MaOEA/A2R:一种基于A2R支配关系的高维多目标进化算法

MaOEA/A2R:A Many-Objective Evolutionary Algorithm Based on A2R Dominance Relation

传统的Pareto支配关系在高维目标空间存在固有缺陷,而一些改进的支配方法在平衡高维目标解群的收敛性与多样性上尚有提升空间.基于此,提出一种参考向量关联区域(小生境)自动缩减的支配关系A2R(dominance relation based on the Automatically reduced region Associated with the Reference vector).该支配方法在进化全过程中逐代缩减小生境规模,从而实现收敛性与多样性自动平衡,而且不引入额外参数.另外,提出利用基于Lp-范式(p=1/M,M为目标数)的拥挤距离度量高维目标解群的多样性.将上述两种策略嵌入到经典的NSGA-II(Nondominated Sorting Genetic Algorithm II)框架,设计一种基于A2R支配关系的高维多目标进化算法MaOEA/A2R(Many-Objective Evolutionary Algorithm base on A2R).该算法与其他5种代表性的高维多目标进化算法一同在5-、10-、15-和20-目标的DTLZ(benchmark MOP proposed by Deb,Thiele,Lau-manns,and Zitzler)和WFG(benchmark MOP pro-posed by Walking Fish Group)基准测试问题上进行IGD(Inverted Generational Distance)和HV(Hyper Volume)性能测试.结果表明,MaOEA/A2R算法总体上具有较好的收敛性和多样性.由此表明,MaOEA/A2R是一种颇具前景的高维多目标进化算法.

There exist some inherent defects in the traditional Pareto dominance relation in many-objective optimiza⁃tion space,while some modified dominance relations have much room for improvement in balancing the convergence and diversity of many-objective evolutionary population.Based on this,a new dominance relation(dominance relation based on the Automatically reduced region Associated with the Reference vector,A2R)automatically shrinks the region(niche)asso⁃ciated with the reference vector.Specially,it reduces the size of the niche from generation to generation along the whole evolutionary process in order to achieve a balance of convergence and diversity adaptively.Furthermore,the A2R does not introduce any additional parameter.In addition,the crowding distance measure based on Lp-normal form(p equals 1/M,and M denotes the number of objectives)is used to improve the diversity of the solution set in many-objective space.Finally,the above two strategies are embedded into the framework of NSGA-II(Nondominated Sorting Genetic Algorithm II),and then a many-objective evolutionary algorithm based on A2R(MaOEA/A2R)is designed.The MaOEA/A2R is compared with other five representative many-objective evolutionary algorithms(MaOEAs)on the DTLZ and WFG benchmark functions with 5-,10-,15-,and 20-objective in terms of IGD(Inverted Generational Distance)and HV(HyperVolume)indicators.The empirical results overally show that MaOEA/A2R can obtain better convergence and diversity.Therefore,the proposed MaOEA/A2R is a promising many-objective evolutionary algorithm.