Large-scale overlapping problems are prevalent in practical engineering applications, and the optimization challenge is significantly amplified due to the existence of shared variables. Decomposition-based cooperative coevolution (CC) algorithms have demonstrated promising performance in addressing large-scale overlapping problems. However, current CC frameworks designed for overlapping problems rely on grouping methods for the identification of overlapping problem structures and the current grouping methods for large-scale overlapping problems fail to consider both accuracy and efficiency simultaneously. In this article, we propose a two-stage enhanced grouping method for large-scale overlapping problems, called OEDG, which achieves accurate grouping while significantly reducing computational resource consumption. In the first stage, OEDG employs a grouping method based on the finite differences principle to identify all subcomponents and shared variables. In the second stage, we propose two grouping refinement methods, called subcomponent union detection (SUD) and subcomponent detection (SD), to enhance and refine the grouping results. SUD examines the information of the subcomponents and shared variables obtained in the previous stage, and SD corrects inaccurate grouping results. To better verify the performance of the proposed OEDG, we propose a series of novel benchmarks that consider various properties of large-scale overlapping problems, including the topology structure, overlapping degree, and separability. Extensive experimental results demonstrate that OEDG is capable of accurately grouping different types of large-scale overlapping problems while consuming fewer computational resources. Finally, we empirically verify that the proposed OEDG can effectively improve the optimization performance of diverse large-scale overlapping problems.

翻译：大规模重叠问题在实际工程应用中普遍存在，由于共享变量的存在，其优化难度显著增加。基于分解的协同进化算法在解决大规模重叠问题上展现出良好性能。然而，当前针对重叠问题的协同进化框架依赖分组方法识别重叠问题结构，且现有的大规模重叠问题分组方法无法同时兼顾准确性与效率。本文提出了一种面向大规模重叠问题的两阶段增强型分组方法OEDG，该方法在实现精确分组的同时显著降低了计算资源消耗。在第一阶段，OEDG采用基于有限差分原理的分组方法识别所有子组件和共享变量。在第二阶段，我们提出了两种分组精化方法——子组件联合检测（SUD）和子组件检测（SD），以增强和细化分组结果。SUD用于检查前一阶段获得的子组件与共享变量信息，而SD则修正不准确的分组结果。为更好地验证所提OEDG方法的性能，我们提出了一系列新型基准测试，这些基准测试考虑了大规模重叠问题的多种特性，包括拓扑结构、重叠度和可分离性。大量实验结果表明，OEDG能够以更少的计算资源消耗实现对不同类型大规模重叠问题的精确分组。最后，我们通过实证验证了所提出的OEDG能有效提升多种大规模重叠问题的优化性能。