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.
School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK. J.E.Rowe@cs.bham.ac.uk
Jonathan E
JE
Rowe
Michael D
MD
Vose
Alden H
AH
Wright
D000328:Adult; D000465:Algorithms; D001185:Artificial Intelligence; D002648:Child; D003434:Crossing Over, Genetic; D006801:Humans; D008957:Models, Genetic; D009154:Mutation; D010290:Parents