Optimizing Multimodal Functions by Differential Evolution with Speciation Using Proximity Graph

Abstract

In multimodal function optimization problems, which have multiple global optimal solutions, it is important to find all the global optima in one trial. Several species-based methods have been proposed to search for multiple global optima. In the methods, speciation mechanism is used for dividing individuals into some species, and each species searches a solution locally. The species-radius is used for the determination of the species' territory. But the parameter setting of the radius is dependent on objective functions. Therefore, it is difficult to determine the appropriate radius. To solve the problem, we propose a new speciation method using proximity graphs instead of the species radius. The proximity graph for individuals is constructed based on the concept of neighborhood in the graph theory. In our proposed method, Differential Evolution is used as the optimization algorithm. Moreover, several kinds of proximity graphs, relative neighborhood graph, Gabriel graph, beta-skeleton graph and so on, can be adopt for the speciation. We applied our proposed methods to several test functions and examined their effectiveness.