A scalability study of the multi-guide particle swarm optimization algorithm to many-objectives

Abstract Scalability of the multi-guide particle swarm optimization (MGPSO) algorithm to many objective optimization problems is investigated in this paper. As a sub-objective, the effects of different archive balance coefficient update strategies on the scaling ability of the MGPSO algorithm are investigated. The results indicate that the MGPSO algorithm scaled to many-objectives competitively compared to other state-of-the-art many-objective optimization algorithms, without requiring any specialized modifications to the MGPSO algorithm. The MGPSO algorithm utilizes multiple subswarms (one per objective) as well as multiple guides (personal best, neighbourhood best, and archive guides) to help balance and promote solution accuracy and solution diversity during the search process. The investigated dynamic archive balance coefficient update strategies did not improve the scalability of the MGPSO algorithm significantly.

[1]  Michael N. Vrahatis,et al.  Recent approaches to global optimization problems through Particle Swarm Optimization , 2002, Natural Computing.

[2]  Akira Oyama,et al.  An Alternative Preference Relation to Deal with Many-Objective Optimization Problems , 2013, EMO.

[3]  Kiyoshi Tanaka,et al.  Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs , 2007, EMO.

[4]  Kalyanmoy Deb,et al.  Dimensionality reduction of objectives and constraints in multi-objective optimization problems: A system design perspective , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[5]  David J. Sheskin,et al.  Handbook of Parametric and Nonparametric Statistical Procedures , 1997 .

[6]  Maria Blettner,et al.  Choosing statistical tests: part 12 of a series on evaluation of scientific publications. , 2010, Deutsches Arzteblatt international.

[7]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[8]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[9]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[10]  Lishan Kang,et al.  A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[12]  Gary G. Yen,et al.  Performance Metric Ensemble for Multiobjective Evolutionary Algorithms , 2014, IEEE Transactions on Evolutionary Computation.

[13]  Kalyanmoy Deb,et al.  An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions , 2010, IEEE Transactions on Evolutionary Computation.

[14]  Andries Petrus Engelbrecht,et al.  Knowledge Transfer Strategies for Vector Evaluated Particle Swarm Optimization , 2013, EMO.

[15]  Aurora Trinidad Ramirez Pozo,et al.  The Control of Dominance Area in Particle Swarm Optimization Algorithms for Many-Objective Problems , 2010, 2010 Eleventh Brazilian Symposium on Neural Networks.

[16]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[17]  J. L. Hodges,et al.  Discriminatory Analysis - Nonparametric Discrimination: Consistency Properties , 1989 .

[18]  Hua Xu,et al.  Multiobjective Flexible Job Shop Scheduling Using Memetic Algorithms , 2015, IEEE Transactions on Automation Science and Engineering.

[19]  Malek Alrashidi,et al.  IoT networks 3D deployment using hybrid many-objective optimization algorithms , 2020, J. Heuristics.

[20]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[21]  D. Bauer Constructing Confidence Sets Using Rank Statistics , 1972 .

[22]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[23]  Andries P. Engelbrecht,et al.  Multi-guide particle swarm optimization for multi-objective optimization: empirical and stability analysis , 2019, Swarm Intelligence.

[24]  S. Holm A Simple Sequentially Rejective Multiple Test Procedure , 1979 .

[25]  Tapabrata Ray,et al.  A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems , 2011, IEEE Transactions on Evolutionary Computation.

[26]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.

[27]  Wanzhong Zhao,et al.  Performance optimization of electric power steering based on multi-objective genetic algorithm , 2013 .

[28]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[29]  Eckart Zitzler,et al.  Are All Objectives Necessary? On Dimensionality Reduction in Evolutionary Multiobjective Optimization , 2006, PPSN.

[30]  Beatrice M. Ombuki-Berman,et al.  A Scalability Study of Many-Objective Optimization Algorithms , 2018, IEEE Transactions on Evolutionary Computation.

[31]  J. Marchal Cours d'economie politique , 1950 .

[32]  Masao Arakawa,et al.  Sequential approximate multi-objective optimization using radial basis function network , 2013 .

[33]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[34]  M. Friedman The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance , 1937 .

[35]  Claude Baron,et al.  Ant colony algorithm hybridized with tabu and greedy searches as applied to multi-objective optimization in project management , 2007 .

[36]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[37]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[38]  Ye Tian,et al.  A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[39]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[40]  Elizabeth F. Wanner,et al.  Dimensionality Reduction Approach for Many-Objective Vehicle Routing Problem with Demand Responsive Transport , 2017, EMO.

[41]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[42]  Michael Patriksson,et al.  Approximating the Pareto optimal set using a reduced set of objective functions , 2010, Eur. J. Oper. Res..

[43]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[44]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[45]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

[46]  Lily Rachmawati,et al.  A Multi-Objective Genetic Algorithm with Controllable Convergence on Knee Regions , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[47]  Kalyanmoy Deb,et al.  Finding Knees in Multi-objective Optimization , 2004, PPSN.

[48]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

[49]  Andries Petrus Engelbrecht,et al.  Fitness function evaluations: A fair stopping condition? , 2014, 2014 IEEE Symposium on Swarm Intelligence.

[50]  Khaled Ghédira,et al.  Searching for knee regions in multi-objective optimization using mobile reference points , 2010, SAC '10.

[51]  Lucas Bradstreet,et al.  A Fast Way of Calculating Exact Hypervolumes , 2012, IEEE Transactions on Evolutionary Computation.

[52]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[53]  Gaoping Wang,et al.  Fuzzy-Dominance and Its Application in Evolutionary Many Objective Optimization , 2007, 2007 International Conference on Computational Intelligence and Security Workshops (CISW 2007).

[54]  Kiyoshi Tanaka,et al.  Self-Controlling Dominance Area of Solutions in Evolutionary Many-Objective Optimization , 2010, SEAL.

[55]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[56]  M. N. Vrahatis,et al.  Particle swarm optimization method in multiobjective problems , 2002, SAC '02.

[57]  Lily Rachmawati,et al.  A multi-objective evolutionary algorithm with weighted-sum niching for convergence on knee regions , 2006, GECCO '06.

[58]  Jinhua Zheng,et al.  A grid-based fitness strategy for evolutionary many-objective optimization , 2010, GECCO '10.

[59]  Carlos M. Fonseca,et al.  An Improved Dimension-Sweep Algorithm for the Hypervolume Indicator , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[60]  Tobias Friedrich,et al.  An Efficient Algorithm for Computing Hypervolume Contributions , 2010, Evolutionary Computation.

[61]  Patrick M. Reed,et al.  Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework , 2013, Evolutionary Computation.

[62]  Marco Farina,et al.  A fuzzy definition of "optimality" for many-criteria optimization problems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[63]  Indraneel Das On characterizing the “knee” of the Pareto curve based on Normal-Boundary Intersection , 1999 .

[64]  F. Djeffal,et al.  An optimised submicron Dual-Material gate (DM) GaAs-MESFETs design to improve the analog performance using multi-objective computation , 2013, 2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO).

[65]  K. Deb,et al.  Understanding knee points in bicriteria problems and their implications as preferred solution principles , 2011 .

[66]  F. Wilcoxon Individual Comparisons by Ranking Methods , 1945 .

[67]  V. Pareto,et al.  Vilfredo Pareto. Cours d’Économie Politique , 1897 .

[68]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[69]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[70]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[71]  Andries Petrus Engelbrecht,et al.  Control parameter sensitivity analysis of the multi-guide particle swarm optimization algorithm , 2019, GECCO.

[72]  Francisco Herrera,et al.  Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power , 2010, Inf. Sci..

[73]  Aurora Trinidad Ramirez Pozo,et al.  Measuring the convergence and diversity of CDAS Multi-Objective Particle Swarm Optimization Algorithms: A study of many-objective problems , 2012, Neurocomputing.

[74]  Jun Zhang,et al.  Fuzzy-Based Pareto Optimality for Many-Objective Evolutionary Algorithms , 2014, IEEE Transactions on Evolutionary Computation.

[75]  M. Clerc,et al.  The swarm and the queen: towards a deterministic and adaptive particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[76]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[77]  Andries Petrus Engelbrecht,et al.  An adaptive particle swarm optimization algorithm based on optimal parameter regions , 2017, 2017 IEEE Symposium Series on Computational Intelligence (SSCI).

[78]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[79]  Marco Laumanns,et al.  Approximating the Knee of an MOP with Stochastic Search Algorithms , 2008, PPSN.

[80]  Douglas A. Wolfe,et al.  Nonparametric Statistical Methods , 1973 .

[81]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[82]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[83]  Peter J. Fleming,et al.  A Real-World Application of a Many-Objective Optimisation Complexity Reduction Process , 2013, EMO.

[84]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[85]  Kaname Narukawa,et al.  Examining the Performance of Evolutionary Many-Objective Optimization Algorithms on a Real-World Application , 2012, 2012 Sixth International Conference on Genetic and Evolutionary Computing.

[86]  Enrique Alba,et al.  SMPSO: A new PSO-based metaheuristic for multi-objective optimization , 2009, 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making(MCDM).

[87]  M. Friedman A Comparison of Alternative Tests of Significance for the Problem of $m$ Rankings , 1940 .

[88]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[89]  Andries Petrus Engelbrecht,et al.  Stability Analysis of the Multi-objective Multi-guided Particle Swarm Optimizer , 2018, ANTS Conference.

[90]  Daniel Zwillinger,et al.  CRC Standard Probability and Statistics Tables and Formulae, Student Edition , 1999 .

[91]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[92]  Rolf Drechsler,et al.  Robust Multi-Objective Optimization in High Dimensional Spaces , 2007, EMO.

[93]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

[94]  R. Iman,et al.  Approximations of the critical region of the fbietkan statistic , 1980 .

[95]  Carlos A. Coello Coello,et al.  Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and epsilon-Dominance , 2005, EMO.

[96]  Andries Petrus Engelbrecht,et al.  Pareto-based many-objective optimization using knee points , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[97]  Carlos A. Coello Coello,et al.  A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm , 2004, MICAI.

[98]  Carlos A. Coello Coello,et al.  On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem , 2011, IEEE Transactions on Evolutionary Computation.

[99]  Mario Köppen,et al.  Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems , 2007, EMO.

[100]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..