Group Properties of Crossover and Mutation

It is supposed that the finite search space has certain symmetries which 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 are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on to induce a group structure on itself. Keywords genetic algorithms, mixing matrix, group, schema, group action, isotropy group, order crossover, pure crossover, permutation group

• Type: Journal
• Year: 2002
• Where: EC
• Authors: Jonathan E. Rowe, Michael D. Vose, Alden H. Wright
• Keywords: Crossover, EC 2002, ECommerce, Group, Permutation