Optimization of fitness functions with non-ordered parameters by genetic algorithms

Abstract

This paper describes a Genetic Algorithm (GA) convergence study for a highly multi-modal fitness function with non-ordered parameters. The measures of GA performance used are best single solution performance, effectiveness in finding the optimum and percentage of total search space (PTSS) covered. We developed several ways of adapting the crossover and mutation probabilities, and we compare the results of these methods with a canonical GA, a mutation-only GA, and the Srinivas' adaptive method. The results indicate that a large constant probability of crossover, regardless of the mutation method used does not provide high efficiency, for medium and large populations if covering a small PTSS. The most effective method while covering the smallest PTSS, is an adaptive mutation-only method. Our results suggest that when convergence speed is of utmost interest, for functions with non-ordered parameters mutation is more important than crossover despite massive multi-modality of the function optimized. Methods with adaptive crossover can, however, also give good results as long as mutation with a constant high probability is also performed.