  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.
