Document Type

Article

Publication Title

Evolutionary Computation

Publisher

Massachusetts Institute of Technology Press

Publication Date

2002

Volume

10

Issue

2

Disciplines

Computer Sciences

Abstract

It is supposed that the finite search space Ω has certain symmetries that can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries, then these operators can be described in terms of a mixing matrix and a group of permutation matrices. Conditions under which certain subsets of Ω are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on Ω to induce a group structure on Ω itself.

Keywords

Genetic algorithms, mixing matrix, group, schema, group action, isotropy group, order crossover, pure crossover, permutation group.

DOI

10.1162/106365602320169839

Comments

Group Properties of Crossover and Mutation (with Jonathan E. Rowe and Michael D. Vose) Evolutionary Computation 10(2), 2002, pages 151-184. View original published article at 10.1162/106365602320169839.

Download

Share

COinS