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Evolutionary Computation

Summer 2002, Vol. 10, No. 2, Pages 151-184
(doi: 10.1162/106365602320169839)
© 2002 Massachusetts Institute of Technology
Group Properties of Crossover and Mutation
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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.