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.

翻译：基于分治策略的合作协同进化（CC）算法已成为解决大规模全局优化（LSGO）问题的主流方法。分组阶段的效率和准确性显著影响优化过程的性能。尽管通用可分性分组（GSG）方法通过实现非加性可分离函数的分解，克服了先前差分分组（DG）方法的局限性，但其存在计算复杂度高的问题。为解决这一挑战，本文提出一种复合可分性分组（CSG）方法，将DG和GSG无缝集成到问题分解框架中，以充分利用两种方法的优势。CSG引入了一种逐步分解框架，能够使用更少的计算资源精确分解各类问题。通过依次识别加性、乘性和一般可分离变量，CSG通过递归考虑每个非可分离变量与已形成的非可分离组之间的交互作用，逐步对非可分离变量进行分组。此外，为提高CSG的效率和准确性，我们引入了两种创新方法：乘性可分离变量检测方法和非可分离变量分组方法。这两种方法分别用于有效检测乘性可分离变量和高效分组非可分离变量。大量实验结果表明，与GSG及最先进的DG系列设计相比，CSG能够在更低计算复杂度下实现更精确的变量分组。