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Evolutionary Computation

Winter 2010, Vol. 18, No. 4, Pages 635-660
(doi: 10.1162/EVCO_a_00007)
© 2010 by the Massachusetts Institute of Technology
Representation Invariant Genetic Operators
Article PDF (192.16 KB)

A genetic algorithm is invariant with respect to a set of representations if it runs the same no matter which of the representations is used. We formalize this concept mathematically, showing that the representations generate a group that acts upon the search space. Invariant genetic operators are those that commute with this group action. We then consider the problem of characterizing crossover and mutation operators that have such invariance properties. In the case where the corresponding group action acts transitively on the search space, we provide a complete characterization, including high-level representation-independent algorithms implementing these operators.