On convergence of 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 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 control the convergence behavior of the algorithm to the Pareto front in the objective function space. Limited simulation supports have also been provided to substantiate the theoretical derivations.

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

[2]  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).

[3]  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.

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

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

[6]  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).

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

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

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

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

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

[12]  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.

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

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

[15]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

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

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

[18]  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).

[19]  Suet Yee Chu.  Particle swarm optimization , 2009 .

[20]  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).

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

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

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

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

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

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

[27]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.

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

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

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

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

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