中文摘要：

高维多目标优化问题普遍存在且难以解决,到目前为止,尚缺乏有效解决该问题的进化优化方法.本文提出一种基于目标分解的高维多目标并行进化优化方法,首先,将高维多目标优化问题分解为若干子优化问题,每一子优化问题除了包含原优化问题的少数目标函数之外,还具有由其他目标函数聚合成的一个目标函数,以降低问题求解的难度;其次,采用多种群并行进化算法,求解分解后的每一子优化问题,并在求解过程中,充分利用其他子种群的信息,以提高Pareto非被占优解的选择压力;最后,基于各子种群的非被占优解形成外部保存集,从而得到高维多目标优化问题的Pareto最优解集.性能分析表明,本文提出的方法具有较小的计算复杂度.将所提方法应用于多个基准优化问题,并与NSGA-II、PPD-MOEA、ε-MOEA、Hyp E和MSOPS等方法比较,实验结果表明,所提方法能够产生收敛性、分布性,以及延展性优越的Pareto最优解集.

英文摘要：

Many-objective optimization problem is common in real-world applications, however, so far few evolutionary algorithms are suitable for them due to the difficulties of the problem. A parallel many-objective evolutionary optimization algorithm based on objectives decomposition is proposed. First, the many-objective optimization problem is decomposed into several sub-problems, which contain only some objectives of the original optimization problem together with a constructed objective by aggregating all the other objectives. Then, a multi-population parallel evolutionary algorithm is adopted to solve these sub-problems. The pressure on selecting non-dominated solutions for a sub-problem is improved by taking full advantage of the information obtained from other sub-populations. The final Pareto set of the optimized many-objective is achieved by archiving those sets of non-dominated solutions coming from the sub-populations. The performance of the proposed algorithm on reducing computation complexity is qualitatively analyzed. Furthermore, the algorithm is applied to several benchmark problems and compared with NSGA-II, PPD-MOEA, ε-MOEA, HypE, and MSOPS. The results experimentally demonstrate that the algorithm is strengthened in obtaining solutions with better convergence, distribution and approximation.