Replacement Strategies in Steady State Genetic Algorithms: Static Environments

This paper investigates the effects of a number of replacement strategies for use in steady state genetic algorithms. Some of these (deleting the oldest, worst or random members, or deletion by “Kill Tournament”) are well known from the literature. The last, “conservative” replacement was developed for use in timevarying problems and combines a Replace–Oldest strategy with modified selection tournaments, where one candidate is always the oldest member of the population. A Markov chain analysis is provided to model the expected time for a single member of the optimal class to take over finite populations. For strategies which replace the oldest member, a linear approximation is developed for the probability that it belongs to the optimal class. It is shown that under certain conditions this approximation yields a transition matrix which is identical to a strategy of deletion by binary Kill Tournament. Predicted and simulation results confirm that without enforced elitism Replace– Random and Replace–Oldest strategies cannot guarantee takeover, and for a fixed parent selection method the speed of takeover is dramatically altered by the choice of replacement strategy.