MOEA/PC: Multiobjective Evolutionary Algorithm Based on Polar Coordinates Roman Denysiuk 1(B ) , Lino Costa 2 , Isabel Esp´ ırito Santo 2 , and Jos´ e C. Matos 3 1 Algoritmi R&D Center, University of Minho, Braga, Portugal roman.denysiuk@algoritmi.uminho.pt 2 Department of Production and Systems Engineering, University of Minho, Braga, Portugal {lac,iapinho}@dps.uminho.pt 3 Institute for Sustainability and Innovation in Structural Engineering, University of Minho, Braga, Portugal jmatos@civil.uminho.pt Abstract. The need to perform the search in the objective space con- stitutes 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 diver- sity 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 main- taining 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 pro- posed 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. 1 Introduction Evolutionary algorithms have gained popularity as a powerful tool for solving multiobjective optimization problems (MOPs) [1], [2]. They draw inspiration from the process of natural evolution to iteratively evolve to a better set of potential solutions. An important driving force behind evolution is natural selec- tion. It is the one process that is responsible for the evolution of adaptations c  Springer International Publishing Switzerland 2015 A. Gaspar-Cunha et al. (Eds.): EMO 2015, Part I, LNCS 9018, pp. 141–155, 2015. DOI: 10.1007/978-3-319-15934-8 10