An analysis of the automatic adaptation of the crossover rate in differential evolution

Differential Evolution (DE) is a very efficient meta-heuristic for optimization over continuous spaces which has gained much popularity in recent years. Several parameter control strategies have been proposed to automatically adapt its internal parameters. The most advanced DE variants take into account the feedback obtained in the optimization process to guide the dynamic setting of the DE parameters. Indeed, the automatic adaptation of the crossover rate (CR) has attracted a lot of research in the last decades. In most of such strategies, the quality of using a given CR value is measured by considering the probability of performing a replacement in the DE selection stage when such a value is applied. One of the main contributions of this paper is to experimentally show that the probability of replacement induced by the application of a given CR value and the quality of the obtained results are not as correlated as expected. This might cause a performance deterioration that avoids the achievement of good quality solutions even in the long-term. In addition, the experimental evaluation developed with a set of optimization problems of varying complexities clarifies some of the advantages and drawbacks of the different tested strategies. The only component varied among the different tested schemes has been the CR control strategy. The study presented in this paper provides advances in the understanding of the inner working of several state-of-the-art adaptive DE variants.