基于子区域PBI支配选择算子的高维多目标优化

Many⁃objective Optimization Based on Sub⁃region PBI Selection Operator

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摘要针对现有多目标进化算法在高维多目标优化问题上选择压力不足,收敛性和多样性表现不平衡的问题,提出一种基于子区域惩罚边界交叉(PBI)支配选择算子的高维多目标进化算法MaOEA-SOS。其中,PBI支配策略增加了算法的选择压力,促进种群收敛,子区域划分操作将个体支配关系限制在子区域内,维护种群多样。MaOEA-SOS引入1个包含模拟二进制交叉算子和权重差分进化(WDE)算子的算子池,算法根据子区域PBI支配准则判断个体进化状态,从算子池中选择合适的进化算子,在进化过程中为每个解寻求探究和探索之间的平衡。WDE算子中包含一个根据函数计算量改变的权重因子,自适应控制WDE算子的搜索范围。为了增强WDE算子的鲁棒性,引入双精英存档机制。将MaOEA-SOS和5种代表性算法在15和20目标WFG测试集上进行对比。结果表明,18个测试问题中,MaOEA-SOS在12个测试问题上可获得收敛性和多样性更优的Pareto解集。 Aiming at the problem that the existing multi-objective evolutionary algorithms have insufficient selection pressure and unbalanced convergence and diversity performance in many-objective optimization problems,a many-objective evolutionary algorithm MaOEA-SOS based on sub-region penalty boundary intersection(PBI)dominant selection operator is proposed.Among them,PBI dominance strategy increases selection pressure of algorithm and promotes the convergence of population.The sub-region division operation limits individual dominance relationship to the sub-region and maintains diversity of the population.MaOEA-SOS introduces an operator pool containing simulated binary crossover(SBX)operator and weighted differential evolution(WDE)operator.The algorithm judges the individual evolution state according to subregion PBI dominance criterion,selects the appropriate evolution operator from operator pool,and seeks the balance between development and exploration for each solution during the evolution process.The WDE operator contains a weight factor that changes according to the amount of calculation of the function,and adaptively controls the search range of the WDE operator.In order to enhance the robustness of the WDE operator,a double elite archiving mechanism is introduced.MaOEA-SOS and five representative algorithms are compared on 15 and 20 objectives WFG test set.The results show that,a total of 18 test problems,MaOEA-SOS can obtain Pareto solution sets with better convergence and diversity on 12 test problems.

作者赵志伟解彦金熊志坚李涛邓家浩李桂梅 ZHAO Zhiwei;XIE Yanjin;XIONG Zhijian;LI Tao;DENG Jiahao;LI Guimei(North China University of Science and Technology,Tangshan,Hebei 063210,China;Tangshan University,Tangshan,Hebei 063000,China;Aerospace Wanyuan Cloud Data Hebei Co.,Ltd.,Tangshan,Hebei 063300,China;Tangshan Liran Machinery Manufacturing Co.,Ltd.,Tangshan,Hebei 063000,China)

机构地区华北理工大学唐山学院航天万源云数据河北有限公司唐山立冉机械制造有限公司

出处《计量学报》北大核心 2025年第8期1225-1232,共8页 Acta Metrologica Sinica

基金唐山市人才资助项目(A2021110015,A202203032,B202302007) 唐山市科技计划项目(21130213C,21130233C)。

关键词算法理论 PBI支配子区域算子选择动态权重因子精英存档高维多目标优化 algorithm theory PBI dominance sub‑region operator selection dynamic weighting factor elite archive many-objective optimization