Adaptive probabilities of crossover and mutation in genetic algorithms

Abstract

In this paper we describe an efficient approach for multimodal function optimization using genetic algorithms (GAs). We recommend the use of adaptive probabilities of crossover & mutation to realize the twin goals of maintaining diversity in the population & sustaining the, convergence capacity of the GA. In the adaptive genetic algorithm (AGA), the probabilities of crossover & mutation, p_c & p_m, are varied depending on the fitness values of the solutions. High-fitness solutions are `protected', while solutions with subaverage fitnesses are totally disrupted. By using adaptively varying p_c and p, we also provide a solution to the problem of deciding the optimal values of p_c and p_m, i.e., p_c & p_m need not be specified at all. The AGA is compared with previous approaches for adapting operator probabilities in genetic algorithms. The Schema theorem is derived for the AGA, & the working of the AGA is analyzed. We compare the performance of the AGA with that of the standard GA (SGA) in optimizing several nontrivial multimodal functions with varying degrees of complexity.