Adaptive Variable-Size Random Grouping for Evolutionary Large-Scale Global Optimization

Abstract

In recent years many real-world optimization problems have had to deal with growing dimensionality. Optimization problems with many hundreds or thousands of variables are called large-scale global optimization (LSGO) problems. Many well-known real-world LSGO problems are not separable and are complex for detailed analysis, thus they are viewed as the black-box optimization problems. The most advanced algorithms for LSGO are based on cooperative coevolution with problem decomposition using grouping methods, which form low-dimensional non-overlapping subcomponents of a high-dimensional objective vector. The standard random grouping can be applied to the wide range of separable and non-separable LSGO problems, but it does not use any feedback from the search process for creating more efficient variables combinations. Many learning-based dynamic grouping methods are able to identify interacting variables and to group them into the same subcomponent. At the same time, the majority of the proposed learning-based methods demonstrate greedy search and perform well only with separable problems. In this study, we proposed a new adaptive random grouping approach that create and adaptively change a probability distribution for assigning variables to subcomponents. The approach is able to form subcomponents of different size or can be used with predefined fix-sized subcomponents. The results of numerical experiments for benchmark problems are presented and discussed. The experiments show that the proposed approach outperforms the standard random grouping method.