An Efficient Adaptive Differential Grouping Algorithm for Large-Scale Black-Box Optimization

Decomposition plays a significant role in cooperative coevolution (CC), which shows great potential in large-scale black-box optimization (LSBO). However, current learning-based decomposition algorithms require many fitness evaluations (FEs) to detect variable interdependencies and encounter the difficulty of threshold setting. To address these issues, this study proposes an efficient adaptive differential grouping (EADG) algorithm. Instead of homogeneously tackling different types of LSBO instances, EADG first identifies the instance type by detecting the interdependencies of a few pairs of variable subsets. Only if the instance is partially separable dose EADG further engages with it by converting its decomposition process into a search process in a binary tree. This facilitates the systematic reutilization of evaluated solutions so that half the interdependencies can be directly deduced without extra FEs. To promote the decomposition accuracy, EADG specially designs a normalized interdependency indicator that can adaptively generate a decomposition threshold according to its ordinal distribution. Theoretical analysis and experimental results show that EADG outperforms current popular decomposition algorithms. Further tests indicate that it can help CC achieve highly competitive optimization performance.