A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in certain model fitness landscapes. The resultant genotypephenotype mapping is degenerate in fitness space, there being no direct selective advantage for one probability versus another. Thus there is a “symmetry” between various genotypes that all correspond to the same phenotype. We show that the action of mutation and crossover lifts this degeneracy, that is, the genetic operators induce a breaking of the genotype-phenotype symmetry, thus leading to a preference for those genotypes that propagate most successfully into future generations. We demonstrate that this induced symmetry breaking allows the system to self-adapt in a time-dependent environment.

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