A new web based solver tool for flowshop permutation* Lamia Trabelsi1 and Talel Ladhari2
Abstract— This paper deals with a web based-tool destined for young researchers to solve flowshop by heuristic approaches. The expected tool functionalities are based on a requirement model expressed as a MAP model. The first requirement implemented is the development of the solver to solve flowshop by predefined metaheuristic genetic algorithm. Accordingly, This new tool will provide the opportunities to browse related works proposed for the flowshop and genetic algorithm. It will evaluate several versions of metaheuristic, and then, to give a best approximated solution to a studied COPP thanks to the design of experiment (DOE) module. Moreover, young researcher are able to download the executable code of the best generated version of genetic algorithm and the documentation of the selected flowshop variant.
I.
INTRODUCTION
Combinatorial (or discrete) optimization with permutation property (COP-PP) is one of the most attractive topics in operations research. COP-PP represents a synergy between applied mathematics, computer science and management science. Combinatorial optimization problems arise in several real-world applications. In this paper, we are interested in permutation flowshop scheduling problem. Flowshop is shown [1] to be strongly NP-hard for m > 3 and a major trend is to use approximate algorithms to address such problems, essentially, metaheuristic methods. In this paper, we proposed a web-based solver tool destined for young researchers to solve flowshop problem. The solver tool is the core of our new to-be-developed support system destined for combinatorial problem under permutation property. In section , a review is done to assess how previous tools managed to deal with solving optimization problem in general and in particulary flowshop problem. In section , a requirement model is proposed to enact the researcher requirements in optimization field. Section will present the developed solver according to our proposed requirement model. II. L ITERATURE REVIEW Several ready-use tools have been proposed in the literature to deal with heuristic methods to solve combinatorial problem in general, we mainly focus on references dealing with frameworks such as HeuristiticLAB [2], HotFrame [3], Templar [4], Paradis-EO [5], Searcher [6] and OSGI [7] and applications like E-OCEA [8], LEKIN [9] or LISA [10] dealing with scheduling problems and in particulary flowshop permutation. *This work was not supported by any organization 1 Lamia Trabelsi is with Ecole Suprieure des Sciences Economiques et Commercial de Tunis (ESSECT), 4, Rue Abou Zakaria El Hafsi - 1089 Montfleury - Tunisie. lamia
[email protected] 2 Talal Ladhari is College of Business, Umm Al-Qura University, Umm Al-Qura, Saudi Arabia talel
[email protected]
Frameworks like Paradis-EO [5]; HeuristiticLAB [2] have been proposed to deal with approximate approaches in general. Other frameworks have addressed specific approximate approaches like metaheuristics-based local search like HotFrame [3]; [4] and Searcher [6] or OSGI [7] for evolutionary algorithm. For more details about frameworks, Interested readers are invited to read the [11] survey which compare features of several frameworks. Applications such E-OCEA [8], LEIKIN [9] or LISA [10] are proposed to solve scheduling problem by exact algorithms like Branch & Bound or simple rules. Moreover, they proposed a basic heuristics to solve their problems. In general, the studied tools have been proposed documentation such tutorials and annotated bibliographies in order to help users to understand the proposed approaches and how to manipulate them. Moreover applications (E-Ocea [8], LEIKIN [9]and LISA [10]) and web-based frameworks OSGI [7] and HeuristicLab [2] provide visualization tools. There is no doubt that ready-to-use tools in optimization help to improve the quality of searches. However, most of them are not available like Templar [4] and E-OCEA [8]. Moreover, the available frameworks like ParadisEO [5] and HeuristicLab [2] need a deeper programming knowledge. As a consequence, they are complex frameworks and often hard to use. Moreover, no frameworks or support tools have tried to provide tools for handling solution encoding schemes as an adaptation between different solutions encoding or for handling constraints for solution infeasibility, except ParadisEO [5] which provides classes to handle penalized objective functions. Evaluation of the performance of an optimization approach is omitted by the studied works except E-OCEA [8] which provides tools to find the best algorithm to solve a scheduling problem. Moreover, calibration and intensification tools have not been supported by the most studied cases. Frameworks proposed classes in order to create new approaches by hybridizing or by assembling components. Hybridization has not been considered by the other studied tools. However, E-Ocea [8] proposed a semi-automatic tool for the generation of new algorithms. Recently, several works tends to hybridize heuristic with exact approaches. In the studied projects, this functionality is not supported. III. A STRATEGIC PROCESS
TO EXPRESS OPTIMIZATION
RESEARCH REQUIREMENT
By studying the capability of tools, the user requirements has been our interest. In fact, most of the works lack evaluation, calibration and analysis of robustness tools in order to improve optimization approaches. We believe that the Requirement Engineering (RE) [12] is a fundamental phase for
Fig. 1.
Optimization Requirements
Fig. 2.
Path example
Fig. 3.
Section (ab1)
designing robust and effective software. We are interested, as a first step, to the enactment of the researchers requirements in order to develop the expected functionalities of a new decision system for flowshop scheduling system. A detailed survey of the approaches used in requirements engineering to elicit user requirements has be done in [13]. Our interest has been focused on goal-driven approaches. From a comparative study of the most known goal-oriented approaches, we retained the MAP model to express researcher requirements because of the models flexibility and simplicity. MAP model is a to is a labeled directed graph with intentions1 like nodes and strategies2 as edges between intentions. The result model to express the researcher’s requirements in optimization field is shown the figure 1. From start, user select an intention according his actual situation. He could progress ”Find optimal solution” by applying strategies like exact methods or simple rules. He could select to progress to ”Construct a new approximate approach” intention. Several strategies are proposed to achieve this intention like hybridization, new constructive heuristic creation and components re-utilization
strategies. Moreover, user could from start find new nearoptimal solution by the existed predefined metaheuristic or the predefined constructive heuristic available for a given problem. Thanks strategies like Results comparisons3 and LB4 strategies. Evaluation optimization approaches intention can be also achieved by strategies like Robustness and Real word application results. When researchers is satisfied, he can stop the navigation into the MAP by validation of him results. IV. A
From the proposed requirement model, we have developed the a selected path (see figure 2). From start, a PhD researcher reaches a near solution by achieving the predefined approximate approach resolution. When the best configuration and the near optimal solution are found, the process is stopped by a results validation strategy. In this path, two sections5 will be developed. 3 such
Average Relative Percentage Deviation (ARPD) Bound 5 Sections are codified by juxtaposing(i) source intention letters (ii) target intention letters and (iii) strategy numbers 4 Lower
1a
goal that can be achieved of achieving this goal
2 ways
NEW SOLVER FOR PERMUTATION FLOWSHOP
•
•
Section (ab1): Section (bf1): < Find near optimal solution, Stop, by results validation >
A. Section (ab1)> Figure 3 details how to achieve the strategy in section (ab1). The signature associated to this section is < {Approximate approach=∅ , COP= ∅ }, find near optimal solution by a predefined approximate approach resolution strategy >. This section is consisting of : • The selection a COP problem variant • The select predefined approximate approach parameters • The calibration of selected approach 1) Select a COP problem variant :: Selection of a COP variant deals with the main concepts: Objective function {Mono, Multi}, benchmark {Real, Random, library benchmark}, and the COP variant parameters to be resolved, the annotated bibliography and complexity {open, NP-hard}. Figure 4 provides an interface to select a variant for permutation flowshop scheduling problem and to specify its constraints. It allows the choice of the procedures of the generation of the test problems or instances (figure 4). After
Fig. 4.
Fig. 5.
Problem information interface
current phase provides the different controls to be checked to achieve the initialization phase. In this interface, the researcher can check the desired population size from the available ones and/or type another size. And, in addition to random construction of population, he can use the available constructive heuristics to enhance the population quality. In this way, he can select the knowing heuristic NEH proposed by [14]. In this example, researcher selects a 30 % of population which will be constructed by modified NEH and the rest will be constructed by a random construction operator.
Flow shop interface
selecting a variant of the problem to be studied, ”ProblemInformation” provides the description for the problem under consideration: the three field notation, the complexity, an annotated bibliography, the mathematical formulations existing in the literature, etc. As it is showed in the figure 5, for the most known problem Flowshop with makespan, this interface provides the notation, the available references in our database handling such problem that young researcher could open it or visit it in the original web site. 2) Select predefined approximate approach parameters :: It deals with the selection of parameters and the approach operators to be tested. In our case, we have implemented the genetic algorithm as the first case application. The figure 6 presents an example of the wizard for genetic solver tool. In the left bar, the different genetic phases are provided. The figure 6 presents the current phase in the bold link. The
Fig. 6.
Initialization phase
3) Calibrate approach :: It deals with the used technique to calibrate the approximate approach with statistical analysis. Statistical analysis allows selecting the DOE6 [15] to compare the different metaheuristic generated versions. At now, we have used the student test. According to a selected value of a risk level α, this test allows us to find the best version among the generated metaheuristic versions (see figure 8). When the different metaheuristic parameters have been selected, the solver proceeds to the solving process and to finding the best result. The best result will be shown in the result page (see figure 9 ) 6 Design
Of Experiment
Fig. 7.
Section (bf1)
The result interface will provide an opportunity to download the different generated files (the binary code and the annotated bibliography). Figure 10 shows the resulting binary code of the best generated configuration and the execution of the file on the researcher side.
Fig. 8.
Statistical analysis
Fig. 10. Example of an execution of the binary code in the researcher side Fig. 9.
Example of a result page
V. C ONCLUSION B. Section (bf1) Several possibilities can be provided to stop the ”Find near optimal solution intention” (figure 7) such as: 1) Stop by code generation : it deals with the generation of the best approximate approach code as an executable file. 2) Stop by documentation : it deals with extracting documentation about the selected problems, the selected approach or with adding new documentation. 3) Stop by validation : it deals with exiting from the support tools.
Flow shop Solver tool is a web-based application developed in order to help young researcher. To develop the new functionalities of our tool, the researchers requirements should be enacted.Our survey of the proposed models in the requirements fields allowed us to select a MAP model as a solution to express researchers’ requirements in an optimization field. The proposed requirement model allow as to develop the expected functionalities of the new solver tool for flowshop scheduling problem. It consists on the Genetic solver for flow shop problem. According our proposed map model, user are able to select Flowshop problem variant, the selection of the genetic metaheuristic parameters and to calibrate the selected metaheuristic. Moreover, our young
searcher is able to download the associated documentation and the executable code. For instance, we have implemented genetic algorithm to permutation flow shop problem. However, Flowshop solver tool is extensible and future metaheuristics could be added. Moreover, solver should integrate more sophisticated and more powerful statistical data analysis such ANOVA [15] to return best reliable parameters value of a selected metaheuristic. To be more efficient and faster, solver should be developed in parallel implementation instead of sequential implementation. Furthermore, the remaining sections in the presented requirements model should be developed. In particular, our focus is the integration of exact tools into our decision support system. R EFERENCES [1] M. Garey, D. Johnson, and R. Sethi, “The complexity of flowshop and job shop scheduling,” Mathematics of Operations Research, pp. 117–129, 1976. [2] S. Wagner, A. Beham, G. Kronberger, M. Kommenda, E. Pitzer, M. Kofler, S. Vonolfen, S. Winkler, V. Dorfer, and M. Affenzeller, “Heuristiclab 3.3: A unified approach to metaheuristic optimization,” Proceedings of the VII Congreso Espanol sobre Metaheursticas, Algoritmos Evolutivos y Bioinspirados (MAEB 2010), Valencia, Spain., 2010. [3] A. Fink and S. Vo, “Hotframe: A heuristic optimization framework,” in Optimization Software Class Libraries, ser. Operations Research/Computer Science Interfaces Series, S. Vo and D. L. Woodruff, Eds. Springer US, 2002, vol. 18, pp. 81–154. [4] M. S. Jones, G. P. McKeown, and V. J. Rayward-Smith, “Distribution, Cooperation, And Hybridization For Combinatorial Optimization,” in Optimization Software Class Libraries. Kluwer, 2002, pp. 26–57. [5] E.-G. Talbi, Metaheuristics : from design to implementation. Wiley, 2009. [6] S. Andreatta A., Carvalho and R. C., “A framework for local search heuristics for combinatorial optimization problems,” in Optimization Software Class Libraries, ser. Operations Research/Computer Science Interfaces Series, S. Vo and D. L. Woodruff, Eds. Springer US, 2002, vol. 18, pp. 59–79. [7] P. Garc´ıa-S´anchez, J. Gonz´alez, P. A. Castillo, M. G. Arenas, and J. J. M. Guerv´os, “Service oriented evolutionary algorithms,” Soft Comput., vol. 17, no. 6, pp. 1059–1075, 2013. ´ [8] V. Tkindt, J.-C. Billaut, J.-L. Bouquard, C. Lente, P. Martineau, E. Nron, C. Proust, and C. Tacquard, “The e-ocea project: towards an internet decision system for scheduling problems,” Decision Support Systems, vol. 40, pp. 329–337, 2005. [9] N. Asadathorn, “Scheduling of assembly type of manufacturing systems: Algorithms and systems developments,” Ph.D. dissertation, Department of Industrial and Manufacturing Engineering, New Jersey Institute of Technology, Newark (USA),, 1997. [10] H. Braesel and S. N., “Lisa–fit for cooperative development,,” Sixth Workshop on Models and Algorithms for Planning and Scheduling Problems (MAPSP’03), pp. 107 – 108, 2003. [11] J. A. Parejo, A. R. Corts, S. Lozano, and P. Fernandez, “Metaheuristic optimization frameworks: a survey and benchmarking.” Soft Comput., vol. 16, no. 3, pp. 527–561, 2012. [12] A. Aurum and C. Wohlin, Engineering and Managing Software Requirements. Secaucus, NJ, USA: Springer-Verlag New York, Inc., 2005. [13] T. Lamia and L. Talel, “A goal-driven approach for optimization requirements,” 2014, writing paper. [14] M. Nawaz, E. Enscore, and J. Ham, “A heuristic algorithm for permutation flow shop problem,” OMEGA, vol. 11, no. 1, pp. 91–95, 1983. [15] D. Montegromy, Design and Analysis of Experiments, 5th ed. John Wiley and Sons Inc, 2001.
