Self-adaptation in evolving systems

A theoretical and experimental analysis is made of the effects of self-adap tation in a simple evolving system. Specifically, we consider the effects o f coding the mutation and crossover probabilities of a genetic algorithm ev olving in certain model fitness landscapes. The resultant genotype-phenotyp e mapping is degenerate in fitness space, there being no direct selective a dvantage for one probability versus another. Thus there is a "symmetry" bet ween various genotypes that all correspond to the same phenotype. We show t hat the action of mutation and crossover lifts this degeneracy, that is, th e genetic operators induce a breaking of the genotype-phenotype symmetry, t hus leading to a preference for those genotypes that propagate most success fully into future generations. We demonstrate that this induced symmetry br eaking allows the system to self-adapt in a time-dependent environment.