In multimodal multiobjective optimization problems, multiple Pareto optimal sets, even some good local Pareto optimal sets, should be reserved, which can provide more choices for decision-makers. To solve MMOPs, this paper proposes an evolutionary algorithm with clustering-based assisted selection strategy for multimodal multiobjective optimization, in which the addition operator and deletion operator are proposed to comprehensively consider the diversity in both decision and objective spaces. Specifically, in decision space, the union population is partitioned into multiple clusters by using a density-based (...) clustering method, aiming to assist the addition operator to strengthen the population diversity. Then, a number of weight vectors are adopted to divide population into N subregions in objective space. Moreover, in the deletion operator, the solutions in the most crowded subregion are first collected into previous clusters, and then the worst solution in the most crowded cluster is deleted until there are N solutions left. Our algorithm is compared with other multimodal multiobjective evolutionary algorithms on the well-known benchmark MMOPs. Numerical experiments report the effectiveness and advantages of our proposed algorithm. (shrink)

This paper proposes a constrained solution update strategy for multiobjective evolutionary algorithm based on decomposition, in which each agent aims to optimize one decomposed subproblem. Different from the existing approaches that assign one solution to each agent, our approach allocates the closest solutions to each agent and thus the number of solutions in an agent may be zero and no less than one. Regarding the agent with no solution, it will be assigned one solution in priority, once offspring are generated (...) closest to its subproblem. To keep the same population size, the agent with the largest number of solutions will remove one solution showing the worst convergence. This improves diversity for one agent, while the convergence of other agents is not lowered. On the agent with no less than one solution, offspring assigned to this agent are only allowed to update its original solutions. Thus, the convergence of this agent is enhanced, while the diversity of other agents will not be affected. After a period of evolution, our approach may gradually reach a stable status for solution assignment; i.e., each agent is only assigned with one solution. When compared to six competitive multiobjective evolutionary algorithms with different population selection or update strategies, the experiments validated the advantages of our approach on tackling two sets of test problems. (shrink)