DAV-MOEA:一种采用动态角度向量支配关系的高维多目标进化算法  

DAV-MOEA:A Many-Objective Evolutionary Algorithm Adopting Dynamic Angle Vector Based Dominance Relation

作　　者：谢承旺 余伟伟 郭华 张伟 张琼冰 XIE Cheng-Wang;YU Wei-Wei;GUO Hua;ZHANG Wei;ZHANG Qiong-Bing(School of Data Science&Engineering,South China Normal University,Shanwei,Guangdong 516600;College of Computer and Information Engineering,Nanning Normal University,Nanning 530100;School of Computer Science and Engineering,Beihang University,Beijing 100191;School of Science,East China Jiaotong University,Nanchang 330013;School of Computer Science and Engineering,Hunan University of Science and Technology,Xiangtan,Hunan 411201)

机构地区：[1]华南师范大学数据科学与工程学院,广东汕尾516600 [2]南宁师范大学计算机与信息工程学院,南宁530100 [3]北京航空航天大学计算机学院,北京100191 [4]华东交通大学理学院,南昌330013 [5]湖南科技大学计算机科学与工程学院,湖南湘潭411201

出　　处：《计算机学报》2022年第2期317-333,共17页Chinese Journal of Computers

基　　金：国家自然科学基金项目(61763010,61802125,12161039);广西自然科学基金项目(2021GXNSFAA075011);广西“八桂学者”项目(厅[2016]21号);江西省自然科学基金项目20212ACB211002);湖南省自然科学基金青年项目(2020JJ5202);湖南省教育厅科研项目(18C0331);广西研究生教育创新计划资助项目(YCSW2020194)资助.

摘　　要：现实中不断涌现的高维多目标优化问题对传统的基于Pareto支配的多目标进化算法构成巨大挑战.一些研究者提出了若干改进的支配关系,但仍难以有效地平衡高维多目标进化算法的收敛性和多样性.提出一种动态角度向量支配关系动态地刻画进化种群在高维目标空间的分布状况,以较好地在收敛性与多样性之间取得平衡;另外,提出一种改进的基于L_(p-)范式(p<1)的拥挤距离度量方法以有效地度量高维目标空间中解群的多样性.设计了一种采用动态角度向量支配关系的高维多目标进化算法DAV-MOEA,该算法利用动态角度向量支配关系增强选择压力,运用改进的基于L_(p-)范式(p<1)的拥挤距离维持解群的多样性.实验研究了动态角度向量支配关系、改进的拥挤距离方法以及DAV-MOEA算法在5-、8-和10-目标的DTLZ和WFG基准测试实例上的IGD与HV指标性能.实验结果表明,动态角度向量支配关系、改进的拥挤距离方法和DAV-MOEA算法在高维目标空间中能够获得显著较优或颇具竞争力的收敛性和多样性.由此表明所提出的支配关系、拥挤距离度量方法和DAV-MOEA算法在高维目标空间中颇具前景.More and more many-objective optimization problems(MaOPs)are presented in the real-world,which pose a stiff challenge to the conventional Pareto based multi-objective evolutionary algorithms(MOEAs).Some researchers have proposed some modified dominance relations for solving MaOPs by modifying the Pareto dominance relation.However,these modified ones still have difficulties in balancing the convergence and diversity.A dynamic angle vector based dominance relation(DAV)is proposed to dynamically describe the distribution of evolutionary populations in the objective space to better balance the convergence and diversity.In addition,a modified simplified Harmonic normalized crowding distance method based on L_(p-)norm(p<1)(SHND-L p)is also proposed to measure the diversity in many-objective space more effectively and efficiently.Based on the above,a many-objective evolutionary algorithm based on DAV and SHND-L p(DAV-MOEA)is developed to solve MaOPs.Several experiments are conducted to validate the performance of the DAV,SHND-L p,and DAV-MOEA in terms of IGD and HV indicators on the 5-,8-,and 10-objective DTLZ and WFG benchmark test instances.The empirical results demonstrate that the DAV,SHND-L p,and DAV-MOEA can obtain significantly superior or competitive performance in terms of convergence and diversity in solving MaOPs.Overall,the DAV,SHND-L p,and DAV-MOEA are promising in solving MaOPs.

关 键 词：动态角度向量支配关系 高维多目标优化 进化算法 多样性 收敛性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]