Ming Fei, Gong Wenyin, Wang Ling, Gao Liang
IEEE Trans Cybern. 2023 Aug;53(8):4934-4946. doi: 10.1109/TCYB.2022.3151793. Epub 2023 Jul 18.
Unlike the considerable research on solving many-objective optimization problems (MaOPs) with evolutionary algorithms (EAs), there has been much less research on constrained MaOPs (CMaOPs). Generally, to effectively solve CMaOPs, an algorithm needs to balance feasibility, convergence, and diversity simultaneously. It is essential for handling CMaOPs yet most of the existing research encounters difficulties. This article proposes a novel constrained many-objective optimization EA with enhanced mating and environmental selections, namely, CMME. It can be featured as: 1) two novel ranking strategies are proposed and used in the mating and environmental selections to enrich feasibility, diversity, and convergence; 2) a novel individual density estimation is designed, and the crowding distance is integrated to promote diversity; and 3) the θ -dominance is used to strengthen the selection pressure on promoting both the convergence and diversity. The synergy of these components can achieve the goal of balancing feasibility, convergence, and diversity for solving CMaOPs. The proposed CMME is extensively evaluated on 13 CMaOPs and 3 real-world applications. Experimental results demonstrate the superiority and competitiveness of CMME over nine related algorithms.
与利用进化算法（EAs）解决多目标优化问题（MaOPs）的大量研究不同，针对约束多目标优化问题（CMaOPs）的研究要少得多。一般来说，为了有效解决CMaOPs，算法需要同时平衡可行性、收敛性和多样性。这对于处理CMaOPs至关重要，但现有的大多数研究都遇到了困难。本文提出了一种具有增强交配和环境选择的新型约束多目标优化进化算法，即CMME。它具有以下特点：1）提出了两种新颖的排序策略，并将其用于交配和环境选择，以丰富可行性、多样性和收敛性；2）设计了一种新颖的个体密度估计方法，并结合拥挤距离来促进多样性；3）使用θ-支配来加强在促进收敛性和多样性方面的选择压力。这些组件的协同作用可以实现平衡可行性、收敛性和多样性以解决CMaOPs的目标。所提出的CMME在13个CMaOPs和3个实际应用中进行了广泛评估。实验结果证明了CMME相对于九种相关算法的优越性和竞争力。
