Although the multiobjective evolutionary algorithms (MOEAs) have been proved to bring promising prospects for solving multiobjective optimization problems (MOPs), the performance of the algorithm deteriorates sharply in high-dimensional objective space due to the weak selection pressure and the unregulated balance, which is caused by the increase of objective space dimension. Some current MOEAs with two-stage strategy (TS) strive to address above issues by dividing the evolutionary process into two independent stages, in which convergence and diversity are handled separately within successive generations of different stages. However, TS-MOEAs have some weaknesses, such as sensitivity to stage division, and incomplete separation of convergence and diversity. In this paper, TS/KW-MaOEA is proposed for solving many-objective optimization problems (MaOPs), which keeps TS as the central and equips a perfect control mechanism for separated balance. More specifically, TS/KW-MaOEA can automatically adjust the balance trend and provide appropriate selection pressure for MaOPs according to the Kondratiev wave (KW) search model and the objective space dimension. To verify the effectiveness of the proposed algorithm, a series of experiments are carried out against seven state-of-the-art many-objective optimization algorithms on 15 benchmark problems with up to 30 objectives. Experimental results indicate that the proposed algorithm is highly competitive against peer competitors.

尽管多目标进化算法（MOEA）已被证明为解决多目标优化问题（MOP）带来了良好的前景，但由于弱选择压力和不受调节的平衡，算法的性能在高维目标空间中急剧恶化，是由于客观空间维度的增加造成的。目前一些采用两阶段策略（TS）的 MOEA 致力于通过将进化过程分为两个独立的阶段来解决上述问题，其中收敛性和多样性在不同阶段的连续几代中分别处理。然而，TS-MOEA 也存在一些弱点，例如对阶段划分敏感、收敛性与多样性分离不完全等。本文提出了TS/KW-MaOEA来解决多目标优化问题(MaOPs)，它以TS为中心，并配备了完善的分离平衡控制机制。更具体地说，TS/KW-MaOEA可以根据康德拉季耶夫波（KW）搜索模型和目标空间维度自动调整平衡趋势，并为MaOP提供适当的选择压力。为了验证所提出算法的有效性，针对 7 种最先进的多目标优化算法，针对 15 个基准问题（最多 30 个目标）进行了一系列实验。实验结果表明，所提出的算法相对于同行竞争者具有很强的竞争力。