Adaptive threshold parameter estimation with recursive differential grouping for problem decomposition

Problem decomposition plays an essential role in the success of cooperative co-evolution (CC), when used for solving large-scale optimization problems. The recently proposed recursive differential grouping (RDG) method has been shown to be very efficient, especially in terms of time complexity. However, it requires an appropriate parameter setting to estimate a threshold value in order to determine if two subsets of decision variables interact or not. Furthermore, using one global threshold value may be insufficient to identify variable interactions in components with different contribution to the fitness value. Inspired by the different grouping 2 (DG2) method, in this paper, we adaptively estimates a threshold value based on computational round-off errors for RDG. We derive an upper bound of the round-off errors, which is shown to be sufficient when identifying variable interactions across a wide range of large-scale benchmark problems. Comprehensive numerical experimental results showed that the proposed RDG2 method achieved higher decomposition accuracy than RDG and DG2. When embedded into a CC framework, it achieved statistically equal or significantly better solution quality than RDG and DG2, when used to solve the benchmark problems.