基于目标迁移和条件替代的高维多目标进化算法

尽管许多高维多目标进化算法已被提出,但大多仍无法有效处理具有不规则Pareto前沿的高维多目标优化问题.鉴于此,提出基于目标迁移和条件替代的高维多目标进化算法(MaOEA-OTCR),在环境选择过程中利用目标迁移策略和条件替代准则协作逐一选择收敛性和多样性好的个体进入下一代.前者首先选择位于Pareto前沿边界的极值解进入下一代,以确定Pareto前沿的范围,同时选择收敛性最好的若干个体进入下一代,以加速种群收敛;然后迁移已选解集且利用迁移解集和未迁移解集的最大距离来选择收敛性和多样性好的个体进入下一代.后者利用基于角度和收敛性评估的条件取代准则来防止前者过度强调多样性.此外,提出一个多标准决策的匹配选择策略,旨在增加具有良好收敛性和多样性种群个体结合的概率,进一步提升算法的搜索效率.为了验证MaOEA-OTCR的有效性,在3个测试集上与8个先进的高维多目标进化算法进行对比实验.实验结果表明, MaOEA-OTCR在处理高维多目标优化问题时不仅能够获得较强的竞争性能,而且有能力处理具有不规则Pareto前沿的高维多目标优化问题.

Many-objective evolutionary algorithm based on objective transferring and condition replacement

Although lots of many-objective evolutionary algorithms have been proposed, most of them cannot effectively deal with many-objective optimization problems with irregular Pareto fronts. In view of the issue, this paper proposes a many-objective evolutionary algorithm based on objective transferring and conditional replacement(MaOEA-OTCR). In the procedure of environmental selection, this algorithm utilizes the designed objective transferring strategy and the developed conditional replacement criterion to select individuals with good convergence and diversity one by one. Specifically, the former first selects these individual located at the boundary of Pareto fronts for determining the boundary of Pareto fronts, while picking out several individuals with better convergence for accelerating the population convergence. Then, it transfers these individuals entered the next generation, and uses the maximum distance between transferred individuals and not transferred individuals to select individuals for the next generation. The latter utilizes the developed conditional replacement criterion based angle and convergence measure to avoid that the former overemphasizes the population diversity. In addition, we propose a multi-criteria decision based mating selection mechanism, which aims at increasing the probability of individuals with favourable convergence and diversity combination, and further promotes the search efficiency of the MaOEA-OTCR. To verify the effectiveness of the MaOEA-OTCR, the MaOEA-OTCR is compared with eight state-of-the-art MaOEAs on three test suites. Experimental results demonstrate that the MaOEA-OTCR not only obtains the highly competitive performance in dealing with many-objective optimization problems, but also has ability to solve many-objective optimization problems with irregular Pareto fronts.