Neighborhood graphs and symmetric genetic operators

Authors:
Jonathan E. Rowe;Michael D. Vose;Alden H. Wright
Affiliations:
School of Computer Science, University of Birmingham, Birmingham, Great Britain;Computer Science Department, University of Tennessee, Knoxville, TN;Dept. of Computer Science, University of Montana, Missoula, Montana
Venue:
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Year:
2007

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Abstract

In the case where the search space has a group structure, classical genetic operators (mutation and two-parent crossover) which respect the group action are completely characterized by formulas defining them in terms of the search space and its group operation. This provides a representation-free implementation for those operators, in the sense that the genotypic encoding of search space elements is irrelevant. The implementations are parameterized by distributions which may be chosen arbitrarily, and which are analogous to specifying distributions for mutation and crossover masks.