The detrimentality of crossover

Abstract

The traditional concept of a genetic algorithm (GA) is that of selection, crossover and mutation. However, data from the literature has suggested that the niche for the beneficial effect of crossover upon GA performance may be smaller than has been traditionally held. We explored the class of problems for which crossover is detrimental by performing a statistical analysis of two test problem suites, one comprising linear-separable non-rotated functions and the other comprising the same functions rotated by 45 degrees rendering them not-linear-separable. We find that for the difficult rotated functions the crossover operator is detrimental to the performance of the GA. We conjecture that what makes a problem difficult for the GA is complex and involves factors such as the degree of optimization at local minima due to crossover, the bias associated with the mutation operator and the Hamming Distances present in the individual problems due to the encoding. Finally, we test our GA on a practical landscape minimization problem to see if the results obtained match those from the difficult rotated functions. We find that they match and that the features which make certain of the test functions difficult are also present in the real world problem. © Springer-Verlag Berlin Heidelberg 2007.