Cooperative co-evolution (CC) algorithms, based on the divide-and-conquer
strategy, have emerged as the predominant approach to solving large-scale
global optimization (LSGO) problems. The efficiency and accuracy of the
grouping stage significantly impact the performance of the optimization
process. While the general separability grouping (GSG) method has overcome the
limitation of previous differential grouping (DG) methods by enabling the
decomposition of non-additively separable functions, it suffers from high
computational complexity. To address this challenge, this article proposes a
composite separability grouping (CSG) method, seamlessly integrating DG and GSG
into a problem decomposition framework to utilize the strengths of both
approaches. CSG introduces a step-by-step decomposition framework that
accurately decomposes various problem types using fewer computational
resources. By sequentially identifying additively, multiplicatively and
generally separable variables, CSG progressively groups non-separable variables
by recursively considering the interactions between each non-separable variable
and the formed non-separable groups. Furthermore, to enhance the efficiency and
accuracy of CSG, we introduce two innovative methods: a multiplicatively
separable variable detection method and a non-separable variable grouping
method. These two methods are designed to effectively detect multiplicatively
separable variables and efficiently group non-separable variables,
respectively. Extensive experimental results demonstrate that CSG achieves more
accurate variable grouping with lower computational complexity compared to GSG
and state-of-the-art DG series designs.

合作共进化算法（CC）经过密切结合策略发展为解决大规模全局优化（LSGO）问题的主导方法，而其效率和准确性主要受到分组阶段的影响。本文提出了一种复合可分性分组（CSG）方法，将差分分组（DG）和一般分离分组（GSG）有机整合到问题分解框架中，充分发挥两种方法的优势，以应对高计算复杂度的挑战。CSG 引入了逐步分解框架，通过递归地考虑每个非可分变量与已形成的非可分组之间的相互作用，准确地分解各种问题类型，并使用较少的计算资源。此外，为了增强 CSG 的效率和准确性，我们引入了两种创新方法：一种是乘性可分变量检测方法，另一种是非可分变量分组方法。通过广泛的实验结果表明，与 GSG 和最先进的 DG 系列设计相比，CSG 在更低的计算复杂度下实现了更准确的变量分组。