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、HypE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。%Many-ob jective 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-ob jective 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 ob jectives 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.
展开▼
