A Composite Decomposition Method for Large-Scale Global Optimization

Cooperative coevolution (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 nonadditively 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 nonseparable variables by recursively considering the interactions between each nonseparable variable and the formed nonseparable groups. Furthermore, to enhance the efficiency and accuracy of CSG, we introduce two innovative methods: a multiplicatively separable variable detection method and a nonseparable variable grouping method. These two methods are designed to effectively detect multiplicatively separable variables and efficiently group nonseparable 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.