Particle Swarm Optimization Applications to ...

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ScienceDirect Materials Today: Proceedings 2 (2015) 2631 – 2639

4th International Conference on Materials Processing and Characterization

Particle Swarm Optimization Applications to Mechanical Engineering- A Review. Mr. Ninad K Kulkarni1, Ms. Sujata Patekar2, Ms. Trupti Bhoskar3, Mr. Omkar Kulkarni4, Dr. G. M. Kakandikar5, Dr. V. M. Nandedkar6* 1, 2, 3, 4 P.G

Research Scholar in Mechanical Engineering, Dnyanganga College of Engineering & Research, Narhe, Pune-41

5 Associate

Professor and Head, Mechanical Engineering, Dnyanganga College of Engineering & Research, Savitribai Phule Pune University, Pune-41

6Professor

in Production Engineering, Shri Guru Gobind Singhji Institute of Engineering & Technology, Nanded

Abstract Particle swarm optimization (PSO) is a population based stochastic optimization technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behaviour of bird flocking or fish schooling. The particle swarm optimization concept consists of, at each time step, changing the velocity of (accelerating) each particle toward its pbest and lbest locations (local version of PSO). In past several years, PSO has been successfully applied in many research and application areas. This paper reviews the applications of PSO algorithm in mechanical domain. The applications of PSO include optimal weight design of a gear train, Simultaneous Optimization of Design and Machining Tolerances, Process Parameter Optimization in Casting, and Machine Scheduling Problem. The paper also describes the improved version of PSO algorithm namely: Hybrid PSO, Multiobjective PSO, Adaptive PSO and Discrete PSO. © 2015 2014Elsevier The Authors. Ltd. All rights reserved. © Ltd. AllElsevier rights reserved. Selection under responsibility of theofconference committee members of the 4th conferenceconference on Materialson Selectionand andpeer-review peer-review under responsibility the conference committee members ofInternational the 4th International Processing and Characterization. Materials Processing and Characterization. Keywords: Particle Swarm Optimization, Variants, Applications.

* Corresponding author. Tel.: +918793800353; E-mail address:[email protected],[email protected], [email protected], [email protected], [email protected], [email protected].

2214-7853 © 2015 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the conference committee members of the 4th International conference on Materials Processing and Characterization. doi:10.1016/j.matpr.2015.07.223

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1. Introduction Nature inspired Algorithms have become quite popular in the previous decade due to their ability to stochastic nature. Many real-world optimization problems have become increasingly large, complex and dynamic.[1,2] The size and complexity of the problems nowadays require the development of methods and solutions whose efficiency is measured by their ability to find acceptable results within a reasonable amount of time, rather than an ability to guarantee the optimal solution. The commonly used nature inspired algorithms are Genetic algorithm, Firefly, Artificial bee colony, Ant colony optimization, Cuckoo Search, PSO, Bat, Cat, Dolphins, Elephant and many more. This paper briefs about the PSO algorithm and its applications in the mechanical domain. Section 2 describes the working of original PSO algorithm and variants of PSO algorithm. Section 3 briefs about the applications of PSO algorithm in various domain followed by conclusion in Section 4. 2. Particle Swarm Optimization Algorithm Particle Swarm Optimization (PSO) [3, 4, and 5] is a population-based stochastic optimization method proposed by James Kennedy and R. C. Eberhart in 1995. It is motivated by social behavior of organisms such as bird flocking and fish schooling. In the PSO algorithm, the potential solutions called particles are flown in the problem hyperspace. Change of position of a particle is called velocity. The particle changes their position with time. During flight, particle’s velocity is stochastically accelerated toward its previous best position and toward a neighborhood best solution. In PSO, individuals (potential solutions) are referred as a particles which flown through hyperdimensional search space. Changes to the position of particles within the search space are based on the socialpsychological tendency of individuals to emulate the success of other individuals. The change to a particle within the swarm is therefore influenced by the experience, or knowledge, of its neighbors. A swarm consists of a set of particles, and each particle represents a potential solution. Particles fly through the hyperspace, where the position of each particle is changed according to its own experience and that of its neighbors. PSO simulates the behaviors of bird flocking. Suppose the following scenario: a group of birds are randomly searching food in an area. There is only one piece of food in the area being searched. All the birds do not know where the food is. But they know how far the food is in each iteration. So what's the best strategy to find the food? The effective one is to follow the bird which is nearest to the food. PSO learned from the scenario and used it to solve the optimization problems. In PSO, each single solution is a "bird" in the search space. We call it "particle". All of particles have fitness values which are evaluated by the fitness function to be optimized, and have velocities which direct the flying of the particles. The particles fly through the problem space by following the current optimum particles. PSO is initialized with a group of random particles (solutions) and then searches for optima by updating generations. In every iteration, each particle is updated by following two "best" values. The first one is the best solution (fitness) it has achieved so far. (The fitness value is also stored.) This value is called pbest. Another "best" value that is tracked by the particle swarm optimizer is the best value, obtained so far by any particle in the population. This best value is a global best and called gbest. When a particle takes part of the population as its topological neighbors, the best value is a local best and is called lbest. After finding the two best values, the particle updates its velocity and positions with following equation (a) and (b). ‫ݒ‬௜ ሺ݇ ൅ ͳሻ ൌ ሺ߱ ൈ ‫ݒ‬௜ ሺ݇ሻሻ ൅  ሺܿଵ ൈ ‫݀݊ܽݎ‬ଵ ൈ ൫‫݌‬௕௘௦௧ െ ‫ݔ‬௜ ሺ݇ሻ൯ ൅ ሺܿଶ ൈ ‫݀݊ܽݎ‬ଶ ൈ ൫݃௕௘௦௧ െ ‫ݔ‬௜ ሺ݇ሻ൯……. (a) ‫ݔ‬௜ ሺ݇ ൅ ͳሻ ൌ ‫ݔ‬௜ ሺ݇ሻ ൅ ‫ݒ‬௜ ሺ݇ ൅ ͳሻ……………… (b) Where ‫ݒ‬௜ ሺ݇ ൅ ͳሻ is the new particle velocity, ‫ݔ‬௜ ሺ݇ሻ is the current particle (solution), ‫݌‬௕௘௦௧ and ݃௕௘௦௧ are defined as stated below ‫݀݊ܽݎ‬ଵ and ‫݀݊ܽݎ‬ଶ are random numbers between (0, 1), ܿଵ and ܿଶ are learning factors, usually ܿଵ =ܿଶ =2.

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2.1. Variants of PSO There have been numerous variants done in PSO in recent years [9]. There are 2 motives for the existence of these variants: 1. To incorporate the capabilities of other evolutionary computation techniques, such as hybrid versions of PSO and 2. The adaptation of PSO parameters for a better performance (adaptive PSO). In most of the cases, the nature of the problem led to the modifications in PSO. So, some of the variants of PSO are briefed below: 2.1.1. Hybrid PSO Many researchers have considered incorporating selection, mutation and crossover as well as the differential evolution (DE) as in other evolutionary algorithms into the PSO algorithm. The main goal is to increase the diversity of the population by: 1) Either preventing the particles to move too close to each other and collide or 2) To self-adapt parameters such as the constriction factor, acceleration constants, or inertia weight. Thus, there have been following hybrid PSO’s: a. Hybrid of Genetic Algorithm and PSO (GA-PSO employs the major aspect of GA approach i.e. the capability of breeding.). b. Hybrid of Evolutionary Programming and PSO (EPSO uses the Tournament selection approach used in Evolutionary programming in which the update formulas(velocity and position) remain the same as in the original PSO algorithm, however the particles are selected as follows: x The fitness value of each particle is compared with other particles and scores a point for each particle with a worse fitness value. The population is sorted based on this score. x The current positions and velocities of the best half of the swarm replace the positions and velocities of the worst half. x The individual best of each particle of the swarm (best and worst half) remain unmodified. Therefore, at each iteration step, half of the individuals are moved to positions of the search space that are closer to the optimal solution than their previous positions while keeping their personal best points. c. Hybrid of Differential Evolution and PSO (DEPSO and C-PSO employs a differential operator to the original PSO algorithm which has two roles : i. To eliminate the particles falling into the local minima. ii. To find the optimal parameters (Inertia and acceleration constants) for a composite PSO. 2.1.2. Adaptive PSO In adaptive PSO, some adjustments to the parameters of the PSO algorithm are done such as adding a random component to the inertia weight, applying Fuzzy logic, using a secondary PSO to find the optimal parameters of a primary PSO, Q-learning, and by adding an improvement index. [10] 2.1.3. Multi objective PSO(MOPSO) Multiobjective optimization problems are complex type of problems with multiple objectives to be optimized simultaneously. In classical approach to solve Multiobjective problems, the objectives are aggregated into a single objective function considering weights that can be fixed or dynamically changing during the optimization process. The drawbacks in this approach are: x The objectives have to be aggregated into a single optimization function which cannot be possible every time. x Only one solution can be detected per optimization run.

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MOPSO approach has been found quite effective in solving multiobjective problems. The main issue to be addressed in MOPSO is the selection of the cognitive and social leaders (pbest and lbest) so that they can provide an effective guidance to reach the most promising Pareto front region but at the same time maintain the population diversity. 2.1.4. Discrete PSO The Discrete PSO has been developed by modifications to the binary version of PSO in order to improve the performance of the algorithm in different applications. Three approaches have been proposed for Discrete PSO:i. Direct approach: - In this approach, the classical PSO algorithm is applied and the solutions are converted into bit strings using a hard decision decoding process. ii. Bias vector approach: - In this approach, the velocity’s update is randomly selected using probabilities depending on the value of the fitness function. iii. Mixed search approach: - In this approach, the particles are divided into multiple groups and each of them can dynamically adapt a local or a global version of PSO. 3. APPLICATIONS OF PSO PSO has been successfully applied to solve various optimization problems, artificial neural network training, fuzzy system control, and others. In mechanical domain, PSO has been successfully applied to optimize various solutions like optimal weight design of a gear train, Simultaneous Optimization of Design and Machining Tolerances, Process Parameter Optimization in Casting, and Machine Scheduling Problem. Saurabh Garg et.al [11] used the PSO in an important machining application i.e. prediction of flank wear in drilling. The Neural Network is trained using PSO and its performance is compared with the standard BPNN. They optimized 32 objectives which implies that the swarm of birds moves in a 32- dimensional space to search for the weights and the minimum value of the Mean square error (MSE). The improved prediction results show that PSO is superior in searching the optimal solution in multi-dimensional search space to the conventional gradient approach followed by BP algorithm. Liang Gao et.al [12] has applied PSO in simultaneous optimization of design and Machining tolerances. The machining tolerances are of critical importance in product development as they vastly affect the actual cost. Here, PSO is applied for designing the piston-cylinder assembly where cost is taken as the objective function and the design and manufacturing tolerances as constraints. The PSO is modified by introducing a factor called Particle feasibility factor (PF) which is used to record whether the particle has satisfied all the constraints. The results have been compared to Genetic Algorithm (GA) and the comparison indicates that the convergence of PSO is much fast as compared to that of GA. SHU Fu-hua [13] used PSO in combination with Artificial Neural Network (ANN) in ZA27 squeeze casting process parameter optimization. The four most influential process parameters that were selected namely pressure, Mold temperature, Pouring temperature and Pressure-time. Also, the Tensile strength, percentage elongation, Hardness, and percentage reduction of area were selected as measurement parameters of the mechanical properties. The PSO has been improved in order to overcome its shortcoming to converge at the local extreme point. The modification has been done such that the inertia weight value can be dynamically changes after each iteration. The improved PSO gives the optimized process parameters and the actual mechanical properties are in close agreement with the forecast mechanical properties. PSO has also been applied to minimize the total weighted tardiness in manufacturing scheduling problem by Davide Anghinolfi et.al [14]. The tardiness of the job is defined as Tj = max (0, Cj-dj) where Cj and dj are the job completion date and job due date respectively. The Discrete PSO approach is used to face the single machine total

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weighted tardiness scheduling with sequence-dependent setup times (STWTSDS) problem which corresponds to the scheduling of n independent jobs on a single machine. In the proposed DPSO approach, a set of m particles is prepared with each particle associated with a sequence and possessing a fitness represented as cost. Also a sequence metric is introduced which computes the velocities of the particles and updates particles’ position consistently. After the DPSO is run, the solution is compared with the overall best known solutions (OBK), with a set of best results obtained by the Ant colony optimization (ACO) (ACO-LJ) and with the most recent set of best results produced by the authors with an ACO-approach (ACO-AP). The comparison showed that the best results of the DPSO outperform the OBK and ACO-LJ, while they are substantially equivalent to the solutions in ACO-AP approach with minimum deviation. There has been another application of PSO in which the process parameters of the Laser beam cutting have been optimized to obtain the optimum surface roughness of Acrylic sheet. M.M. Noor et.al [15]. showed that using PSO ,the optimized parameters obtained were cutting speed(2600 pulse/s), tip distance(9.7 mm), Power(95%), and material thickness(9 mm) which produce surface roughness around 0.0129 μm. The experiment was performed on a 30 W pulsed Nd:YAG laser beam system with CNC worktable. The process parameters which were most influential on the surface roughness were found out to be cutting speed, Tip distance, Beam power and material thickness. Other parameters such as focal length of lens, nozzle diameter, and nozzle tip distance were kept constant throughout the experiment. The experiment results showed that the surface roughness is significantly affected by the tip distance followed by the power requirement, cutting speed and material thickness. Also the optimum roughness predicted using PSO is 0.0129 μm with an error of 0.085%. The PSO model also predicted the critical values of process parameters which could result in melting and burning of the sheet. Ketan Tamboli et.al. [16] have minimized the volume of a heavy duty helical gear pair using PSO. The objective function was formulated as minimization of volume which is the function of five design variables viz. module, face width, No. of teeth on pinion and gear and the helix angle. The constraints were Factor of safety from pitting and tooth breakage, minimum number of teeth to avoid interference, Face width constraints, and helix angle constraints. The PSO code was developed on MATLAB and experimented with various iterations and population size. The helical gear pair for heavy duty application was thus optimized for minimum volume using PSO and the optimum volume as predicted by PSO was 1.8046x10-3 mm3 of the pair with b=53, Z1=30, Z2=142, and β=11.90 . Joshua Clarke and James T. McLeskey Jr.[17] used MOPSO for optimizing the work output of the power plant as well as the specific heat exchanger area. The constraints were taken as the quality of water vapour, the evaporator pressure, the outlet temperature of the geothermal brine, brine re-injection temperature and finally the silica saturation index (SSI). In the MOPSO algorithm, an approach called ‘Dynamic Weighted Aggregation’ (DWA) utilized which resolves all the objective functions to a single objective function value according to individual weights of the functions. Thus, by varying the weight of each objective function with each iteration, the particle swarm is forced to move along the Pareto-optimal front. The results show various combinations of the brine temperatures, dry bulb temperatures and brine re-injection temperatures allowing the examination of the trade-offs between specific work output and specific heat exchanger area. A complete pareto-optimal front is generated using MOPSO algorithm, with the help of which, if a plant designer is given brine temperature, dry-bulb temperature and brine re-injection temperature, can determine the range of possible combinations of specific work output and specific heat exchanger area. C.Y. Liu et.al. [18] utilized hybrid Particle swarm optimization algorithm and optimized the weight of the vertical electrical heating pressurizer. The PSO is used with the modified Nelder-Mead simplex algorithm which is a very efficient local optimization algorithm. There is only single objective function i.e. total weight minimization. The design variables are taken as primary loop operation pressure, reactor outlet coolant temperature, reactor inlet coolant temperature and pressurizer inner diameter. The pressurizer height, pressurizer water volume, pressurizer steam volume and the minimization steam volume were considered as constraints. The minimized pressurizer weight obtained using HPSO is 0.830779.

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Manjunath K., et.al. [19] used PSO algorithm to optimize ply stacking sequence of single piece E-Glass/ Epoxy and Boron/ Epoxy composite drive shafts. Here, the objective function is considered as minimization of weight of composite drive shaft which is dependent on inner and outer diameter of shaft, Length of the shaft and the density of shaft. The minimum number of plies, stacking sequence, and the thickness of the ply were considered as constraints. The results obtained from PSO algorithm suggest that the optimum number of layers of E-Glass/Epoxy and Boron/ Epoxy is 16 and 15 respectively. The weight savings obtained using composite materials is also substantial (ranging 50%-85%). Also the weight of the composite shaft obtained from PSO is compared with the results of genetic algorithm for E-Glass/Epoxy and Boron/ Epoxy and the comparison shows that PSO clearly outperforms GA. There has been another application of PSO which uses mutation (MPSO) along with Taguchi method for optimization of process parameters in a multi-hole extrusion process.[20] The MPSO algorithm uses a real-coded mutation operator in order to increase the diversity of the solutions and the mutation occurs only if the random number generated is less than the given mutation probability. The process parameters that were optimized using Taguchi based MPSO algorithm are extrusion velocity, eccentricity ratio, billet temperature and friction coefficient at the die interface. The results were compared to Taguchi and GA and the comparison indicates that minimal mandrel eccentric and exit tube bending angles were reduced to 0.030. This shows that Taguchi based MPSO algorithm can efficiently optimize the process parameters and optimize the extrusion process. PSO has also been used in order to achieve manufacturing scheduling optimization by Y.W. Guo et.al. [21] The integration of Process planning and scheduling is an important issue to achieve manufacturing planning optimization. The PSO algorithm has been modified and several operators including mutation, crossover and shift have been incorporated into the traditional PSO algorithm. Thus, PSO has been used to model and optimize the operation sequencing and the Integrated Process Planning and Scheduling (IPPS) problems. The results are compared with GA and SA, and the results indicate that PSO clearly outperforms the other two when computation efficiency, optimality and robustness are taken into consideration. There has been a very useful application of PSO for enhanced cyclic steam stimulation in a offshore heavy oil reservoir [22]. The objective of the study is to optimize the thermal oil recovery of cyclic steam stimulation (CSS) process in an oil field in Bohai Bay, China. Five parameters are selected as controlling parameters: temperature of the injecting fluid, stream injection rate of injection wells, additive gas injection rate of all injection wells, CO2 composition in the additive gas, and liquid production rate of production wells. Three different variations of PSO algorithm i.e. Canonical, Gaussian Bare-bone and Levy Bare-bone PSO are tested to optimize the ultimate oil recovery of a heavy oil reservoir. The results suggested that Levy Bare-bone is effective in the large field optimization problem with a recovery factor of 19.31. Also it has a much stable convergence behavior when compared to other two variants. PSO has been found as a useful technique in robot path planning in dynamic environment with mobile obstacles and goals. The objective of robot path planning is to minimize the resultant path lengths. A mutation operator is incorporated in the PSO algorithm to allow dynamic search while maintaining efficient convergence. When obstacles are taken into consideration, a penalty function approach is used in which if robot sees an obstacle, the objective function is enhanced with a penalty function. The results indicate that PSO approach gives better results than the improved penalty function method. [23] PSO has also been employed to determine the optimal Blank Holder shape and its gap (BHG) in deep drawing process in order to avoid defects like tearing and wrinkling of blank sheet. There are three objectives in this process viz. the thickness deviation, the standard deviation from mean thickness, and the difference of maximum and minimum thickness after forming. The BHG is taken as design variable and the two constraints for tearing and wrinkling are taken into consideration. The optimum blank holder shape and the required gap are obtained via PSO. [24]

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R. Venketesan [25] applied the PSO to find the optimum shape design of extrusion die. The objective function is to minimize the extrusion force by optimizing the die cone angle and the extrusion ratio. The optimum value of die cone angle and the extrusion ratio are found out using PSO and simulated annealing. The optimum results obtained from both algorithms suggests that better results can be obtained by combining SA and PSO. The values of Min. Die pressure obtained using SA and PSO were 123.141 MPa and 118.77 Mpa respectively which shows that PSO is superior to SA when it comes to Multiobjective optimization. L. Sasi Rekha Lathan, et.al. [26] used the PSO approach for Multi-objective Optimization of Green Sand Mould System parameters. The objective functions were taken as Green compression strength (GCS), Permeability, Hardness and Bulk Density. These objective functions are weighted as a single objective function. The process variables were taken as Grain fitness Number, % of clay, % of water and number of strokes. Five different cases have been considered by varying the weighing factors of the multiple objectives and by varying one parameter of PSO, namely swarm size, inertia weight and generations at a time. The case 3 (w1=0.1, w2=0.7, w3=0.1 and w4=0.1) was found to be optimized one as it produced maximum fitness. K. Ramanathan et.al. [27] applied Particle Swarm Optimization technique to optimize the hardness and the parameters that affect the hardness in the Ni- Diamond composite coatings. Particle Swarm Optimization was done for the particle size of 20 and for 500 iterations. The process parameters were taken as the Current density, Temperature and pH. The results were converged at around 150th iteration and the optimized value of the hardness obtained was 431.9470 (VHN). The proposed approach utilized the global exploration capabilities of PSO to search for the optimal solution. F. Cus et.al. [28] used PSO approach to optimize machining parameters like cutting speed and feed rate in high speed end-milling. PSO has several advantages and benefits and was found suitable for use combined with Artificial neural network simulation models (ANN). Seven constraints which arise from technological specifications, were considered during the optimization process. The problem was solved using the PSO algorithm. The machining time was reduced by 35 % as a result of optimizing the cutting speed and feed. R. Spina [29] used the ANN-PSO approach to optimize injection molded warpage in injection molded parts. The particle was represented as a four-dimension vector consisting of main decision variables. The process parameters were taken as Mold temperature, Melt Temperature, Flow rate, Packing Pressure, Avg. Volumetric shrinkage, Shear stress, Avg. Difference Bulk temperature, Final Part weight. The main advantages of using the PSO-ANN approach were the reduction of volumetric shrinkage and filling of the part, with the possibility to automate optimization task. The results were confirmed from finite element simulations and real fabrication of the investigated component. Fatemah Sarayloo et.al. [30] used Multi objective PSO for a Dynamic cell formation problem in Cellular Manufacturing. There are three objectives in the problem viz. Total cost, coefficient of intra-cellular movements and the sum of standard deviation of intra and inter cellular workload. The cell formation was considered as an N-P hard problem. The performance of MOPSO was compared with Non-dominated Sorting Genetic algorithm II (NSGA-II). Five test problems were generated randomly and the comparison between two algorithms was made. The comparision shows MOPSO was found superior to NSGA-II regarding to quality metric, number of non-dominated solutions and time metric; however MOPSO provided lower diversity metric. Based on the obtained results, MOPSO gave better performance in comparison with NSGA-II. 4. CONCLUSION PSO is an influential search algorithm that is inspired by social behavior of organisms such as bird flocking and fish schooling. Based on the literature review, this paper reviews the different applications of the PSO algorithm in mechanical engineering ranging from optimization of machining tolerances, multi objective optimization of power plant to weight optimization of pressurizer and manufacturing scheduling problem. This survey also reveals that

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