Statistical exploratory analysis of genetic algorithms: the importance of interaction

Genetic algorithms have been extensively used and studied, yet limited research has addressed the importance of the interaction between crossover and mutation. Two questions, namely, "what type of functions is likely to demonstrate interaction between crossover and mutation", and, "what is the practical implication of interaction for obtaining optimal rates for these parameters", have been unanswered. This work continues work using a rigorous yet practical statistical methodology for the exploratory study of genetic algorithms. In the present research we examine the relationship between the statistical significance of interaction among crossover and mutation and increasing modality of a problem. We present initial answers to these questions in this context. First, we find that as our test function increases in modality the interaction between crossover and mutation becomes statistically significant. The effect of the interaction is striking when examining response curves, which illustrate distinct inflection. We conjecture that for highly modal functions the possibility of interaction between crossover and mutation must be considered. Secondly, the practical implication of interaction is that when attempting to fine tune a genetic algorithm on a highly modal problem the optimal rates for crossover and mutation cannot be obtained independently. All combinations of crossover and mutation, within given starting ranges, must be investigated in order to allow for the interaction effect.