  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.
