Differential evolution with hybrid linkage crossover

In the field of evolutionary algorithms (EAs), differential evolution (DE) has been the subject of much attention due to its strong global optimization capability and simple implementation. However, in most DE algorithms, crossover operator often ignores the consideration of interactions between pairs of variables. That is, DE is linkage-blind, and the problem-specific linkages are not utilized effectively to guide the search process. Furthermore, linkage learning techniques have been verified to play an important role in EA optimization. Therefore, to alleviate the drawback of linkage-blind in DE and enhance its performance, a novel linkage utilization technique, called hybrid linkage crossover (HLX), is proposed in this study. HLX utilizes the perturbation-based method to automatically extract the linkage information of a specific problem and then uses the linkage information to guide the crossover process. By incorporating HLX into DE, the resulting algorithm, named HLXDE, is presented. In order to evaluate the effectiveness of HLXDE, HLX is incorporated into six original DE algorithms, as well as several advanced DE variants. Experimental results demonstrate the high performance of HLX for the DE algorithms studied.