Cluster-centroid-based mutation strategies for Differential Evolution

Mutation is the main operator of differential evolution (DE), as it is responsible for combining the information of distinct solutions to generate a donor vector. Aiming at improving the search effectivity of DE, previous research incorporated the calculation of centroids into the DE mutations. In some of the existing methods, the centroids are simply calculated as the center of some selected solutions (or, the entire population); in other cases, one-step clustering is used to perform a local search, or the centroids themselves are used as actual solutions in the population. As opposed to these methods, in this paper we extend some traditional DE mutation strategies to incorporate centroids calculated by deterministic hierarchical clustering. Experimental results on two sets of well-known benchmark problems show that the proposed cluster-centroid-based mutation strategies outperform, in general, the traditional rand/1 strategy, as well as several metaheuristics from the literature. Therefore, the use of clustering is an effective way to improve the search performance that could be exploited also in other population-based metaheuristics.