Group properties of crossover and mutation

Jonathan Rowe, MD Vose, AH Wright

Research output: Contribution to journalArticle

32 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)151-184
Number of pages34
JournalEvolutionary Computation
Issue number2
Publication statusPublished - 1 Jun 2002


  • schema
  • mixing matrix
  • pure crossover
  • genetic algorithms
  • group action
  • order crossover
  • isotropy group
  • permutation group
  • group


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