A Fuzzy Adaptive Differential Evolution Algorithm

Abstract.The differential evolution algorithm is a floating-point encoded evolutionary algorithm for global optimization over continuous spaces. The algorithm has so far used empirically chosen values for its search parameters that are kept fixed through an optimization process. The objective of this paper is to introduce a new version of the Differential Evolution algorithm with adaptive control parameters – the fuzzy adaptive differential evolution algorithm, which uses fuzzy logic controllers to adapt the search parameters for the mutation operation and crossover operation. The control inputs incorporate the relative objective function values and individuals of the successive generations. The emphasis of this paper is analysis of the dynamics and behavior of the algorithm. Experimental results, provided by the proposed algorithm for a set of standard test functions, outperformed those of the standard differential evolution algorithm for optimization problems with higher dimensionality.

[1]  S. Gottwald,et al.  Fuzzy sets, fuzzy logic, fuzzy methods with applications , 1995 .

[2]  Radomil Matousek,et al.  GA with fuzzy inference system , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

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

[4]  Hideyuki Takagi,et al.  Dynamic Control of Genetic Algorithms Using Fuzzy Logic Techniques , 1993, ICGA.

[5]  Zbigniew Michalewicz,et al.  Parameter control in evolutionary algorithms , 1999, IEEE Trans. Evol. Comput..

[6]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[7]  L. G. van Willigenburg,et al.  Parameter control strategy in differential evolution algorithm for optimal control , 2001 .

[8]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[9]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[10]  R. Storn,et al.  On the usage of differential evolution for function optimization , 1996, Proceedings of North American Fuzzy Information Processing.