Genetic algorithms in time-dependent environments

The influence of time-dependent fitnesses, on the infinite population dynamics of simple genetic algorithms (GAs) without crossover is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize the asymptotic states in dependence on the mutation rate and the time scale of changes. Furthermore, the notion of regular changes is raised for which the population can be shown to converge towards a generalized quasispecies. Based on this, error thresholds and an optimal mutation rate are approximately calculated for a generational GA with a moving needle-in-the-haystack landscape. The phase diagram thus found is fully consistent with our general considerations.