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Full-Text Articles in Physical Sciences and Mathematics
Group Properties Of Crossover And Mutation, Jonathan E. Rowe, Michael D. Vose, Alden H. Wright
Group Properties Of Crossover And Mutation, Jonathan E. Rowe, Michael D. Vose, Alden H. Wright
Computer Science Faculty Publications
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.