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