基于分解的高维多目标改进进化算法

Improved high-dimensional many-objective evolutionary algorithm based on decomposition

针对基于参考向量的高维多目标进化算法中随机选择父代个体会降低算法的收敛速度,以及部分参考向量分配个体的缺失会减弱种群多样性的问题,提出了一种基于分解的高维多目标改进优化算法(IMaOEA/D)。首先,在分解策略框架下,当一个参考向量至少分配了2个个体时,对该参考向量分配的个体根据其到理想点的距离选择父代个体来繁殖子代,从而提高搜索速度。然后,针对未能分配到至少2个个体的参考向量,则从所有个体中选择沿该参考向量和理想点距离最小的点,使得该参考向量至少有2个个体与其相关。同时,确保环境选择后每个参考向量有一个个体与其相关,从而保证种群的多样性。在10个和15个目标的MaF测试问题集上将所提算法与其他4个基于分解的高维多目标优化算法进行了测试对比,实验结果表明所提算法对于高维多目标优化问题具有较好的寻优能力,且该算法在30个测试问题中的14个测试问题上得到的优化结果均优于其他4个对比算法,特别是对于退化问题具有一定的寻优优势。

In the reference vector based high-dimensional many-objective evolutionary algorithms,the random selection of parent individuals will slow down the speed of convergence,and the lack of individuals assigned to some reference vectors will weaken the diversity of population.In order to solve these problems,an Improved high-dimensional Many-Objective Evolutionary Algorithm based on Decomposition(IMaOEA/D)was proposed.Firstly,when a reference vector was assigned at least two individuals in the framework of decomposition strategy,the parent individuals were selected for reproduction of offspring according to the distance from the individual assigned to the reference vector to the ideal point,so as to increase the search speed.Then,for the reference vector that was not assigned at least two individuals,the point with the smallest distance from the ideal point along the reference vector was selected from all the individuals,so that at least two individuals and the reference vector were associated.Meanwhile,by guaranteeing one individual was related to each reference vector after environmental selection,the diversity of population was ensured.The proposed method was tested and compared with other four high-dimensional many-objective optimization algorithms based on decomposition on the MaF test problem sets with 10 and 15 objectives.Experimental results show that,the proposed algorithm has good optimization ability for high-dimensional many-objective optimization problems:the optimization results of the proposed algorithm on 14 test problems of the 30 test problems are better than those of the other four comparison algorithms.Especially,the proposed algorithm has certain advantage on the degradation problem optimization.