Multi-optima search using Differential Evolution and unsupervised clustering

The aim of this paper is the combination of an Evolutionary Algorithm and a Data Mining technique for the location and computation of multiple local and global optima of an objective function. To accomplish this task we exploit the spatial concentration of the population members around the optima of the objective function. Such concentration regions are determined by applying clustering algorithms on the actual positions of the members of the population. Subsequently, the evolutionary search is confined in the interior of the regions discovered. To enable the simultaneous discovery of more than one global and local optima, we propose the use of unsupervised clustering algorithms that also provide intuitive approximations for the number of clusters. Furthermore, as shown by the experimental analysis, the proposed scheme has often the potential of accelerating the convergence speed of the Evolutionary Algorithm, without the need for extra function evaluations.