Adaptive Convergence Indicator and Neighborhood Fuzzy Crowding Distance for Multimodal Multi-Objective Optimization

Multimodal multi-objective optimization is a popular research direction characterized by different points on different Pareto optimal solution sets (PSs) in the decision space, corresponding to the same point on the Pareto front in the objective space. In addition, there may exist some multimodal multi-objective optimization problems (MMOPs) with local PSs. Finding all the equivalent global PSs and local PSs is the key to solving MMOPs. To solve these problems, this paper proposes a multimodal multi-objective evolutionary algorithm (MMOEA) based on the adaptive convergence indicator and neighborhood fuzzy crowding distance (ACEA-NFCD). The adaptive convergence indicator is able to calculate the local convergence indicator and global convergence indicator through the adaptive selection of neighborhood knowledge, which can effectively preserve all global PSs and local PSs and exclude the interference of isolated solutions. Moreover, in order to increase the diversity of the population, neighborhood crowding distances in the decision space and the objective space are integrated via fuzzy set theory, improving the truncation and selection process. The superior performance of ACEA-NFCD is demonstrated by experimentally comparing it with nine of the most advanced MMOEAs on four benchmark suites and one practical application of map-based distance minimization.