Massachusetts Institute of Technology Press
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.
Genetic algorithms, mixing matrix, group, schema, group action, isotropy group, order crossover, pure crossover, permutation group.
Rowe, Jonathan E.; Vose, Michael D.; and Wright, Alden H., "Group Properties of Crossover and Mutation" (2002). Computer Science Faculty Publications. 11.