MaOEA/d2:一种基于双距离构造的高维多目标进化算法

传统的基于Pareto支配关系的多目标进化算法(MOEA)难以有效求解高维多目标优化问题(MaOP). 提出一种利用PBI效用函数的双距离构造的支配关系, 且无需引入额外的参数. 其次, 利用双距离定义了一种多样性保持方法, 该方法不仅考虑了解个体的双距离, 而且还可以根据优化问题的目标数目自适应地调整多样性占比, 以较好地平衡高维目标解群的收敛性和多样性. 最后, 将基于双距离构造的支配关系和多样性保持方法嵌入到NSGA-II算法框架中, 设计了一种基于双距离的高维多目标进化算法MaOEA/d². 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和WFG基准测试问题上进行了IGD和HV性能测试, 结果表明, MaOEA/d²算法具有较好的收敛性和多样性. 由此表明, MaOEA/d²算法是一种颇具前景的高维多目标进化算法.

MaOEA/d2: Many-objective Evolutionary Algorithm Based on Double Distances

It is difficult to solve many-objective optimization problems (MaOPs) effectively by using the traditional multi-objective evolutionary algorithms (MOEAs) based on Pareto dominance relation. A dominance relation is proposed firstly by combing double distances of PBI utility function without introducing extra parameter. Secondly, a diversity maintenance method based on double distances is also defined, which not only considers the double distances of the individual, but also adaptively adjusts the weight of diversity according to the objective number of MaOP, so as to better balance the convergence and diversity of the solution set in many-objective space. Finally, the proposed dominance relation and diversity maintenance method are embedded into the framework of NSGA-II, and then a many-objective evolutionary algorithm based on double distances (MaOEA/d²) is designed. The MaOEA/d² is compared with other five representative many-objective evolutionary algorithms on the DTLZ and WFG benchmark functions with 5-,10-,15-, and 20-objective in terms of IGD and HV indicators. The empirical results show that MaOEA/d²can obtain better convergence and diversity. Therefore, the proposed MaOEA/d²is a promising many-objective evolutionary algorithm.