Locating multiple optima using particle swarm optimization

Many scientific and engineering applications require optimization methods to find more than one solution to multimodal optimization problems. This paper presents a new particle swarm optimization (PSO) technique to locate and refine multiple solutions to such problems. The technique, NichePSO, extends the inherent unimodal nature of the standard PSO approach by growing multiple swarms from an initial particle population. Each subswarm represents a different solution or niche; optimized individually. The outcome of the NichePSO algorithm is a set of particle swarms, each representing a unique solution. Experimental results are provided to show that NichePSO can successfully locate all optima on a small set of test functions. These results are compared with another PSO niching algorithm, lbest PSO, and two genetic algorithm niching approaches. The influence of control parameters is investigated, including the relationship between the swarm size

[1]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[2]  Andries Petrus Engelbrecht,et al.  Niching ability of basic particle swarm optimization algorithms , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[3]  Russell Beale,et al.  Handbook of Neural Computation , 1996 .

[4]  Carlos A. Coello Coello,et al.  An updated survey of evolutionary multiobjective optimization techniques: state of the art and future trends , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[6]  A. Engelbrecht,et al.  A new locally convergent particle swarm optimiser , 2002, IEEE International Conference on Systems, Man and Cybernetics.

[7]  Jeffrey Horn,et al.  The nature of niching: genetic algorithms and the evolution of optimal, cooperative populations , 1997 .

[8]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

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

[10]  Jeffrey Horn,et al.  Handbook of evolutionary computation , 1997 .

[11]  Samir W. Mahfoud Niching methods for genetic algorithms , 1996 .

[12]  Michael N. Vrahatis,et al.  Modification of the Particle Swarm Optimizer for Locating All the Global Minima , 2001 .

[13]  R. Brits,et al.  Solving systems of unconstrained equations using particle swarm optimization , 2002, IEEE International Conference on Systems, Man and Cybernetics.

[14]  Riaan Brits Niching strategies for particle swarm optimization , 2005 .

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

[16]  David E. Goldberg,et al.  Probabilistic Crowding: Deterministic Crowding with Probabilistic Replacement , 1999 .

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

[18]  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).

[19]  James Kennedy,et al.  Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[20]  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).

[21]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[22]  Thomas Kiel Rasmussen,et al.  Hybrid Particle Swarm Optimiser with breeding and subpopulations , 2001 .

[23]  R. Eberhart,et al.  Empirical study of particle swarm optimization , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[24]  Andries Petrus Engelbrecht,et al.  Cooperative learning in neural networks using particle swarm optimizers , 2000, South Afr. Comput. J..

[25]  Michael J. Shaw,et al.  Genetic algorithms with dynamic niche sharing for multimodal function optimization , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[26]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[27]  Ralph R. Martin,et al.  A Sequential Niche Technique for Multimodal Function Optimization , 1993, Evolutionary Computation.

[28]  Jonathan E. Fieldsend,et al.  A Multi-Objective Algorithm based upon Particle Swarm Optimisation, an Efficient Data Structure and , 2002 .

[29]  William H. Press,et al.  Numerical recipes in C++: the art of scientific computing, 2nd Edition (C++ ed., print. is corrected to software version 2.10) , 1994 .

[30]  Thomas Stützle,et al.  Ant Colony Optimization , 2009, EMO.

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

[32]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

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

[34]  Samir W. Mahfoud A Comparison of Parallel and Sequential Niching Methods , 1995, ICGA.

[35]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[36]  François E. Cellier,et al.  Artificial Neural Networks and Genetic Algorithms , 1991 .

[37]  J. Kennedy,et al.  Population structure and particle swarm performance , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[38]  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).

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

[40]  K. Parsopoulos,et al.  Stretching technique for obtaining global minimizers through Particle Swarm Optimization , 2001 .

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