Study of computational performance of Genetic Algorithm for 3-satisfiability problem

In order to improve the computing performance of Genetic Algorithms (GAs), it is important to study the effects of crossover and mutation. In this study, we examine the relations of first hitting time T of optimum solution in population, success probability S, mutation rate p(m) and crossover rate p(c) by GA experiments, which are carried out on the 3-satisfiability (3-SAT) problem. Here, S is defined as that there is at least one optimum solution in a population at the stationary distribution. We found that, when mutation rate is small, the effects of crossover on T and S are large. S with crossover is larger than that without crossover, and T is smaller than that without crossover. We also observed the relation between T and a/S when mutation rate becomes large, and found that T = a/S. When p(m) = 0.02, T approximate to 1/S.