MOEA/PC: Multiobjective Evolutionary Algorithm Based on Polar Coordinates

Abstract

The need to perform the search in the objective space constitutes one of the fundamental differences between multiobjective and single-objective optimization. The performance of any multiobjective evolutionary algorithm (MOEA) is strongly related to the efficacy of its selection mechanism. The population convergence and diversity are two different but equally important goals that must be ensured by the selection mechanism. Despite the equal importance of the two goals, the convergence is often used as the first sorting criterion, whereas the diversity is considered as the second one. In some cases, this can lead to a poor performance, as a severe loss of diversity occurs.

This paper suggests a selection mechanism to guide the search in the objective space focusing on maintaining the population diversity. For this purpose, the objective space is divided into a set of grids using polar coordinates. A proper distribution of the population is ensured by maintaining individuals in corresponding grids. Eventual similarities between individuals belonging to neighboring grids are explored. The convergence is ensured by minimizing the distances from individuals in the population to a reference point. The experimental results show that the proposed approach can solve a set of problems producing competitive performance when compared with state-of-the-art algorithms. The ability of the proposed selection to maintain diversity during the evolution appears to be indispensable for dealing with some problems, allowing to produce significantly better results than other considered approaches relying on different selection strategies.