基于全局密度更新策略的两阶段多模态多目标进化算法  

Two-stage multimodal multi-objective evolutionary algorithm based on global density updating strategy

作　　者：贺娟娟 杨倩[1,2] 许志伟 张凯[1,2] 张兴义[3] 葛明峰 Juanjuan HE;Qian YANG;Zhiwei XU;Kai ZHANG;Xingyi ZHANG;Mingfeng GE(School of Computer Science and Technology,Wuhan University of Science and Technology,Wuhan 430065,China;Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System,Wuhan University of Science and Technology,Wuhan 430065,China;School of Computer Science and Technology,Anhui University,Hefei 230093,China;School of Mechanical Engineering and Electronic Information,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]武汉科技大学计算机科学与技术学院,武汉430065 [2]武汉科技大学智能信息处理与实时工业系统湖北省重点实验室,武汉430065 [3]安徽大学计算机科学与技术学院,合肥230093 [4]中国地质大学(武汉)机械与电子信息学院,武汉430074

出　　处：《中国科学：信息科学》2024年第10期2385-2408,共24页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:62272355,62176191,61702383,62473349);智能信息处理与实时工业系统湖北省重点实验室开放基金(批准号:ZNXX2023ZD01)资助项目。

摘　　要：多模态多目标问题需要求解多个全局或局部最优帕累托解集,找到这些最优解集具有极大的理论意义和实际经济效益.近年来,学者们提出许多进化算法用于解决该问题.然而,多数算法在进化过程中首先选择收敛性好的个体构建交配池,然后再考虑决策空间和目标空间的多样性.因此,决策空间中多样性好的个体可能被目标空间收敛性好的个体所替代.另外,由于帕累托最优子集在决策空间中有不同的形状和位置,因此个体很难均匀地收敛到每个帕累托子区域.本文提出了基于全局密度更新策略的两阶段多模态多目标进化算法.首先,为减轻交配池和亲本与子代一对一比较的负面影响,我们并不构建交配池,而是提出了新的算法框架,分两阶段寻优.该框架利用不同阶段进化算法的特征进行子代更新,有利于平衡种群的搜索和开发.然后,为了解决帕累托子集分布不均的问题,我们设计了目标空间密度自适应策略和全局密度估计更新种群策略,用于保持目标空间和决策空间种群多样性.我们将提出的算法与7种有代表性的多模态多目标算法进行比较.实验结果表明,我们的算法在决策空间中能找到更多等价的解,并且能更好地保持决策空间和目标空间多样性和收敛性的平衡,整体性能要好于所比较算法.Multimodal multi-objective problems involve identifying global and local optimal Pareto solution sets.Providing decision-makers with comprehensive Pareto sets is crucial for theoretical understanding and practical application.In recent years,numerous evolutionary algorithms have been proposed to address these issues.However,most of these algorithms first select individuals based on their convergence properties to form mating pools and then consider individuals with good diversity in decision and objective spaces.This method often leads to the replacement of individuals with characteristics in the decision space by those who exhibit strong convergence in the objective area.Additionally,achieving uniform convergence of individuals to each Pareto subregion is challenging because of the varying shapes and positions of Pareto optimal subsets in the decision space.In this paper,we introduce a novel two-stage multimodal multi-objective evolutionary algorithm that employs a global density updating strategy.First,we propose an alternative two-stage optimization framework to address the limitations of traditional mating pools and one-to-one parent-progeny comparisons.The proposed framework dynamically adjusts the population size at different stages and uses distinct optimization methods,promoting a balanced exploration and exploitation of the population.Second,to resolve the uneven distribution of Pareto subsets,we designed adaptive and global density estimation strategies that update the objective space density and population.These mechanisms ensure the maintenance of diversity within the objective and decision spaces.We compared the proposed algorithm with seven representative multimodal multi-objective algorithms.The experimental results demonstrate that the proposed algorithm finds equivalent solutions in the decision space and effectively balances diversity and convergence between the decision and objective space.Overall,the proposed algorithm outperforms the compared algorithms.

关 键 词：多目标进化算法 多模态多目标优化问题 进化算法 全局密度 参考向量 边界点聚集 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]