A decomposition framework based on memorized binary search for large-scale optimization problems

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Cooperative co-evolution (CC) is an evolutionary framework for dealing with large-scale optimization problems. The divide-and-conquer strategy is widely used in CC. The large-scale problem is decomposed into multiple smaller and easier to optimize subcomponents to reduce the complexity and improve the optimization performance. However, CC typically requires appropriate decomposition methods and numerous functional evaluations. To address this problem, this study proposes a new decomposition framework known as hierarchical differential grouping (HDG). Hierarchy 1 is used to identify the separable and nonseparable variables. The core of the HDG is Hierarchy 2, where a memorized binary search is used to group nonseparable variables into multiple subcomponents. Hierarchy 3 merges the variables with indirect interactions. Finally, Hierarchy 4 implements sequential decomposition for the larger subcomponents. Furthermore, this study theoretically analyzes the computational resources consumed by HDG to decompose large-scale problems. The experimental results demonstrate that HDG outperforms other state-of-the-art differential grouping methods in terms of both the decomposition accuracy and computational complexity. HDG combined with the covariance matrix adaptive evolution strategy can be competitive on multiple benchmark functions.