A New Many-Objective Evolutionary Algorithm Based on Generalized Pareto Dominance
A New Many-Objective Evolutionary Algorithm Based on Generalized Pareto Dominance
复制标题
一种基于广义Pareto优势的新多目标进化算法
DOI：
10.1109/tcyb.2021.3051078
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发表时间：
2021
影响因子：
11.8
通讯作者：
Zhichao Lu
中科院分区：
文献类型：
--
作者：
Shuwei Zhu;Lihong Xu;E. Goodman;Zhichao Lu
在过去的几年中，它已经变得很明显，帕累托优势为基础的多目标进化算法的有效性逐渐恶化的问题中的目标的数量，由<inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>，增长。这主要是由于帕累托最优性在多目标空间（通常为<inline-formula><tex-math notation="LaTeX">$M\geq 4$</tex-math></inline-formula>）中的可辨别性较差。因此，研究工作已经朝着开发不依赖于帕累托优势的解决方案排名方法的一般方向进行（例如，基于分解的技术），这可以提供足够的选择压力。然而，它仍然是一个重要的问题，许多现有的非Pareto优势为基础的进化算法来处理未知的不规则的Pareto前沿形状。本文提出了一种基于Pareto最优性推广的多目标进化算法，该算法简单有效，可用于求解多目标优化问题。该算法在环境选择步骤中采用“（<inline-formula><tex-math notation="LaTeX">$M-1$</tex-math></inline-formula>）+ 1”的遗传优势框架（简称（<inline-formula><tex-math notation="LaTeX">$M-1$</tex-math></inline-formula>）-GPD）对解进行排序，以同时促进收敛性和多样性。具体来说，我们应用<inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>对称的情况下（<inline-formula><tex-math notation="LaTeX">$M-1$</tex-math></inline-formula>）-GPD，其中每个增强选择压力<inline-formula><tex-math notation="LaTeX">的$M-1$的</tex-math></inline-formula>目标，通过扩大优势领域的解决方案，而保持不变的一个目标离开了该过程。实验表明，该算法是非常有竞争力的国家的最先进的方法，它相比，在各种可扩展的基准问题。此外，三个现实世界的问题上的实验已经验证了所提出的算法可以优于其他对这些问题。
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 <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>, grows. This is mainly due to the poor discriminability of Pareto optimality in many-objective spaces (typically <inline-formula> <tex-math notation="LaTeX">$M\geq 4$ </tex-math></inline-formula>). 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 “(<inline-formula> <tex-math notation="LaTeX">$M-1$ </tex-math></inline-formula>) + 1” framework of GPO dominance, (<inline-formula> <tex-math notation="LaTeX">$M-1$ </tex-math></inline-formula>)-GPD for short, to rank solutions in the environmental selection step, in order to promote convergence and diversity simultaneously. To be specific, we apply <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> symmetrical cases of (<inline-formula> <tex-math notation="LaTeX">$M-1$ </tex-math></inline-formula>)-GPD, where each enhances the selection pressure of <inline-formula> <tex-math notation="LaTeX">$M-1$ </tex-math></inline-formula> 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.