On convergence of the multi-objective particle swarm optimizers

Several variants of the particle swarm optimization (PSO) algorithm have been proposed in recent past to tackle the multi-objective optimization (MO) problems based on the concept of Pareto optimality. Although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of PSO as a single-objective optimizer, till date, to the best of our knowledge, no such analysis exists for the multi-objective PSO (MOPSO) algorithms. This paper presents a first, simple analysis of the general Pareto-based MOPSO and finds conditions on its most important control parameters (the inertia factor and acceleration coefficients) that govern the convergence behavior of the algorithm to the optimal Pareto front in the objective function space. Computer simulations over benchmark MO problems have also been provided to substantiate the theoretical derivations.

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

[2]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[3]  Carlos A. Coello Coello,et al.  Advances in Multi-Objective Nature Inspired Computing , 2010, Advances in Multi-Objective Nature Inspired Computing.

[4]  Enrique Alba,et al.  On the Velocity Update in Multi-Objective Particle Swarm Optimizers , 2010, Advances in Multi-Objective Nature Inspired Computing.

[5]  Russell C. Eberhart,et al.  Multiobjective optimization using dynamic neighborhood particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[6]  Xiaodong Li,et al.  A Non-dominated Sorting Particle Swarm Optimizer for Multiobjective Optimization , 2003, GECCO.

[7]  Shawki Areibi,et al.  Strength Pareto Particle Swarm Optimization and Hybrid EA-PSO for Multi-Objective Optimization , 2010, Evolutionary Computation.

[8]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[9]  Tapabrata Ray,et al.  A Swarm Metaphor for Multiobjective Design Optimization , 2002 .

[10]  T. Ray.  Constrained robust optimal design using a multiobjective evolutionary algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[11]  Sanghamitra Bandyopadhyay,et al.  Multi-Objective Particle Swarm Optimization with time variant inertia and acceleration coefficients , 2007, Inf. Sci..

[12]  Jürgen Teich,et al.  Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO) , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[13]  Chukwudi Anyakoha,et al.  A review of particle swarm optimization. Part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications , 2008, Natural Computing.

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

[15]  Mohamed E. El-Hawary,et al.  A Survey of Particle Swarm Optimization Applications in Electric Power Systems , 2009, IEEE Transactions on Evolutionary Computation.

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

[17]  Jonathan E. Rowe,et al.  Particle swarm optimization and fitness sharing to solve multi-objective optimization problems , 2005, 2005 IEEE Congress on Evolutionary Computation.

[18]  Thomas Hanne,et al.  On the convergence of multiobjective evolutionary algorithms , 1999, Eur. J. Oper. Res..

[19]  Andries Petrus Engelbrecht,et al.  A study of particle swarm optimization particle trajectories , 2006, Inf. Sci..

[20]  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).

[21]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[22]  Emilio F. Campana,et al.  Dynamic system analysis and initial particles position in Particle Swarm Optimization , 2006 .

[23]  Chukwudi Anyakoha,et al.  A review of particle swarm optimization. Part I: background and development , 2007, Natural Computing.

[24]  Riccardo Poli,et al.  Mean and Variance of the Sampling Distribution of Particle Swarm Optimizers During Stagnation , 2009, IEEE Transactions on Evolutionary Computation.

[25]  Frans van den Bergh,et al.  An analysis of particle swarm optimizers , 2002 .

[26]  Rolf Wanka,et al.  Theoretical Analysis of Initial Particle Swarm Behavior , 2008, PPSN.

[27]  Carlos A. Coello Coello,et al.  Multi-Objective Particle Swarm Optimizers: An Experimental Comparison , 2009, EMO.

[28]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .

[29]  Yujia Wang,et al.  Particle swarm optimization with preference order ranking for multi-objective optimization , 2009, Inf. Sci..

[30]  Jonathan E. Fieldsend,et al.  Using unconstrained elite archives for multiobjective optimization , 2003, IEEE Trans. Evol. Comput..

[31]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[32]  Salman Mohagheghi,et al.  Particle Swarm Optimization: Basic Concepts, Variants and Applications in Power Systems , 2008, IEEE Transactions on Evolutionary Computation.

[33]  Ponnuthurai Nagaratnam Suganthan,et al.  Two-lbests based multi-objective particle swarm optimizer , 2011 .

[34]  Manoj Kumar Tiwari,et al.  Interactive Particle Swarm: A Pareto-Adaptive Metaheuristic to Multiobjective Optimization , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[35]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[36]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[37]  Katsuhiko Ogata,et al.  Discrete-time control systems , 1987 .

[38]  Swagatam Das,et al.  A closed loop stability analysis and parameter selection of the Particle Swarm Optimization dynamics for faster convergence , 2007, 2007 IEEE Congress on Evolutionary Computation.

[39]  Francisco Herrera,et al.  Genetics-Based Machine Learning for Rule Induction: State of the Art, Taxonomy, and Comparative Study , 2010, IEEE Transactions on Evolutionary Computation.

[40]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

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

[42]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[43]  Visakan Kadirkamanathan,et al.  Stability analysis of the particle dynamics in particle swarm optimizer , 2006, IEEE Transactions on Evolutionary Computation.