Group properties of crossover and mutation

  • Authors:
  • Jonathan E. Rowe;Michael D. Vose;Alden H. Wright

  • Affiliations:
  • School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK;Computer Science Department, University of Tennessee, Knoxville, TN;Department of Computer Science, University of Montana, Missoula, MT

  • Venue:
  • Evolutionary Computation
  • Year:
  • 2002

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Abstract

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.