一种基于信息分离的高维多目标进化算法

摘要

高维多目标优化是指对目标维数大于三维的多目标问题(multi-objective optimization problem,简称MOP)进行优化.大多数传统的多目标进化算法采用 Pareto 支配关系指导搜索,很难在高维多目标优化问题上得到较为理想的结果.为此,提出了一种基于信息分离的高维多目标进化算法(multi-objective evolutionary algorithm based on information separation,简称ISEA).该算法在目标空间中将原坐标系进行旋转,使第1条坐标轴与向量(1,1,…,1)T平行.ISEA定义转换坐标的第1个坐标值为收敛信息(convergence information,简称CI),剩余的坐标代表个体分布信息(diversity information,简称DI).同时,采用一种基于分层选择的邻域惩罚机制,利用一种由两个超圆锥组成的邻域形状保持种群的分布性,当个体被选入归档集后,其邻域内的个体将被惩罚进入下一层选择,防止邻近的个体同时被选入归档集.邻域形状的第 1 部分利用分布信息覆盖邻近的个体,第 2 部分覆盖边界上的差个体.与 NNIA,ε-MOEA, MSOPS,AR+DMO以及IBEA这5种经典算法进行了比较.实验结果表明,ISEA在处理高维多目标优化问题时具有良好的收敛性和分布性.%Many-Objective optimization refers to optimizing the multi-objective optimization problems (MOPs) where the number of objectives is more than three. Most classical multi-objective evolutionary algorithms (MOEAs) use the Pareto dominance relation to guide the search and thus are hard to perform well in many-objective optimization problems. In this paper, a multi-objective evolutionary algorithm based on information separation (ISEA) is proposed. ISEA rotates the original coordinate system in the objective space, and makes the first axis parallel to the vector (1,1,…,1)T. The first member of the new coordinate is defined as convergence information, andthe remaining members are defined as diversity information. Moreover, a neighborhood penalty mechanism based on layered selection is adopted using the information of the neighborhood shape made of two hyper-cones to maintain the diversity of individuals. The first hyper-cone is used to cover neighbors, and the second one to cover extreme individual whose convergence performs significantly worse than others. Additionally, after an individual is selected into the archive set, its neighbors are punished into an inferior layer. From comparative experiments with other representative MOEAs, including NNIA,ε-MOEA, MSOPS, AR+DMO, and IBEA, the proposed algorithm is found to be successful in finding well-converged and well-distributed solution set.