A A Competitive Divide-and-Conquer Algorithm for Unconstrained Large-Scale Black-Box Optimization

This paper proposes a competitive divide-and-conquer algorithm for solving large-scale black-box optimization problems, where there are thousands of decision variables, and the algebraic models of the problems are unavailable. We focus on problems that are partially additively separable, since this type of problem can be further decomposed into a number of smaller independent sub-problems. The proposed algorithm addresses two important issues in solving large-scale black-box optimization: (1) the identification of the independent sub-problems without explicitly knowing the formula of the objective function and (2) the optimization of the identified black-box sub-problems. First, a Global Differential Grouping (GDG) method is proposed to identify the independent sub-problems. Then, a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is adopted to solve the sub-problems resulting from its rotation invariance property. GDG and CMA-ES work together under the cooperative co-evolution framework. The resultant algorithm named CC-GDG-CMAES is then evaluated on the CEC’2010 large-scale global optimization (LSGO) benchmark functions, which have a thousand decision variables and black-box objective functions. The experimental results show that on most test functions evaluated in this study, GDG manages to obtain an ideal partition of the index set of the decision variables, and CC-GDG-CMAES outperforms the state-of-the-art results. Moreover, the competitive performance of the well-known CMA-ES is extended from low-dimensional to high-dimensional black-box problems.