融合分区和局部搜索的多模态多目标优化

为解决多模态多目标优化中种群多样性维持难和所得等价解数量不足问题，基于分区搜索和局部搜索，本研究提出一种融合分区和局部搜索的多模态多目标粒子群算法(multimodal multi-objective particle swarm optimization combing zoning search and local search，ZLS-SMPSO-MM)。在所提算法中，整个搜索空间被分割成多个子空间以维持种群多样性和降低搜索难度；然后，使用已有的自组织多模态多目标粒子群算法在每个子空间搜索等价解和挖掘邻域信息，并利用局部搜索能力较强的协方差矩阵自适应算法对有潜力的区域进行精细搜索。通过14个多模态多目标优化问题测试，并与其他5种知名算法进行比较；实验结果表明ZLS-SMPSO-MM在决策空间能够找到更多的等价解，且整体性能要好于所比较算法。

Multimodal multi-objective optimization combining zoning and local search

To maintain population diversity and find a sufficient number of equivalent solutions in multimodal multi-objective optimization, a multimodal multi-objective particle swarm optimization algorithm with zoning and local searches (ZLS-SMPSO-MM) is proposed in this study. In the proposed algorithm, which is based on zoning search and local search, the entire search space is divided into several subspaces to maintain population diversity and reduce search difficulty. Subsequently, an existing self-organizing multimodal multi-objective particle swarm algorithm is used to search equivalent solutions and mine neighborhood information in each subspace, and the covariance matrix adaptation algorithm, which has a better local search ability, is utilized for a refined search in promising regions. Lastly, the performance of ZLS-SMPSO-MM is tested on 14 multimodal multi-objective optimization problems and compared with that of other five state-of-the-art algorithms. Experimental results show that the proposed algorithm can find more equivalent solutions in the decision space and its overall performance is better than that of the compared algorithms.