Recombination Without Respect: Schema Combination and Disruption in Genetic Algorithm Grossover

One-point (or n-point) crossover has the property that schemata exhibited by both parents are 'respected'—transferred to the offspring without disruption. In addition, new schemata may, potentially, be created by combination of the genes on which the parents differ. Some argue that the preservation of similarity is the important aspect of crossover, and that the combination of differences (key to the building-block hypothesis) is unlikely to be valuable. In this paper, we discuss the operation of recombination on a hierarchical building-block problem. Uniform crossover, which preserves similarity, fails on this problem. Whereas, one-point crossover, that both preserves similarity and combines differences, succeeds. In fact, a somewhat perverse recombination operator, that combines differences but destroys schemata that are common to both parents, also succeeds. Thus, in this problem, combination of schemata from dissimilar parents is required, and preserving similarity is not required. The test problem represents an extreme case, but it serves to illustrate the different aspects of recombination that are available in regular operators such as one-point crossover.

[1]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[2]  Nicholas J. Radcliffe,et al.  Forma Analysis and Random Respectful Recombination , 1991, ICGA.

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

[4]  Stephen F. Smith,et al.  Is the common good? a new perspective developed in genetic algorithms , 1999 .

[5]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .

[6]  Lee Altenberg,et al.  The Schema Theorem and Price's Theorem , 1994, FOGA.

[7]  Jordan B. Pollack,et al.  Incremental commitment in genetic algorithms , 1999 .

[8]  Jordan B. Pollack,et al.  Modeling Building-Block Interdependency , 1998, PPSN.

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

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

[11]  Melanie Mitchell,et al.  Relative Building-Block Fitness and the Building Block Hypothesis , 1992, FOGA.

[12]  L. Darrell Whitley,et al.  Building Better Test Functions , 1995, ICGA.

[13]  Stephen Chen,et al.  Commonality and Genetic Algorithms , 1996 .

[14]  Keith E. Mathias,et al.  Convergence Controlled Variation , 1996, FOGA.

[15]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.

[16]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[17]  L. Darrell Whitley,et al.  Optimization Using Distributed Genetic Algorithms , 1990, PPSN.

[18]  J. Pollack,et al.  Hierarchically consistent test problems for genetic algorithms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).