基于分解的差分进化算法求解多模态多目标优化问题  

A decomposition-based differential evolution algorithm for multimodal multi-objective optimization

作　　者：杨雪洲 徐伟 王琼 李龙跃[3] 高晓利[1] 高富豪 YANG Xuezhou;XU Wei;WANG Qiong;LI Longyue;GAO Xiaoli;GAO Fuhao(Sichuan Jiuzhou Electric Appliance Group Co.Ltd,Mianyang 621000,Sichuan,China;School of Mathematics and Statistics,Xidian University,Xi'an 710126,Shaanxi,China;College of Air Defense and Missile Defense,Air Force Engineering University,Xi'an 710051,Shaanxi,China)

机构地区：[1]四川九洲电器集团有限责任公司,四川绵阳621000 [2]西安电子科技大学数学与统计学院,陕西西安710126 [3]空军工程大学防空反导学院,陕西西安710051

出　　处：《陕西师范大学学报(自然科学版)》2025年第1期103-113,共11页Journal of Shaanxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(61772391)。

摘　　要：针对多模态多目标优化问题求解时难以获得多个Pareto解集的问题,提出了一种基于分解的差分进化算法。在所提算法中,为了寻找多个不同的Pareto解集,将分配给同一权重向量的多个个体划分成同一子种群。然后,设计了一种环境选择方法定位子种群中等价的Pareto最优解。最后,采用两种差分进化策略更新种群搜索最优解。对IEEE CEC 2019基准测试集的仿真实验结果表明,所提算法在决策空间上具有良好的分布性,且能获得更多的Pareto最优解。Aiming at the disadvantage that it is hard to obtain multiple Pareto sets in solving multimodal multi-objective optimization problems,a decomposition-based differential evolution algorithm is presented.In the proposed algorithm,multiple individuals that are assigned to the same weight vector form a subpopulation for finding multiple different Pareto sets.Then,an environmental selection method is designed to locate multiple different Pareto optimal solutions in the subpopulation.Finally,two differential evolution strategies are utilized to generate the offspring.The simulation results of the IEEE CEC 2019 benchmark test suite show that the proposed algorithm has good distribution ability in the decision space and can find more Pareto optimal solutions.

关 键 词：多模态多目标优化 分解 子种群 差分进化 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]