Global optimization of an optical chaotic system by Chaotic Multi Swarm Particle Swarm Optimization

The control and estimation of unknown parameters of chaotic systems are a daunting task till date from the perspective of nonlinear science. Inspired from ecological co-habitation, we propose a variant of Particle Swarm Optimization (PSO), known as Chaotic Multi Swarm Particle Swarm Optimization (CMS-PSO), by modifying the generic PSO with the help of the chaotic sequence for multi-dimension unknown parameter estimation and optimization by forming multiple cooperating swarms. This achieves load balancing by delegating the global optimizing task to concurrently operating swarms. We apply it successfully in estimating the unknown parameters of an autonomous chaotic laser system derived from Maxwell-Bloch equations. Numerical results and comparison demonstrate that for the given system parameters, CMS-PSO can identify the optimized parameters effectively evolving at each iteration to attain the pareto optimal solution with small population size and enhanced convergence speedup.

[1]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[2]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[3]  Hamidreza Modares,et al.  Parameter identification of chaotic dynamic systems through an improved particle swarm optimization , 2010, Expert Syst. Appl..

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

[5]  Jun Sun,et al.  Parameter estimation for chaotic systems with a Drift Particle Swarm Optimization method , 2010 .

[6]  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).

[7]  A. Roy Chowdhury,et al.  Chaotic aspects of lasers with host-induced nonlinearity and its control , 2001 .

[8]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Jeffrey O. Kephart,et al.  A biologically inspired immune system for computers , 1994 .

[10]  Wenbo Mao,et al.  Modern Cryptography: Theory and Practice , 2003 .

[11]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[12]  Jing J. Liang,et al.  Dynamic multi-swarm particle swarm optimizer , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[13]  H. P. Schwefel,et al.  Numerische Optimierung von Computermodellen mittels der Evo-lutionsstrategie , 1977 .

[14]  Wei Zheng,et al.  Co-evolutionary particle swarm optimization to solve constrained optimization problems , 2009, Comput. Math. Appl..

[15]  F. Azuaje.  Artificial Immune Systems: A New Computational Intelligence Approach , 2003 .

[16]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[17]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[18]  M. M. Ali,et al.  Improved particle swarm algorithms for global optimization , 2008, Appl. Math. Comput..

[19]  Pierre L'Ecuyer,et al.  Combined Multiple Recursive Random Number Generators , 1995, Oper. Res..

[20]  Luigi Fortuna,et al.  Chaotic sequences to improve the performance of evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

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

[22]  Tunchan Cura,et al.  Particle swarm optimization approach to portfolio optimization , 2009 .

[23]  Yinggan Tang,et al.  Parameter estimation for time-delay chaotic system by particle swarm optimization , 2009 .

[24]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[25]  Ling Wang,et al.  Parameter estimation for chaotic systems by particle swarm optimization , 2007 .

[26]  Siba K. Udgata,et al.  Integrated Learning Particle Swarm Optimizer for global optimization , 2011, Appl. Soft Comput..

[27]  Alex A. Freitas,et al.  Evolutionary Computation , 2002 .

[28]  Leandro dos Santos Coelho,et al.  Use of chaotic sequences in a biologically inspired algorithm for engineering design optimization , 2008, Expert Syst. Appl..

[29]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[30]  Ling Wang,et al.  An effective hybrid quantum-inspired evolutionary algorithm for parameter estimation of chaotic systems , 2010, Expert Syst. Appl..

[31]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[32]  Shu-Kai S. Fan,et al.  Dynamic multi-swarm particle swarm optimizer using parallel PC cluster systems for global optimization of large-scale multimodal functions , 2010 .

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