A decomposition and dynamic niching distance-based dual elite subpopulation evolutionary algorithm for multimodal multiobjective optimization

Solving multimodal multiobjective optimization problems(MMOPs) require obtaining multiple Pareto optimal solution sets (PSs). In recent years, researchers have proposed some multimodal multiobjective evolutionary algorithms (MMEAs), however, many existing MMEAs perform unsatisfactorily in dealing with complicated MMOPs, and even fail to find all Pareto solution sets in a stable manner. Many existing algorithms rely on globally optimal individuals to guide population evolution, which leads to the population rapidly converging to a few easy-to-find Pareto solution sets (PSs) and losing hard-to-find PSs. MMEAs that cannot consistently find all PSs are difficult to handle the increasing complexity of MMOPs. In order to address these problems, this research proposes a decomposition and dynamic niching distance-based dual elite subpopulation evolutionary algorithm, named MMEA-DES. In the proposed algorithm, decomposition-based methods are employed to maintain the diversity of the objective space of MMOPs, and a dynamic niching distance (DND) is proposed to calculate the crowding of the decision space. In addition, the dual elite subpopulations (DES) based on decomposition and DND are implemented to support the algorithm in obtaining well-distributed solutions in both decision space and objective space. To validate the performance of the proposed algorithm, a comparison with state-of-the-art algorithms on 23 test problems shows that the algorithm proposed in this research can stably solve various types of complicated MMOPs.