Abstract
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 language | English |
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Pages (from-to) | 151-184 |
Number of pages | 34 |
Journal | Evolutionary Computation |
Volume | 10 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jun 2002 |
Keywords
- schema
- mixing matrix
- pure crossover
- genetic algorithms
- group action
- order crossover
- isotropy group
- permutation group
- group