Zhu Shuwei, Xu Lihong, Goodman Erik D, Lu Zhichao
IEEE Trans Cybern. 2022 Aug;52(8):7776-7790. doi: 10.1109/TCYB.2021.3051078. Epub 2022 Jul 19.
In the past several years, it has become apparent that the effectiveness of Pareto-dominance-based multiobjective evolutionary algorithms deteriorates progressively as the number of objectives in the problem, given by M , grows. This is mainly due to the poor discriminability of Pareto optimality in many-objective spaces (typically M ≥ 4 ). As a consequence, research efforts have been driven in the general direction of developing solution ranking methods that do not rely on Pareto dominance (e.g., decomposition-based techniques), which can provide sufficient selection pressure. However, it is still a nontrivial issue for many existing non-Pareto-dominance-based evolutionary algorithms to deal with unknown irregular Pareto front shapes. In this article, a new many-objective evolutionary algorithm based on the generalization of Pareto optimality (GPO) is proposed, which is simple, yet effective, in addressing many-objective optimization problems. The proposed algorithm used an "( M-1 ) + 1" framework of GPO dominance, ( M-1 )-GPD for short, to rank solutions in the environmental selection step, in order to promote convergence and diversity simultaneously. To be specific, we apply M symmetrical cases of ( M-1 )-GPD, where each enhances the selection pressure of M-1 objectives by expanding the dominance area of solutions, while remaining unchanged for the one objective left out of that process. Experiments demonstrate that the proposed algorithm is very competitive with the state-of-the-art methods to which it is compared, on a variety of scalable benchmark problems. Moreover, experiments on three real-world problems have verified that the proposed algorithm can outperform the others on each of these problems.
在过去几年中，很明显，随着问题中目标数量（由M表示）的增加，基于帕累托支配的多目标进化算法的有效性会逐渐恶化。这主要是由于在多目标空间（通常M≥4）中帕累托最优的可区分性较差。因此，研究工作朝着开发不依赖帕累托支配的解决方案排序方法（例如基于分解的技术）的总体方向推进，这些方法可以提供足够的选择压力。然而，对于许多现有的基于非帕累托支配的进化算法来说，处理未知的不规则帕累托前沿形状仍然是一个重要问题。在本文中，提出了一种基于帕累托最优泛化（GPO）的新型多目标进化算法，该算法在解决多目标优化问题时简单而有效。所提出的算法在环境选择步骤中使用“(M - 1)+1”的GPO支配框架，简称为(M - 1)-GPD，对解决方案进行排序，以同时促进收敛和多样性。具体来说，我们应用(M - 1)-GPD的M种对称情况，其中每种情况通过扩大解决方案的支配区域来增强M - 1个目标的选择压力，而对于该过程中被排除的一个目标保持不变。实验表明，在所比较的各种可扩展基准问题上，该算法与最先进的方法相比具有很强的竞争力。此外，在三个实际问题上的实验验证了该算法在每个问题上都能优于其他算法。
