Enhancing clearing-based niching method using Delaunay Triangulation

The interest in multi-modal optimization methods is increasing in the recent years since many of real-world optimization problems have multiple/many optima and decision makers prefer to find all of them. Multiple global/local peaks create difficulties for optimization algorithms. In this context, niching is well-known and widely used technique for finding multiple solutions in multi-modal optimization. One commonly used niching technique in evolutionary algorithms is the Clearing method. However, canonical clearing scheme reduces the exploration capacity of the evolutionary algorithms. In this paper, Delaunay Triangulation based Clearing (DT-Clearing) procedure is proposed to handle multi-modal optimizations more efficiently while preserving simplicity of canonical clearing approach. In DT-Clearing, cleared individuals are reallocated in the biggest empty spaces formed within the search space which are determined through Delaunay Triangulation. The reallocation of cleared individuals discourages wasting of the resources and allows better exploration of the landscape. The algorithm also uses an external memory, an archive of the explored niches, thus preventing the redundant visiting of the individuals, henceforth finding more solutions in lesser number of generations. The method is tested using multi-modal benchmark problems proposed for the IEEE CEC 2013, Special Session on Niching Methods for Multimodal Optimization. Our method obtains promising results in comparison with the canonical clearing and demonstrates to be a competitive niching algorithm.