Search space boundary extension method in real-coded genetic algorithms

Abstract In real-coded genetic algorithms (GAs), some crossover operators do not work well on functions which have their optimum at the corner of the search space. To cope with this problem, we have proposed a boundary extension method which allows individuals to be located within a limited space beyond the boundary of the search space. In this paper, we give an analysis of the boundary extension methods from the viewpoint of sampling bias and perform a comparative study on the effect of applying two boundary extension methods, namely the boundary extension by mirroring (BEM) and the boundary extension with extended selection (BES). We were able to confirm that to use sampling methods which have smaller sampling bias had good performance on both functions which have their optimum at or near the boundaries of the search space, and functions which have their optimum at the center of the search space. The BES/SD/A (BES by shortest distance selection with aging) had good performance on functions which have their optimum at or near the boundaries of the search space. We also confirmed that applying the BES/SD/A did not cause any performance degradation on functions which have their optimum at the center of the search space.

[1]  Yong Gao,et al.  Comments on "Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. I. Basic properties of selection and mutation" [and reply] , 1998, IEEE Trans. Neural Networks.

[2]  Nostrand Reinhold,et al.  the utility of using the genetic algorithm approach on the problem of Davis, L. (1991), Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York. , 1991 .

[3]  Isao Ono,et al.  A Real Coded Genetic Algorithm for Function Optimization Using Unimodal Normal Distributed Crossover , 1997, ICGA.

[4]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[5]  Keith E. Mathias,et al.  Crossover Operator Biases: Exploiting the Population Distribution , 1997, ICGA.

[6]  Larry J. Eshelman,et al.  The CHC Adaptive Search Algorithm: How to Have Safe Search When Engaging in Nontraditional Genetic Recombination , 1990, FOGA.

[7]  Shigeyoshi Tsutsui,et al.  Multi-parent Recombination in Genetic Algorithms with Search Space Boundary Extension by Mirroring , 1998, PPSN.

[8]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

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

[10]  Jean-Michel Renders,et al.  Hybridizing genetic algorithms with hill-climbing methods for global optimization: two possible ways , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[11]  Francesco Palmieri,et al.  Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part I: Basic properties of selection and mutation , 1994, IEEE Trans. Neural Networks.

[12]  M. Yamamura,et al.  Multi-parent recombination with simplex crossover in real coded genetic algorithms , 1999 .

[13]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[14]  David E. Goldberg,et al.  Real-coded Genetic Algorithms, Virtual Alphabets, and Blocking , 1991, Complex Syst..

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

[16]  Alden H. Wright,et al.  Genetic Algorithms for Real Parameter Optimization , 1990, FOGA.

[17]  M. Yamamura,et al.  A functional specialization hypothesis for designing genetic algorithms , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[18]  Shigenobu Kobayashi,et al.  A robust real-coded genetic algorithm using Unimodal Normal Distribution Crossover augmented by Uniform Crossover: effects of self-adaptation of crossover probabilities , 1999 .

[19]  Shigenobu Kobayashi,et al.  A Real-Coded Genetic Algorithm for Function Optimization Using the Unimodal Normal Distribution Crossover , 1999 .

[20]  Francesco Palmieri,et al.  Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part II: Analysis of the diversification role of crossover , 1994, IEEE Trans. Neural Networks.

[21]  Zbigniew Michalewicz,et al.  An Experimental Comparison of Binary and Floating Point Representations in Genetic Algorithms , 1991, ICGA.