Self-adaptation in evolving systems

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 genotype-phenotype 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.