MM-NAEMO : Multimodal Neighborhood-sensitive Archived Evolutionary Many-objective Optimization Algorithm

In certain multi-objective optimization problems, it may happen that there are two or more different Pareto optimal sets corresponding to the exact same Pareto Front. These are known as multimodal multi-objective optimization problems (MMOPs). Algorithms which are able to generate all the Pareto sets can provide more flexibility in choosing solutions and therefore a possible improvement in the performance. In this work, we build upon the original framework of NAEMO (Neighborhood-sensitive Archived Evolutionary Many-objective Optimization Algorithm) and present Multimodal NAEMO (MM-NAEMO). In MM-NAEMO, the mutation occurs between the points which are local neighbors and each reference line always keeps at least two or more candidate solutions associated with it. Clustering is used to maintain the diversity in the population associated with each reference line, thus providing multiple Pareto sets as output. The algorithm is tested on the test problems of MMO test suite of CEC2019. The experimental results suggest that the proposed algorithm effectively finds majority of the Pareto sets without hampering the Pareto fronts for most of the problems.