Chaotic sequences to improve the performance of evolutionary algorithms

This paper proposes an experimental analysis on the convergence of evolutionary algorithms (EAs). The effect of introducing chaotic sequences instead of random ones during all the phases of the evolution process is investigated. The approach is based on the substitution of the random number generator (RNG) with chaotic sequences. Several numerical examples are reported in order to compare the performance of the EA using random and chaotic generators as regards to both the results and the convergence speed. The results obtained show that some chaotic sequences are always able to increase the value of some measured algorithm-performance indexes with respect to random sequences. Moreover, it is shown that EAs can be extremely sensitive to different RNGs. Some t-tests were performed to confirm the improvements introduced by the proposed strategy.

[1]  Mitsuo Gen,et al.  Genetic algorithms and engineering optimization , 1999 .

[2]  William H. Press,et al.  Numerical recipes in C , 2002 .

[3]  Kate Smith-Miles,et al.  On chaotic simulated annealing , 1998, IEEE Trans. Neural Networks.

[4]  S. K. Park,et al.  Random number generators: good ones are hard to find , 1988, CACM.

[5]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[6]  Chang Wook Ahn,et al.  On the practical genetic algorithms , 2005, GECCO '05.

[7]  Pierre L'Ecuyer,et al.  Efficient and portable combined random number generators , 1988, CACM.

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

[9]  M. Yamaguti,et al.  Chaos and Fractals , 1987 .

[10]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[11]  Robert L. Devaney,et al.  Practical Numerical Algorithms for Chaotic Systems (T. S. Parker and L. O. Chua) , 1990, SIAM Rev..

[12]  Amit Mitra,et al.  Statistical Quality Control , 2002, Technometrics.

[13]  Robert Axelrod,et al.  The Evolution of Strategies in the Iterated Prisoner's Dilemma , 2001 .

[14]  G. Manganaro,et al.  DNA computing based on chaos , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[15]  P. Arena,et al.  Self-Organization in nonrecurrent Complex Systems , 2000, Int. J. Bifurc. Chaos.

[16]  Hiroshi Nozawa,et al.  A neural network model as a globally coupled map and applications based on chaos. , 1992, Chaos.

[17]  Luigi Fortuna,et al.  Programmable chaos generator, based on CNN architectures, with applications in chaotic communications , 1998, 1998 Fifth IEEE International Workshop on Cellular Neural Networks and their Applications. Proceedings (Cat. No.98TH8359).

[18]  Kazuyuki Aihara,et al.  Global searching ability of chaotic neural networks , 1999 .

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

[20]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[21]  M. Vose.  The Simple Genetic Algorithm , 1999 .

[22]  James A. Foster,et al.  Using chaos in genetic algorithms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[23]  Michael D. Vose,et al.  The simple genetic algorithm - foundations and theory , 1999, Complex adaptive systems.

[24]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[25]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[26]  Liu Jianqin,et al.  Premature convergence in genetic algorithm: analysis and prevention based on chaos operator , 2000, Proceedings of the 3rd World Congress on Intelligent Control and Automation (Cat. No.00EX393).