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
Recommended Citation
Rowe, Jonathan E.; Vose, Michael D.; and Wright, Alden H., "Group Properties of Crossover and Mutation" (2002). Computer Science Faculty Publications. 11.
https://scholarworks.umt.edu/cs_pubs/11
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.