MOEA/PC: multiobjective evolutionary algorithm based on polar coordinates


Denysiuk, Roman; Costa, L.; Espírito Santo, I. A. C. P.; Matos, José C.

The need to perform the search in the objective space constitutes one of the fundamental differencesbetween multiobjective and single-objective optimization. The performance of any multiobjectiveevolutionary algorithm (MOEA) is strongly related to the efficacy of its selection mechanism. Thepopulation convergence and diversity are two different but equally important goals that must be ensured bythe selection mechanism. Despite the equal importance of the two goals, the convergence is often used asthe first sorting criterion, whereas the diversity is considered as the second one. In some cases, this canlead 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 onmaintaining the population diversity. For this purpose, the objective space is divided into a set of gridsusing polar coordinates. A proper distribution of the population is ensured by maintaining individuals incorresponding grids. Eventual similarities between individuals belonging to neighboring grids areexplored. The convergence is ensured by minimizing the distances from individuals in the population to areference point. The experimental results show that the proposed approach can solve a set of problemsproducing competitive performance when compared with state-of-the-art algorithms. The ability of theproposed selection to maintain diversity during the evolution appears to be indispensable for dealing withsome problems, allowing to produce significantly better results than other considered approaches relyingon different selection strategies.