approaching such a task is to define a measure or a cost measuring the similarity between the (known) reference vectors and the (unknown) test vector, in order to perform the matching operation known as template matching. Systems then make decisions based on this score. A template in our system is represented by a PVP or FVP feature vector. In order to identify a user, the matching process between the test template, φt , and the templates from the database, φi , has to be performed. The matching between corresponding feature vectors is based on the Euclidean distance. In this step, the following distance is obtained:
A. Principal Component Analysis The PCA transform applied to a set of images, can be used to find the subspace that is occupied by all of the images from the analyzed set. The methodology for calculating principal component is given by the following method [10]: Let the training set of vectors of original data (each vector with dimension M ), X, be x1 , x2 , x3 ,· · · , xN . First,∑ compute e = 1 N xi . the mean of original data of the set by: X i=1 N Second, subtract the mean from each original data to generate e Third, form the the mean removed data by φi = xi − X. matrix using mean removed data of (M × N ) dimension, D = [φ1 φ2 φ3 · · · φN ]. Fourth, compute the sample ∑N covariance matrix (C) of dimension (M × M ), C = N1 n=1 φn φTn = DDT and compute the eigen values of the covariance matrix and of the eigen vectors for the eigen values. Finally, keep only the eigen vectors corresponding to L largest eigen values. These eigen values are called as principal components.
√ d(φt , φi ) =
58
(φt − φi )(φt − φi )T
(1)
(a)
(b)
(c)
Fig. 2. PVP based identification system test results. (a) The ROC curve, which is a plot of FRR against FAR, (b) The ROC curve, which is a plot of GAR against FAR and (c) The CMC curve for the PVP modality.
where i = 1, 2, · · · · ·, N are palm templates from the database (reference templates) and N is the total number of templates in the system database (enrolled database). During the identification process, the distance d between the test template, φt , and all of reference templates in the database are computed, therefore the vector scores, V, given all these distance is given as: V = [d1
d2
d3
d4 · · · dN ]
rules consist of the sum (SUM ) and WeigHTed-sum (WHT ) of the two similarity measures, their MINimum (MIN ) and MAXimum (MAX ) of both and finally their MULtiplication (MUL ). The final decision of the classifier is then given by choosing the class, which maximizes the fused similarity measures between the sample and the matching base. VI. E XPERIMENTAL R ESULTS AND D ISCUSSION
(2)
A. Experimental database
An important aspect that has to be addressed in identification process is the normalization of the scores obtained. Normalization typically involves mapping the scores obtained into a common domain. Thus, a Min-Max normalization scheme was employed to transform the scores computed into similarity scores in the same range [11]. e= V
V − min(V) max(V) − min(V)
To evaluate the performance of the proposed Multimodal identification scheme, a database containing palm-vein and finger-vein images was required. In this work, we construct a multibiometric database for our experiments based on Hong Kong Polytechnic University (PolyU) near-infrared palmprint database [15], and SDUMLA-HMT finger-vein database [16]. The multibiometric database consists of 12 FVP images and 12 PVP images per person with total of 106 persons. Three randomly samples, of each FVP and PVP, is selected to construct a training set. The rest of the samples are taken as the test set.
(3)
e denotes the normalized scores. However, these scores where V are compared, and the lowest score is selected. Therefore, the best score is Do and its equal to: e Do = min(V) i
(4)
B. Simulation results
Finally, this score is used for decision making. A threshold To regulates the system decision. The system infers that pairs of biometric samples generating scores lower than or equal to To are mate pairs. Consequently, pairs of biometric samples generating scores higher than To are non mate pairs.
In the system-design phase (all experiments), three images are randomly selected of twelve images of each class (person) were used in the enrolment stage to create the system database; the remaining nine images were used for testing. In the following tests, we setup a database with size of 106 classes, which are similar to the number of employees in small to medium sized companies. Thus, the client experiments were performed by comparing nine test images with the corresponding class in the database. A total of 954 comparisons were made. The impostor experiments were performed by comparing the nine images with each class in the database. A total of 50085 impostor experiments were made. In an identification mode the system examines whether the user is one of enrolled candidates. Therefore, the biometric data is collected and compared to all the templates in the system database. Identification is closed-set if the person is assumed to exist in the system database. In open-set identification, the person is not guaranteed to exist in the system
V. F USION S TRATEGY Multimodal biometric identification/verification, in which two or more modalities are used jointly, has been investigated and found to increase robustness and thus improve the accuracy of such identification/verification system [12]. However, in the multimodal system design, these modalities operate independently and their results are combined using an appropriate fusion scheme. Thus, the fusion can be performed at different levels [13]. These are: fusion at image level, at the feature level, at score level and at decision level. In this paper we combined the modalities at the matching score level. Thus, the fusion of palm-vein and finger-vein images based sub-systems is realized using five simple rules [14]. These
59
(a)
(b)
(c)
Fig. 3. FVP based identification system test results. (a) The ROC curves under different type of fingers, (b) The ROC curve for RF modality and (c) The CMC curve for RF modality. TABLE 1 : FVP BASED MULTIMODAL OPEN SET IDENTIFICATION SYSTEM PERFORMANCES LEVEL OF FUSION
MATCHING SCORE
FEATURE EXTRACTION
FUSION RULE
IMF
IRF
MRF
IMRF
To
EER
To
EER
To
EER
To
EER
SUM
0.1916
1.887
0.1781
1.428
0.1547
1.664
0.1656
1.027
WHT
0.1901
1.848
0.1773
1.450
0.1850
1.782
0.1671
1.048
MUL
0.0413
2.251
0.0401
1.775
0.0296
1.918
0.0066
1.409
MAX
0.2298
2.347
0.2046
1.782
0.1966
2.192
0.2223
1.668
MIN
0.1385
2.621
0.1392
2.369
0.1241
2.542
0.1003
2.052
CONCATENATION
0.2030
2.306
0.1918
1.686
0.1892
2.509
0.2134
1.827
database. In our work, the proposed method was tested for the two modes of identification. 1) Unimodal identification system: a) Palm-Vein modality: The aim of this section is to investigate whether the system performance could be improved by using the PVP modality. Therefore, we found the performance using PVP modality. By adjusting the matching threshold, a Receiver Operating Characteristic (ROC ) curve, which is a plot of False Reject Rate (FRR ) against False Accept Rate (FAR) for all possible thresholds, can be created (see Fig. 2.(a). Thus, the described open set identification system can achieves an Equal Error Rate (EER ) equal to 0.1039 % at the decision threshold To = 0.1170, and a maximum Genuine Acceptance Rate (GAR ) equal to 99.8961 %. Fig. 2.(b) shows the ROC curve, which is a plot of GAR against FAR, when the PVP modality is used. However, the developed system is expected to give higher accuracy. To further validate our idea we have run other test for the closed set identification. The result is presented, Cumulative Match Characteristics (CMC ), in Fig. 2.(c)). The best result of Rank-One Recognition (ROR ) is given as 99.2662 % with lowest Rank of Perfect Recognition (RPR ) of 13. b) Finger-Vein modality: The goal of this experiment was to evaluate the system performance when we using information from each modality (each finger). For this, we found the performance under different modalities {Index Finger (IF ), Ring Finger (RF ), Middle Finger (MF )}. By adjusting the matching threshold, a ROC curve, which is a plot of FRR against FAR for all possible thresholds, can be created. Fig. 3.(a) compares the performance of the system for varying
finger types. It is clear that the system achieved a minimum EER (3.2536 % at To = 0.1799) when the RF modality is used. It is interesting to note that the system can achieve an EER of 3.8784 % at To = 0.2185 for the IF modality. Finally, the system can operate by an EER of 4.4060 % at To = 0.2009 for the MF modality. Fig. 3.(b) presents the ROC curve obtained by the proposed scheme for the RF modality. In the case of a closed set identification, Fig. 3.(c) presents the experimental results, as a CMC curve, obtained for RF modality. From Fig. 3.(c), the best result of ROR produces an accuracy of 83.0189 % with RPR of 86. Each FVP trait contains images from four types of fingers, IF, RF and MF. For this raison, an ideal FVP identification system should be based on the fusion of these fingers. The goal of this section was to investigate the systems performance when we fuse information from some fingers of a person. Therefore, information presented by different biometrics (finger types) is fused, at the feature extraction level and matching score level, to make the system efficient. In the case of fusion at the feature extraction level, the data obtained from each biometric modality (IF, RF and MF ) is used to compute a feature vector. Therefore, the idea of fusion at the feature extraction level is to concatenate the feature vectors of different biometrics (different finger types). Let XPVP be the observation vector (derived from the input PVP modality) and XF VP the observation vector (derived from the input FVP modality). XPVP and XFVP are represented by: XPVP = [x1
60
x2
x3
x4 · · · xN ]
(5)
(a)
(b)
(c)
Fig. 4. Identification test results. (a) Comparison between the different FVP based systems (unimodal and multimodal systems), (b) The CMC curve for FVP based multimodal identification system using fusion at matching score level and (c) Comparison between all the best systems.
XF VP = [y1
y2
y3
y4 · · · yN ]
2) Multimodal identification system: Multimodal approaches to biometric recognition tasks, that is, approaches that combine two or more biometric traits to perform personal identification. The information fusion strategies employed in multimodal biometric systems can be categorized into four levels; (i) fusion at image level, (ii) fusion at feature extraction level, (iii) fusion at matching score level, and (iv) fusion at decision level. The third fusion schemes are considered in this work. The objective of this section is to investigate the integration of PVP & FVP features, and to achieve higher performance that may not be possible with unimodal biometric alone. Thus, to find the better of the all fusion rules, with the lowest EER, Table showing the results were generated (see Table 2). From Table 2, it is clear that our open set identification system achieves the best EER in the case of SUM rule with the fusion of PVP modality with all finger types (IMRF ). However, it can operate at EER = 0.0000 % at the threshold To = 0.0356. The average increase in performance between the best unimodal open set identification system (EER = 0.1039 %) and the multimodal identification system (EER = 0.0000 %) is 100 %.
(6)
The resulting fusion vector XFU S is: XF U S =
(X
PVP
XF VP
) = [z1
z2
z3
z4 · · · zN ]
(7)
The new observation vector, XF U S vector has a higher dimensionality and represents a person identity in a different feature space. Table showing the results were generated (see Table 1, last line). This Table shows that the IF and RF combination (IRF ) offers better results (EER = 1.6857 % and To = 0.1918). We have also performed a closed set identification scenario by applying the fusion rule (concatenation) on the feature extraction level and calculated the ROR and RPR. As the results shows, the closed set identification system based on combination of all finger types (IRMF ) produces the best ROR of 92.1384 % with RPR = 46 when compared against the combinations based on IMF, IRF and MRF which produce a ROR of 87.8407 % (RPR = 59), 90.6709 % (RPR = 74) and 88.1551 % (RPR = 62) accuracies, respectively In the case of the fusion at the matching score level, the individual matching scores are combined to generate a single scalar score, which is then used to make the final decision. Table 1 provides the performance of the open set identification system. From Table 1, it is clear that our identification system achieves a best performance when using all finger (IMRF ) with SUM rule fusion (EER = 1.0268 % and To = 0.1656). Finally, the ROC curves for RF modality, IRF (combination of IF and RF at the feature extraction level) and IMRF (combination of all finger types at the matching score level) are shown in Fig. 4.(a) From this figure, the performance of the open set identification system is significantly improved by using the fusion of all finger types at the matching score level. In the closed set identification experiments, the combination of all finger types with SUM rule is always more efficient than the other combinations and rules, it can work with a maximum ROR of 92.7673 % and a RPR equal to 42. It is noted that, combination of all finger types with WHT rule give a similar results (ROR = 92.7675 % with RPR = 48). Fig. 4.(b) present the FVP identification test results and show the performance of the closed set identification system.
For the evaluation of the closed set identification system performance, Table 2 illustrates the results for all combinations and fusion rules. From this Table, it can be seen that always the fusion of PVP modality with all finger types (IMRF ) and SUM rule offers the best identification rate with ROR equal to 100.000 % with a RPR of 1.
3) Comparison Study: To find the better open set identification systems, unimodal or multimodal systems, graphs showing the ROC curves for the open set identification using unimodal and multimodal systems, were generated (see Fig. 4.(c)). By the analysis of this plot, it can be observed that the performance of the open set identification system is significantly improved by using the fusion. However, it can be concluded that the fusion of the two modalities (palm-vein $ finger-vein) yields much better identification results compared with unimodality. Therefore, the developed multimodal identification system is expected to give higher accuracy.
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TABLE 2 : MULTIMODAL IDENTIFICATION SYSTEMS PERFORMANCE USING FUSION AT THE MATCHING SCORE LEVEL OPEN SET IDENTIFICATION LEVEL OF FUSION
SCORE
FUSION RULE
PVP-RF
CLOSED SET IDENTIFICATION
PVP-IMRF
PVP-RF
PVP-IMRF
To
EER
To
EER
ROR
RPR
ROR
RPR
SUM
0.0718
0.008
0.0356
0.000
99.6855
2
100.000
1
WHT
0.1067
0.046
0.0837
0.010
99.4759
12
99.7904
4
MUL
0.0145
0.210
0.0145
0.210
89.5178
7
95.2830
2
MAX
0.1361
0.172
0.1361
0.172
99.4759
33
99.8951
2
MIN
0.0529
0.315
0.0529
0.315
89.5178
13
95.2830
8
VII. C ONCLUSION AND FURTHER WORK
[4] A. Meraoumia, S. Chitroub and A Bouridane, “Fusion of Finger-KnucklePrint and Palmprint for an Efficient Multi- Biometric System of Person Recognition”, IEEE International Conference on Communications (ICC), Kyoto, japan, june 2011, pp: 1-5. [5] David Zhang, Guangming Lu, Wei Li, “Palmprint Recognition Using 3-D Information”, IEEE Transactions On Systems, Man, And CyberneticsPart C: Applications And Reviews, Vol. 39, No. 5, 2009, pp.505-519. [6] K Kumar Sricharan, A Aneesh Reddy and A G Ramakrishnan, “Knuckle based Hand Correlation for User Authentication”, Biometric Technology for Human Identification III, Proc. of SPIE Vol. 6202, 62020X, 2006. [7] Jin-Rong Cui, “Multispectral palmprint recognition using Image Based Linear Discriminant Analysis”, International Journal of Biometrics, Vol. 4, No. 2 pp. 106-115, 2012. [8] David Zhang, Zhenhua Guo, Guangming Lu, Lei Zhang, and Wangmeng Zuo, “An Online System of Multispectral Palmprint Verification”, IEEE Trans. on Instrumentation and Measruement, vol. 59, no. 2, pp. 480-490, 2010. [9] Gongping Yang, Xiaoming Xi and Yilong Yin, “Finger Vein Recognition Based on a Personalized Best Bit Map”, Sensors, pp:1738-1757, 2012, [10] M.S. Bartlett, J.R.Movellan, and T.J. Sejnowski, “Face recognition by independent component analysis”, IEEE Transactions on Neural Networks, 13(6):1450-1464, 2002. [11] A. Meraoumia, S. Chitroub and A. Bouridane, “Multimodal Biometric Person Recognition System Based on Multi-Spectral Palmprint Features Using Fusion of Wavelet Representations”, Advanced Biometric Technologies. Published by InTech, ISBN 978-953-307-487-0, pp. 21-42, 2011. [12] David Zhang, Zhenhua Guo, Guangming Lu, Lei Zhang, Yahui Liu and Wangmeng Zuo, “Online joint palmprint and palmvein verification”, Expert Systems with Applications, Vol. 38, pp. 26212631, 2011 [13] Audrey Poinsot, Fan Yang and Michel Paindavoine, “Small Sample Biometric Recognition Based on Palmprint and Face Fusion”, Fourth International Multi-Conference on Computing in the Global Information Technology, pp.118-122, 2009. [14] Mingxing He, Shi-Jinn Horng, Pingzhi Fan, Ray-Shine Run, RongJian Chen, Jui-Lin Lai, Muhammad Khurram Khan and Kevin Octavius Sentosa, “Performance evaluation of score level fusion in multimodal biometric systems”, Pattern Recognition Vol 43, pp: 17891800, 2010. [15] The Hong Kong Polytechnic University (PolyU) Palmprint Database, available at: http://www4.comp.polyu.edu.hk/∼biometrics. [16] SDUMLA-HMT finger-vein database, available at: http://mla.sdu.edu.cn/sdumla-hmt.html.
Several studies were shown that multimodal biometric approach can be a possible solution for increased accuracy of the biometric based identification systems. In this work PVP and FVP is integrated in these systems, to enrich their ability of open/closed set identification. The features are extracted using the PCA technique. Finally, information presented by different modalities (sub-system) is fused to make the system efficient using matching score level fusion. The experimental results, obtained on a database of 106 users, show a very high identification accuracy. They also demonstrate that combining different modalities does significantly reduce the accuracy of the system. In addition, our tests show that the multimodal system provides better open/closed set identification accuracy than the best unimodal systems for the two tested modalities in the case of fusion at matching score level. For further improvement, our future work will project to use other biometric modalities (Face and Iris) as well as the use of other fusion level like feature and decision levels. Also we will focus on the performance evaluation in both phases (verification and identification) by using a large size database. R EFERENCES [1] N. V. Boulgouris, K. N. Plataniotis and E. Micheli-Tzanakou, “Biometrics: Theory, Methods, and Applications”, David B. Fogel, Series Editor, Willy publisher, IEEE Press and IEEE Press on Computational Intelligence, 2010. [2] Ajay Kumar, David Zhang, “Improving Biometric Authentication Performance from the User Quality”, IEEE transactions on instrumentation and measurement, vol. 59, no. 3, march 2010. pp. 730-735. [3] K Kumar Sricharan, A Aneesh Reddy and A G Ramakrishnan, “Knuckle based Hand Correlation for User Authentication”, Biometric Technology for Human Identification III, Proc. of SPIE Vol. 6202, 62020X, 2006.
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Applications of Meta-heuristic algorithms to civil engineering problems, a survey A. E. Cercevik, H. Bozkurt, Y. C. Toklu∗ Abstract Civil engineering problems show a great variety in type and formulation and thus necessitate very different techniques for their solutions. One of these techniques is the class called meta-heuristic algorithms. These algorithms, which are being in use since about half a century, have proved themselves very efficient in solving problems that are formulated as optimization problems. Civil engineering cover areas like structural engineering, hydraulic engineering, geotechnical engineering, material engineering, transportation engineering, construction engineering and project management. It is not difficult to name design processes in all these fields, and if one considers that design is always related to optimization, it becomes evident that meta-heuristic methods can be applied in all these fields. In addition to problems which are formulated as optimization methods at first sight, there are also those which have been solved by formulations different from optimization before the advances in metaheuristic techniques, and now being formulated in different ways to be solved by using meta-heuristic techniques. In this study, an assessment has been done on applications of these algorithms on civil engineering problems. Keywords: Metaheuristic algorithms, engineering, global solutions, multiple solutions, TPO/MA, FEM.
1
Introduction
Engineering is known to have two main aspects, design and analysis. Engineering design can be defined as finding suitable solutions to real world problems using knowledge of science, mathematics, logic, economics, system sciences and appropriate experience. The word suitable in this definition can easily be replaced by best meaning most economical, sustainable, effective, maintainable, feasible, i.e. optimum under given conditions of the problem. Thus it is easy to see that engineering design is very strongly tied to optimization. It goes without saying that every design problem is, in fact, an optimization problem. Some examples are named in the present paper to emphasize this aspect. On the ∗ A. E. Cercevik, H. Bozkurt, Y. C. Toklu are with Departmant of Civil Engineering. Bilecik Seyh Edebali Universty, Bilecik, Turkey. (email:
[email protected])
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other hand, it is shown in the scientific literature that, some analysis problems also can be formulated as optimization problems. One can easily add to engineering applications formulated as optimization problems the ones like assignment, scheduling, blending, allocation problems and the like which do not fall directly under the category of design and analysis aspects of engineering. Thus, one can easily state that engineers do always face optimization problems theoretically or in their real life applications and they have to find appropriate techniques to bring relevant solutions to these problems. Metaheuristic methods have emerged in the last quarter of 20th century, and have proved themselves to be very suitable for this purpose, and much more versatile than all other classical ones. In this study, an assessment of meta-heuristic methods will be given insisting on applications on civil engineering problems, and, an attempt will be presented with the aim of having a general look to the named techniques.
2
Metaheuristic Methods
Metaheuristic methods are stochastic optimization methods inspired by observations from various sources like nature, sociology, physics, mathematics, music, politics, etc. Random Search and Local Search are perhaps the first examples of metaheuristic algorithms due to their use of heuristic rules in choosing step sizes, stopping criteria, determination of starting points and new solution candidates. But the first techniques that deserve the right of being called as metaheuristic algorithm formally are Genetic Algorithms and Simulated Annealing which are both forwarded before 1980. These are followed, among many others, by Tabu Search in 1989, Ant Colony Optimization in 1992, Particle Swarm Optimization in 1995, Harmony Search and Big-Bang Big-Crunch Optimization in 2001, Viral Systems in 2007. The number of meta-heuristic algorithms are continuously increasing with new analogies imitating flees, monkeys, charged systems in physics, imperialist states, etc. and with hybrid ones combining one or more of these algorithms with each other or with some conventional techniques. Some of these methods are for problems with discrete variables or continuous variables, and some others can be used for both of them with some modifications. Some of these algorithms are based on improving
one single candidate solution, while in most of them the solutions are searched by improvements in a bunch of candidate vectors. It can be seen in the relevant literature that with all types of algorithms thus developed, it is possible to reach to very successful results in the examples treated. Common characteristics of meta-heuristic algorithms are that they can deal with scientific and engineering problems without necessitating complex mathematical expressions, constraints can be handled with an amazing ease as compared to classical techniques and that they all intend to favorize the search for the global optimal solution instead of local solutions. That is why engineers and scientists are recurring to meta-heuristic methods in solving their problems which can be formulated as numerical optimization problems for the purpose of reaching to the optimal solution or at least to a near-optimal solution.
3
Typical civil engineering 3.2 Hydraulic Works problems solved by meta- One other important area of applications of metaheuristic methods heuristic algorithms in engineering is the hydraulic
Civil engineering is a very important branch of the general class, engineering. It is very closely related to finding optimal solutions to various real life problems, like for instance, determining the best structures to be built, in the most economical, sustainable, durable and quick way, using the most suitable materials, to arrive at the most comfortable state. Therefore, starting with their emergence, meta-heuristic algorithms have found many ways of being applied to engineering problems [1, 2, 3]. Some examples are given in the following paragraphs.
3.1
of displacements and b is the vector of loads acting on the system. There exist elegant and very effective methods for solving linear problems as defined above, while nonlinear problems do always need a special treatment because of their complexity. On the other hand, these problems can be formulated as optimization problems using the well- known minimum potential energy which states that of all the kinematically possible configurations of the system the one with the minimum potential energy corresponds to the stable equilibrium position. Following this principle, the problem becomes reduced to finding the deformed shape minimizing the total potential energy of the system [21, 22]. A method, called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is launched combining this principle and the meta-heuristic methods, which made it is possible to solve structural analysis problems as optimization problems [23].
Structural Design and Structural Analysis
Structural design problems involve optimization of topology, shape and size of the structures. These problems involve many applications from civil, structural and mechanical engineering including almost infinite type of structures or parts of structures. A review of the procedures used in this process can be found in Kicinger et al [4], Gandomi et al [5]. Very recent examples of various aspects of design optimization can be found in Kaveh and Talatahari [6], Bekdas and Nigdeli [7], Dede [8], Zhou [9], Ahraria and Ataib [10], Jahjouh et al. [11]. There are also quite a number of applications on design optimization of reinforced concrete structures [12-20]. Structural analysis problems are usually solved as root finding problems, following formulations which yield matrix equations of type Ax=b, or more generally of type F(A, x, b)=0 for nonlinear problems, where A represents material and geometric properties of the structure, x is the vector
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works including network design [24, 25]. Water management is a special part of civil engineering and there are a lot of problems to be solved by optimization algorithms. Many studies that apply heuristic optimization methods to the solution of water management problems are published in the literature. One of the first applications was done by McKinney and Lin [26] in which three separate management problems were solved including maximization of total pumping and minimization of pumping cost to satisfy the given water demand, and minimization of the remediation cost. Recently, hybrid optimization algorithms were successfully used for the solution of complex optimization problems with a non-convex solution space. These algorithms integrate heuristic and gradient-based algorithms such that the main objective is to utilize the global exploring capability of heuristic and strong fine-tuning property of gradient-based algorithms. Meta-heuristic optimization algorithms can be effective in finding the global optimum precisely [2738].
3.3
Construction Management and Scheduling
This area is also widely covered by meta-heuristic methods to such a degree that many problems which could not be solved by conventional methods are now being solved by these emerging methods. It is also shown that better results can be obtained with these methods as compared to commercial scheduling software packages [39]. Some recent applications include Liao et al. [40], Hanioglu and Arditi [41], Zhou et al. [42]. [43-65]
3.4
4
Geotechnical Engineering
Geotechnical engineering is the branch of engineering dealing with the mechanical behavior of soil, rocks etc. and the interaction of these materials with structures built in or on the ground. Geotechnical engineering uses many empirical mathematical models for analysis the soil. Soil improvement projects are prepared with the help of these mathematical models. In preparation of these projects, over the last decade or so, metaheuristic algorithms has proved to provide a high level of competency in solving many geotechnical engineering problems that are beyond the computational capability of classical mathematics and traditional procedures [66]. Geotechnical engineering has a lot of problem in construction time one of the most exciting is hydropower foundation problem in soft soil. Metaheuristic algorithms have demonstrated their efficiency in solving these problems with a high level of confidence [67-77].
3.5
Transportation Engineering
Transportation engineering is one of the most special issues of construction engineering. Its concerned with design and application of urban and rural transport, all types of highways, railways, ports and tunnels. For example, serious problem of the transportation engineering is determination of the best possible highway pavement. The reason for this highway construction should be both serve throughout the service life and the construction costs low. Recently, meta-heuristic algorithms such as neural networks and fuzzy logic for solving the problem have been used [78]. Other than that, transportation network problems and vehicle routing are very classical and complex transport issues. Therefore meta-heuristic algorithms are used for solving these complex issues [79-91].
3.6
Meta-heuristic methods are strongly entering into lives of engineers and scientists in solving problems which were difficult or even impossible to handle with conventional techniques. It is not difficult to foresee that they will increase their importance in the coming years parallel to advances in computer technology both in hardware and software senses.
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Construction Materials
Another branch of Civil Engineering deals with construction materials. Construction materials for optimal strength need blending with each other at the right rate. For example, meta-heuristic algorithms are used for performing the best aggregates blending computations and many other aspects of optimizing mterials [92-101].
3.7
Conclusions
Others
Meta-heuristic algorithms give effective results also for many other aspects of civil engineering. These studies include disaster relief operations [102], CO2 emission [103], and many others [104-109].
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Estimation of Fault Plane Parameters by Using Stochastic Optimization Methods Özlem Türkşen* Abstract Estimation of fault plane parameters play an important role for determination of an earthquake occurance time. Complex nonlinear structure of the fault plane models make the estimation of fault plane parameters more challenging by using classical optimization methods. In this study, three of the stochastic optimization methods, Nelder-Mead simplex (N-M simplex), Simulated Annealing (SA), Genetic Algorithm (GA), are used to estimate the fault plane parameters. Simulated data set is used for the application of optimization algorithm. The results show that the GA is the most preferred method among the others. Keywords: Fault plane parameters, NelderMead simplex method, Simulated Annealing, Genetic Algorithm.
1
several studies about the usage of stochastic optimization methods. These are Monte-Carlo methods [3], heuristic optimization methods, e.g. Nelder-Mead simplex (N-M simplex) [4,5], metaheuristic optimization merhods, e.g. Simulated Annealing (SA) [6,7,1,8], Genetic Algorithm (GA) [9,10]. In this study, N-M simplex [11], SA [12], and GA [13] are used for parameter estimation of the fault plane model which is expressed by [14]. The rest of the paper is organized as follows: In Section 2, the fault plane geometry is presented and formulation of fault plane model is defined as a nonlinear optimization problem. In Section 3, stochastic optimization methods for fault plane parameters are given briefly. The performance of the optimization algorithms are compared by using synthetically generated data set in Section 4. In Section 5, conclusions are given.
Introduction
Earthquakes are inevitable in real life. An earthquake occurance time can be defined by using fault plane parameters. Therefore, estimation of the fault plane parameters play a crucial role in earthquake studies. Actually, it is hard work and it requires a well defined model. The most commonly used fault models are homogeneous, isotropic, linear, and elastic half space. The elastic half space model is widely used one because of the elastic structure of the crust and simplicity of the expressions [1]. However, fault models are generally represented with complex, nonlinear analytical equations. In this case, derivativebased optimization methods are inadequate to obtain estimation of fault plane model parameters. Although, derivative-based algorithms are used for obtaining fault parameter estimations, e.g. Quasi-Newton method [2], there have been
2 Fault Plane and Nonlinear Optimization Problem 2.1 Fault plane geometry and fault plane model The fault plane model is used to determine the surface displacements on identified coordinates. Obviously, the fault plane model parameters have an important role on the surface displacements. The fault geometry in three dimensions is given in Figure 1.
* Özlem Türkşen is with the Department of Statistics, Faculty of Science, University of Ankara, Tandoğan , Ankara, TURKEY (email:
[email protected])
Figure 1: The fault plane geometry
71
In this study, a fault plane model, expressed by Aktuğ (2003) [14], is considered because of its simplicity and speed in computing. The parameters defined on the fault plane in Figure 1 are
in which the lateral direction is the direction of fault plane and vertical direction is vertical to lateral direction. The I1 , I 2 , I 3 , I 4 , and I5 are analitical equations of fault plane parameters defined in detail [14].
l : the lenght of the fault plane (km), w : the wideness of the fault plane (km), d : the depth of the fault plane (km), : dip angle (radian), : strike (radian), xf , yf : the coordinates of the fault starting
2.2 Formulation of fault plane model as a nonlinear optimization problem In order to estimate the fault plane model parameters, it is wanted to minimize the differences between the observed and predicted surface displacements. Let p be the fault parameters vector denoted by p [ l w d xf yf SS DS ]; N be the dimension of parameter vector ( N 9 ); u be the observed surface displacements vector which consists of two components in lateral and vertical directions as ul uxl u ly uzl and
point where xf (km) is east ofset and yf (km) is north ofset, SS : the component of the slip vector (S) in the direction of the fault (Strike-Slip) (m), DS : the component of the slip vector (S) as vertical to the fault direction (Dip-Slip) (m).
uv uxv u vy uzv , respectively. The nonlinear response model can be written as
Besides, the location of the fault center is denoted as x0 , y0 in Figure 1. The vectorial form of coordinate locations are denoted with x, y which is considered as input of the fault plane model.
u p; x, y ε
where is a nonlinear function of fault plane parameters and locations on the surface; ε is an n1 vector of errors. The estimation of fault plane parameter can be obtained by minimization of sum of square errors which is a kind of loss function given as
Functional relationship between surface displacements, caused by slip vector, and fault plane parameters are defined in two directions as below Lateral directions:
p εε
u q u x 1 tan 1 I1 sin 2 R R qR u1 y q q cos uy I 2 sin 2 R R R u1 d q q sin uz I 4 sin 2 R R R
u p; x, y u p; x, y .
q I1 sin cos R u 2 y q x uy cos tan 1 I1 sin cos 2 RR R u2 2
u uz 2 2
(2)
It is clear that the loss function has nonlinearity because of the complex analytical expressions of the direction functions. In this case, stochastic optimization methods should be more proper rather than classical methods for optimization of the function given in Eq. (2).
Vertical directions: ux
(1)
3 Stochastic Optimization Methods Stochastic optimization is the general class of algorithms and techniques which employ some degree of randomness to find optimal solutions to hard problems. Metaheuristics are the most general of these kinds of algorithms, and are
y q sin tan 1 I 5 sin cos qR R R
72
applied to a wide range of problems [15]. Indeed, the greek prefix “meta”, presents in the name, is used to indicate that these algorithms are “higher level” heuristics. The heuristics are typically used when there is no known way to find an optimal solution, or when it is desirable to give up finding the optimal solution for an improvement in run time. The metaheuristics are divided into two groups: (i) Single-Solution Based Metaheuristics (SSBM), and (ii) PopulationBased Metaheuristics (PBM). In this study, a heuristic method, a SSBM method, and a PBM method, called N-M simplex, SA, and GA, respectively, are used for parameter estimation of the fault plane model.
3.2 Simulated Annealing The Simulated Annealing (SA) was discovered in 80’s independently by two authors, Kirkpatrick et al. (1983) [12] and Cherny (1985) [17]. It is based on an idea of annealing of metals where the slow cooling leads material to the state of minimum energy. This is equivalent to the global minimization. The temperature is simple controllable parameter of the algorithm and consecutive decreasing of the temperature is called cooling schedule. The algorithm starts by generating an initial solution p0 and initial temperature T0 . Then, at each iteration, a solution p is randomly selected in the neighborhood
p
of the
current solution p . The solution p is accepted as new current solution depending on T and on the values of loss function for p and p ,
3.1 Nelder-Mead simplex method The Nelder-Mead simplex (N-M simplex) method, first published in 1965 by Nelder and Mead [11], is a very popular direct search method for multidimensional unconstrained optimization problems. The N-M simplex is a kind of heuristic method and tries to minimize a nonlinear function of N real variables using only fuction values. The method is stated using the term “simplex” which is a generalized triangle in N dimensions. The searching process generates a sequence of triangles (which might have different shapes), for which the function values at the vertices get smaller and smaller. The size of the triangles is reduced and the coordinates of the minimum point are found [16]. Four scalar parameters must be specified to define a complete N-M simplex method; coefficients of reflection , expansion , contraction , and shrinkage . These parameters are chosen to satisfy 0, 1, 0 1, and 0 1 . The N-M simplex method requires stringent initial estimates for the model parameters. The method is advantageous when N is less than 10 ( N 10 ) and good initial vertices are provided. If the initial vertices are generated far from optimum, the loss function ( ) can not reach the global minimum and computation time (CPU) gets large.
denoted by
p p
p
and
p ,
respectively. If
, then p is accepted and it
replaces p . On the other hand, if
p p ,
p can also be accepted with a probability p p P T , p , p exp [18]. T The temperature T is decreased during the search process by using proper cooling schedule. In this study, geometric cooling schedule is chosen Tk T0 c k , 0 c 1 where c is a analogous to the Boltzmann’s constant and k is a counter of iteration number for temperature decreasing, used as stopping criteria.
3.3 Genetic Algorithm The Genetic Algorithm (GA), originally developed by Holland (1975) [13], is the most used and well-known population based metaheuristic method. The algorithm is based on survival of the fittest natural selection principle. Each iteration of the algorithm is called generation. The algorithm starts by creating an initial population which is composed of chromosomes. The chromosomes, represent the parameters, are candidate solutions of the problem. The most common representation of the chromosomes applied in GA is a fixed-lenght binary string [18]. The
73
The straight line in Figure 2 shows the fault direction and n 50 random generated
population size, N pop , is defined as the number of chromosomes in the population. Then, fitness value of each individual chromosomes, which represents the objective function value, is calculated. Parent population is selected by using selection functions, e.g. with replacement, roulette wheel, stochastic uniform. New solutions are created by applying crossover and mutation genetic operators with the defined probabilities Prc and Prm , respectively. New solutions are replaced with the current solution set until the maximum number of generation ( maxgen ) is satisfied. The GA has several specific parameters which are needed to be fitted differently according to the problem. If these parameters are well defined, the global solution is achieved by using the GA.
Figure 2: The 50 surface coordinates fixed around the fault direction
4 Simulation Study
coordinate values are fixed around the fault direction. The surface relocations, denoted as [ u x u y u z ], are generated by using Matlab
In this section, estimation procedure of fault plane parameters is presented by using simulated data set. In order to generate the synthetic data set an operation region, a quadrangular area, is defined for performing simulated data. The region is assumed as a definite place of earth surface where earthquake has been occured. The simulated earthquake area is formed in 30, 20 50, 20 coordinates with 50 geodetic points which are signed on the graph given in Figure 2.
code taken from the geodynamics laboratory page (http:// www.gpsg.mit.edu) of the Massachusetts Technology Institute for each coordinate. The fixed 50 coordinates and the surface relocations are given in Table 1 partially. The entire Table 1 can be seen in [19]. The real fault plane parameter values, used for generating synthetic data set, and the lower and the upper bounds of the parameters are presented in Table 2.
Table 1: The coordinates of locations x, y , and surface relocations ux u y uz No 1 2 3 4 5 . . . 17 18 19 20 21 22 23 24 25
x, y (2 , -34) (-3 , 9) (-20 , 1) (4 , -1) (-18 , -23) . . . (8 , 7) (8 , -35) (10 , -23) (-3 , -47) (-6 , -29) (-8 , 7) (1 , -2) (-26 , 12) (-3 , -44)
ux u y uz (-0.1275 (-0.0014 (0.0009 (-0.0044 (0.0270
(-0.0029 (-0.1184 (-0.0405 (-0.5171 (-0.0870 (-0.0011 (-0.0040 (0.0005 (-0.3982
0.2515 0.0541 0.0625 0.0680 0.1681 . . . 0.0515 0.1944 0.1158 0.6714 0.2555 0.0577 0.0729 0.0412 0.5752
-0.1019) -0.0307) -0.0362) -0.0393) -0.1532)
-0.0283) -0.0574) -0.0549) -0.0800) -0.1988) -0.0333) -0.0432) -0.0217) -0.0957)
No 26 27 28 29 30 . . . 42 43 44 45 46 47 48 49 50
x, y (-20 , -15) (-17 , -20) (-15 , -26) (11 , 14) (-9 , -39) . . . (-23 , 8) (2 , 6) (-25 , -49) (16 , -5) (-6 , -42) (-22 , -35) (-16 , 14) (-23 , -40) (-29 , -35)
74
ux u y uz (0.0098 (0.0128 (0.0101 (-0.0020 (-0.3500
0.1118 0.1496 0.1950 0.0417 0.7122 . . . (0.0005 0.0484 (-0.0023 0.0569 (0.3093 -0.1076 (-0.0100 0.0589 (-0.3824 0.6424 (0.3027 0.7685 (-0.0005 0.0453 (-0.1164 0.0907 (0.1065 0.1422
-0.0765) -0.1237) -0.2330) -0.0222) -0.2765)
-0.0264) -0.0323) 0.2482) -0.0300) -0.1471) -0.0648) -0.0249) 0.6267) 0.1135)
Table 2: The true values and the bounds of the fault plane parameters True Bounds of Parameters Parameters Parameters Lenght ( l ) 60 [20 – 100] Width ( w ) 12 [5 – 15] Depth ( d ) 1 [0 – 5] Dip ( ) 1.2217 [0.8727 - 2.0944] Strike ( ) 5.4978 [4.7124 - 6.2832] East offset ( xf ) -20 [-50 – 0] North offset ( yf )
[-50 – 0] [-5 – 5] [-5 – 5]
-40 2 0.2
Strike Slip ( SS ) Dip Slip ( DS )
The tunable algorithm parameter values for each of the stochastic optimization methods are given in Table 3.
5 Conclusions
Table 3: The tunable parameter values for N-M simplex, SA, and GA methods Methods Tunable parameters 1 , 2 , 1/ 2 , N-M simplex 1 / 2 , 0.00001 SA
Estimation of fault plane parameters is often difficult by using derivative-based optimization methods because of the nonlinearity of the fault plane model. In this study, N-M simplex, SA, and GA, which are stochastic optimization methods, are used for parameter estimation procedure. The N-M simplex is a heuristic method while the SA and the GA are SSBM and PBM methods, respectively. An elastic-half space model is considered as the fault plane model. The simulated data set is generated by using Matlab code obtained from a geodynamic laboratory page. The tunable of the methods are chosen carefully depending on the problem. The results show that the GA has the best estimation performance with the shortest CPU rather than N-M simplex and SA methods since its searching mechanism depends on a set of solutions.
T0 100, Tmin 109 , c 0.9 pop _ size 100 Prcr 0.90 Prm 0.01 Roulette Wheel Selection
GA
It can be seen from the Table 4 that the GA is the most preferred method rather than N-M simplex and SA. Because it achieves the minimal loss function value in short CPU. Even the smallest computational time belongs to the N-M simplex method, it has drawback about definition of the initial parameter values. The simplex method requires strict initial conditions, whereas the SA and GA are able to explore the parameter space and focus on the most promising area without prior knowledge of the parameter values. It is possible to say from Table 4 that the SA reaches the minimum loss function value. However, when it is compared with GA, it is seen that the GA has slightly better loss function value. Moreover, the GA has extremely shorter CPU (26 sc) than the SA (201 sc). This is an advantage of PBM against the SSBM.
Single Po int Crossover Bit flip mutation max gen 100
Table 4 shows the optimization results of the objective function given in Eq. (2) by applying N-M simplex, SA, and GA as the average values of 100 runs.
Table 4: Optimization results of the N-M simplex, SA, and GA methods Methods
p0
pˆ
pˆ
CPU
N-M simplex SA GA
Far from optimum Near the optimum Chosen randomly Chosen randomly
[210.5092 21.9962 -4.63 1.925 4.1669 -210.6472 107.3864 27.4546 -35.0457] [62.6735 11.2466 0.6408 1.2026 5.4962 -19.9768 -39.8784 2.1012 0.2214] [60.2159 9.3609 0 1.3613 5.5095 -19.1055 -38.8713 2.3917 0.2564 242] [71.8319 12.0070 0.9052 1.2756 5.5276 -19.7743 -39.6253 1.8866 0.3107]
7.2495 0.0014 0.0286 0.0144
7 4 201 26
75
algorithm. Geophysical Journal International, 166, 590-600, 2006.
References [1] P. Carvelli, M. H. Murray, P. Segall, Y. Aoki, and T. Kato. Estimating source parameters from deformation data, with an application to the March 1997 earthquake swarm of Izu Peninsula, Japan. Journal of Geophysical Research, 106(B6):11217-11238, 2001.
[11] J. A. Nelder, and R. Mead. A simplex
method for function minimization. Computer Journal, 7, 308-313, 1965. [12] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by Simulated Annealing. Science, 220(4598):671-680, 1983.
[2] T. Arnadottir, and P. Segall. The 1989 Loma Prieta earthquake imaged from inversion of geodetic data. Journal of Geophysical Research, 99(B11):21835-21855, 1994.
[13] J. Holland. Adaptation In Natural and Artificial Systems, University of Michigan Press, 1975. [14] B. Aktuğ. A Dynamic Approach to Elastic
[3] M. Sambridge, and K. Mosegaard. MonteCarlo Methods in Geophysical Inverse Problems. Reviews of Geophysical, 40(3):1-29, 2002.
Half Space Models and Earthquake Coordinate Relocations. Map Journal, 129, 1-16, 2003. [15] S. Luke. Essentials of Metaheuristics. Lulu, 2nd Ed., 2013.
[4] I. L. Ateya, and S. Takemoto. Gravity inversion modelling across a 2-D dike-like structure-A Case Study. Earth Planet Space, 54, 791-796, 2002.
[16] J. H. Mathews, and K. F. Kurtis. Numerical Methods Using Matlab. PrenticeHall, New-Jersey, 4th Ed., 2004.
[5] G. A. Ichinose, K. D. Smith, and J.G. Anderson. Source Parameters of the 15 November 1995 Border Town, Nevada, Eathquake Sequence. Bulletin Seismological Society of America, 87(3):652-667, 1997.
[17] V. Cherny. Thermodynamic approach to the traveling salesman problem: an effcient simulation algorithm. Journal of Optimization Theory and Applications, 45, 41-51, 1985.
[6] A. K. Abdel-Fattah. An approach to investigate earthquake source processes. Acta Geophysica Polonica, 51(3):257-269, 2003.
[18] I. Boussaid, J. Lepagnot, and P. Siarry. A survey on optimization metaheuristics. Information Sciences, 82-117, 2013.
[7] A. K. Abdel-Fattah, and A. Badaway. Source Characteristics and Tectonic Implications of Moderate Earthquake, Northeastern Cairo Prefecture. Acta Geophysica Polonica, 52(1):29-43, 2004.
[19] Ö. Türkşen. The Adaptive Simulated Annealing Method in Estimation of Earthquake Search Parameters Through Surface Measuraments, Master Thesis, 72pp, 2005.
[8] X. Li, T. Koike, and M. Pathmathevan. A very fast re-annealing (VFSA) approach for land data assimilation. Computers and Geosciences, 30, 239-248, 2004. [9] S. J. Chang, C. E. Baag, C. A. Langston. Joint analysis of teleseismicreceiver functions and surface wave dispersion using the genetic algorithm. Bulletin of the Seismological Society of America, 94, 691-704, 2004. [10] W. Kim, I. K. Hahm, S. J. Ahn, and D. H. Lim. Determining hypocentral parameters for local earthquakes in 1-D using a genetic
76
Remarks on Robust and Reliable Design Optimization Simon Gekeler, Rolf Steinbuch∗
Abstract Numerical Optimization of mechanical designs using simulation systems like FEM requires much computing power in terms of jobs, capacity and time. The additional effort to provide sufficient data for the evaluation of the reliability or robustness of the design may become even larger. In consequence efficient strategies have to be used to ensure reliability or robustness. This paper sketches some of the ideas that may help to come up faster with acceptable guesses to evaluate the proposed design. Nevertheless the numerical effort to guarantee small failure probabilities depends on the laws of probability. So the number of test data required to achieve sufficient quality may not be reduced below certain limits given by these laws of probability.
A restriction g(p1,p2) which must not be positive is included in Fig. 1a as well. The distance from the maximum of the goal to the Most Probable Point (MPP) of the restriction on the hyper-surface where g(p1,p2) = 0 is used to quantify the performance of the design. The probability of a design to fall into the forbidden region g(p1,p2)>0 where the designs violate the restriction is
∫(
(1)
)
From this probability of the design by
we derive the reliability .
Many studies have been performed to line out the ways to do such a probabilistic analysis using Keywords: Reliability, robustness, optimization, different approaches [1, 2]. FORM (First Order Reliability Method) and SORM (Second Order stochastic, response surfaces, distributions. Reliability Method) are the most popular and accepted among them. They quantify the measure of the failure area by approximating the restriction by 1 Introduction linear or quadratic hyper-planes (Fig. 1a) and so help to get an idea about the failure probability. With the improved availability of fast computing restriction p2 systems, the optimization of problems with larger 99% g=0 numbers of optimization parameters and many local 95% optima came into the focus of the engineering 50% community. Having found good designs the question if these designs are robust or reliable came into the Opt focus. Reliability is used as measure of a small failure g>0 probability within the expected scatter of the produced parts. Robustness indicates that the MPP performance of the parts within the scatter is g ρ2 < ρ3 < ρ4). Relatively large initial
spaces used in DE for each one and the results of 3D inversion of synthetic data by using DE/best/1/bin. Calculated anomaly map is displayed in Figure 3b.
2.4 Application of SA for 2D tomographic inversion of crosshole radar data
search spaces were used for estimating layer
A sequential hybrid approach was applied to invert
parameters; ρ1 ∈ [400, 900], t1 ∈ [0.1, 5], ρ2 ∈ [30, 500],
synthetic crosshole radar data. The algorithm uses a
ρ3 ∈ [500, 5000], t3 ∈ [3, 30] and ρ4 ∈
combination of a simple SA with a linearized
[5000, 30000], respectively top, relatively high-
smoothness-constrained least-squares inversion. The
resistivity overburden layer (745 Ωm) may be caused
SA was used to generate a background velocity
by dry soil at and near the surface. The second layer,
distribution (an initial model) for linearized inversion
with resistivity of 180 Ωm corresponds to alluvial fill
[31]. The subsurface radar velocity distribution was
while the third one shows relatively higher resistivity
obtained by the following rectangular system in the
(3270 Ωm) originating from the limestone. The
linearized inversion.
t1 ∈ [8, 30],
lowermost layer at the VES station with the highest
135
𝑊𝑑 𝐴 𝑊𝑑 Δ𝑑 [𝜆1 𝑊1 ] Δ𝑝 = [ 0 ] 𝜆2 𝑊2 0
The sources were located at every 0.5 m while the (2)
receivers were located at every 0.25 m along the left and right vertical edges of boreholes, respectively. The
where A is the Jacobian matrix, Wd is the diagonal data
model
given
in
the
Figure
4
represents
a
weighting matrix, W1 and W2 are the weighting matrices
hydrogeological model. Dry sand characterized by
for the model parameters along the horizontal and
higher radar velocity constitutes top layer. The saturated
vertical directions, respectively. λ1 and λ2 control the
zone beneath the water table at the 1.5 m depth includes
relative importance of the model weighting. p is the
silt, gravel, sand and clay, respectively. Inclined and
parameter correction vector and d is the difference
thin layer of clay holds moisture well, but resist water
vector between the observed and calculated data. In this
infiltration. Dry clay penetrates into the fracture zone of
study, the matrix Wd is the identity matrix. A second-
the shale that is the lowermost layer of the model. The
difference regularization was used for smoothness
tomogram obtained by the hybrid optimization using
constrained [42].
the velocity distributions from SA (Figure 5a) as the initial guesses is given in Figure 5b.
Figure 2: The results include observed data, calculated curves, and models obtained from 1D inversion of the VES data using GA (modified from [40]) The velocity updates were obtained by a matrix inversion based on an iterative conjugate gradient-like LSQR algorithm [43]. The Jacobian matrix was constructed by a finite-difference approximation based on the perturbation of the cell slowness. The traveltimes for both hybrid and linearized schemes were obtained by a finite-difference eikonal solver [44]. This hybrid approach includes two times sequential use of SA and LSQR algorithms, that is, i) 1iteration LSQR following the 1000 SA iterations and ii) 3 iterations LSQR following the 1000 SA iterations. The hybrid scheme
Figure 3: a Synthetic total field magnetic model b Calculated anomaly map using the parameters estimated by DE. The square and rectangle indicate the bodies [35]
mentioned above was tested on a synthetic data based on the crosshole geometry (Figure 4). The data set include 20 sources and 40 receivers per source, which
It is obvious that the hybrid inversion approach imaged quite successfully the subsurface in terms of the model geometries and velocities.
yield 800 traveltimes.
136
Table 1: True magnetic source parameters, search spaces used in DE and the results obtained by DE/best/1/bin Body 1
2
Explanation true values search spaces estimated values true values search spaces estimated values
x1 [m] 4 1-7 4.13 13 10-16 13.23
x2 [m] 11 6-16 11.06 17 14-20 17.14
y1[m] 6 3-9 5.84 13 10-16 12.95
Figure 4: Synthetic model used in tomographic inversion of crosshole radar data by a hybrid approach. TH and RH indicate transmitter and receiver holes, respectively
3 Conclusion Four nature-inspired metaheuristics including PSO, GA, DE and SA were used to invert the different type anomalies obtained by some applied geophysical methods including SP, electrical resistivity, magnetic and crosshole radar, respectively. Considering synthetic cases of DE and SA algorithms for the magnetic and crosshole radar applications, respectively, and also field cases of PSO and GA for the SP and electrical resistivity applications each algorithm produced successfully results by providing parameters close to the true ones and efficient solutions for the interpretation of anomalies. As a result, these algorithms that do not require a well-constructed starting model can be used for inversion of data obtained by applied geophysical methods.
137
y2 [m] 9 5-14 8.98 17 14-20 16.8
h1 [m] 1 0.1-10 0.71 0.6 0.1-10 0.4
h2 [m] 3 0.1-20 3.16 2 0.1-20 3.43
I0 [] 60 0-90 63.9 60 0-90 63.7
D0 [] 0 0-30 7.31 0 0-30 12.44
EI [cgs] 10 1-30 7.16 10 1-30 5.69
Figure 5: a Initial model obtained from the SA algorithm at the end of 1000 iterations b Velocity tomogram obtained from the hybrid optimization with the rms value of 0.44 nT
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Exploiting Genetic Algorithm to Path Coverage in Software Testing
Shima Amirsadri, M.Sc Student
Seyed Morteza Babamir, Associate Prof.
Dept. of Computer Engineering Kashan University Kashan, Iran
[email protected]
Dept. of Computer Engineering Kashan University Kashan, Iran
[email protected]
Abstract— In this paper, we aim to present a method to meet the software testing challenge using the genetic algorithm. The challenge is coverage of all paths in the white-box testing by generating test cases. White box testing is a software testing method where the software testing is carried out by considering the software source code. To this end, we first construct the control flow graph of the source code and then use the genetic algorithm. By this way, we obtain the best test suit for testing with highest chance to pass the software critical paths. A critical path is the path in which software may involve a fault. Keywords- software testing; Test case generation; Genetic algorithm; White box testing
I.
INTRODUCTION
Software testing [1, 2, 3] is one of the most sensitive and costliest stages in the cycle of the production of software, and accounts for 50% of the cost of the development of software. Automatic test case generation is an important step to reduce the cost of software development and maintenance. The objective is to generate test cases which pass the paths which have higher probability of execution.
Initialize(population)
2.
The Fitness Function
3.
New Population
Selection
Crossover
Mutation
Accepting
4.
Replace
5.
Test
6.
Loop(Go to step 2)
The initial population of genetic algorithm consists of chromosomes, which are a set of test cases here, and which are chosen randomly. Fitness function measures the fitness of a chromosome (test case) for a specific target. In the intended algorithm, the fittest test suit passes a higher number of critical paths. Selection function decides which chromosomes to participate in the step of the evolution of genetic algorithm which is formed by crossover and mutation operators. Crossover operator replaces two genes from two chromosomes, making two new chromosomes. Mutation operator replaces one gene in a chromosome, and forms another new gene [9, 10, 11, 12, 13]. New offspring is generated by crossover and mutation operators and by accepting step is placed in the new population for reimplementation of the algorithm, and finally, if the reliability condition is satisfied, algorithm ends, and the best result in current population returns. Otherwise, we go back to step 2. In this study, reimplementation of the algorithm continues till we obtain the test suit with greater value of fitness function.
Currently there are methods for test case generation which have been automatized earlier [4, 5, 6]. In the present study we develop random generation of test cases using genetic algorithm, generating a test suit which has a higher chance to find the errors of the program because in satisfying statement coverage, branch coverage, condition coverage and path coverage, genetic algorithm has better results and is more applicable than random testing [7]. In the second section, the main structure of genetic algorithm is explained. In the third section our algorithm for generation of test cases is explained. In section 4, a case study using proposed algorithm is explained, and section 5, 6 and 7 comprises conclusion, related work and future work respectively. II.
1.
III.
PROPOSED ALGORITHM
This section describes details of proposed approach which are product of test cases using genetic algorithm. This algorithm uses control flow graph of the program as input of the algorithm [14, 15, 16, 17], trying to return test suit which discovers a higher number of errors.
GENETIC ALGORITHM
Genetic algorithms [8] start with guesses and improve the guesses by evolution, and are founded to favor the survival of the best choice based on natural genetic processes and Darwin’s principle. Genetic algorithms are computer simulations of biological evolution, and when used for optimization problems, good results are obtained at wonderful speed. General steps of genetic algorithms are:
A. Initializing population The main objective of genetic algorithm here is to identify the best test suit for test [18]. Here a test suit is
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Now we can find the probability factor for the test suit.
taken as a chromosome. Initial population is a set of test suits. Figure 1 shows the complete structure.
2. Nearness to boundary value Considering error probability is higher at the boundary values, therefore, test cases which are close to boundary values have a higher priority for testing. Factor of nearness to boundary values for the test suit (T) is calculated as follows: N(T)=N(t1)*N(t2)*…. (2) where N(t) is the nearness to boundary value factor of a test case, and is calculated as follows:
Figure 1. Model used in the paper
1. Probability 2. Nearness to boundary value
From Boolean term, boundary value terms are evaluated by converting each comparative operator {, ≤, ≥, =} to =.
Change the boundary value terms so that the righthand of the terms become equal to zero.
Nearness to boundary value factor of a test case is calculated as:
If every conditional statement in the program has taken all possible outcomes at least once, and every condition in each decision has taken all possible outcomes at least once then covering this criterion has been done [7]. Most automatic test tools use decision coverage criterion for choosing test cases. Decision coverage means percentage of number of edges/decisions covered in a control flow graph by a test suit. Decision coverage factor for each test suit (T) is denoted as D(T). To calculate D(T), for each test case of the test suit calculate the set of decisions that has been passed and then evaluate the union of all the calculated set of decisions. Count the number of elements of outcome set which is called n. Finally, decision coverage is calculated as:
Average of these three factors as the fitness function decides if a test suit is fitter than others for choosing. 1. Probability If test cases of a test suit pass the paths which have a higher probability of execution, it is more probable to select that test suit for testing. Probability factor (p) of a test suit (T) is chosen as follows: (1) P(T)=1-((1-P(Path(t1)))*(1-P(Path(t2)))*…). Where path(ti) is the path which is passed by test data ti, and p(path(ti)) is the probability factor of the path(ti) which is calculated as follows:
From the input domain calculate the probability of the Boolean term to be true.
Using control flow graph of the program, determine the Boolean term of that path.
3. Decision Coverage
3. Decision Coverage
1-((|e(r,[bi]|))⁄|f(bi)|. (4) Where e(r,[bi]) is the real value of the term for modification of variables to real values of test case and f(bi) is the value of term which stands farthest from zero in the complete input domain.
B. Fitness Function Fitness function used is average of the three factors for a test suit. These three factors include:
Evaluate the Boolean term of the intended path using the control flow graph of the program.
Evaluate the path that the test case passes.
N(t)=N(b1)*N(b2)*…. (3) Where B(bi) is the factor that indicates how much the test case values are closer to the boundary value term, bi (which is of the form [bi]=0). N([bi]=0) is calculated as:
Initially, we do not have any information about test cases, and we don’t know which one passes more critical paths, that is why initial population is initialized randomly.
D(T)=n ⁄e. (5) Where e denotes the total number of edges of control flow graph. C. Selection/Operations Used Selection of parent chromosomes for crossover and mutation operations is implemented based on the value of
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determines which is greater. The code of the program is as Figure 4.
their fitness function, and test suits with higher value of fitness function are selected for crossover and mutation operations. Crossover operator replaces two test cases from two test suits randomly and ignores test cases that are common to both the test suits, making two new test suits. Mutation operator replaces one or more test cases in the parent test suit randomly, and generates a new test suit. Finally, generation of the new test suits continues until the value of the fitness function ceases to change, which test suit will be the best set for software test. Crossover and mutation operators are implemented in Figures 2 and 3 respectively.
Void max(int a, int b, int c) { 1: if(a>b) { 2: if(a>c) 3: printf(“max=%d”,a); else 4: printf(“max=%d”,c); } else { 5: if(b>c) 6: printf(“max=%d”,b); else 7: printf(“max=%d”,c);
}}
Figure 4. Program Code
Control flow graph for this program is as Figure 5.
Figure 2. Crossover
Figure 5. Control Flow Graph
Because the program receives the three integers as inputs, each test suit must have three parameters. Their values range from -32768 to 32767. Randomly produced test suits are as follows:
Figure 3. Mutation
IV.
T1={{15, -5, 30}, {2, 166,166}, {-2, -2, -2}} T2={{1, 0, 1}, {170, 27, 10}, {13, 60, 20}}
CASE STUDY
T3={{-32768, 32767, 0}, {5, -15, 1990}, {2228, 17438, -170}}
We check intended algorithm on case study. This program receives three integers as input parameters and
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Probability factor of T1 is calculated as:
F(T2)=(P(T2)+N(T2)+D(T2))/3=(0.5781+0.9939+0.8)/ 3=0.7907.
P(T1) =1-((1-P (Path ({15, -5, 30})))*
F(T3)=(P(T3)+N(T3)+D(T3))/3=(0.5781+0+0.6)/3= 0.3927.
(1-P(Path ({2, 166, 166})))*(1-P(Path ({-2, -2, -2})))) or P(T1) =1-((1-P({1, 2, 4}))*(1-P({1, 5, 7}))* (1-P({1, 5, 7})))
Now we select T1 and T2 for crossover operation:
P(T1) = 1-((1-0.25)* (1-0.25) *(1-0.25) =1(0.75*0.75*0.75) =1-0.4219
T1={{15, -5, 30}, {2, 166,166}, {-2, -2, -2}} T2={{1, 0, 1}, {170, 27, 10}, {13, 60, 20}}
P(T1) =0.5781.
After applying crossover on T1 and T2, two new test suits are generated as:
Similarly P(T2) =0.5781 and P (T3) = 0.5781.
T4={{15, -5, 30}, {170, 27, 10}, {-2, -2, -2}} as:
Nearness to boundary value factor of T1 is calculated
T5={{1, 0, 1}, {2, 166, 166}, {13, 60, 20}} The fitness function of T4 and T5 is calculated as follows:
N(T1) =N({15, -5, 30}) * N({2, 166, 166}) * N({-2, -2, -2}))
F(T4)=(P(T4)+N(T4)+D(T4))/3=(0.5781+0.9948+0.8)/ 3=0.791
Test case {15, -5, 30} follows the path {1, 2, 4} and for this path the Boolean term is a>b ^ ab and ab→ a-b=0
T6={{9, 9, 3}, {170, 27, 10}, {-2, -2, -2}}
a
