GA performance in a babel-like fitness landscape

The performance of genetic algorithms (GAs) is studied under a babel-like fitness landscape, in which only a one bit sequence is significantly advantageous over the others. Under this landscape, the most dominant process to determine the GA performance is creation of the advantageous sequence, and crossover facilitates the creation, thereby improves the GA performance. We first conduct a computer simulation using the simple GA, and examine the waiting time until domination of the advantageous sequence (T_d). It is shown that crossover with mildly high rate reduces T_d significantly and that the magnitude of this reduction (A_cross) is the largest when the mutation rate is an intermediate value. Second, we mathematically analyze the model and estimate the value of A_cross. From these observations, we determine implementation criteria for GAs, which are useful when we apply GAs to engineering problems such as having a conspicuously discontinuous fitness landscape.