A Decomposition Method for Both Additively and Nonadditively Separable Problems

Abstract

Problem decomposition is crucial for coping with large-scale global optimization problems, which relies heavily on highly precise variable grouping methods. The state-of-the-art decomposition methods identify separability based on the finite differences principle, which is valid only for additively separable functions but not applicable to non-additively separable functions. Therefore, we need to investigate separability in more depth in order to propose a more general principle and design more universal decomposition methods. In this paper, we conduct a comprehensive theoretical investigation on separability, the core of which is proposing an innovative separability identification principle: the minimum points shift principle. By utilizing the new principle, we develop a general separability grouping (GSG) method that can handle both additively and non-additively separable functions with high accuracy. In addition, we design a new set of benchmark functions based on non-additive separability, which compensates for the lack of non-additively separable functions in the previous test suites. Extensive experiments demonstrate that the proposed GSG achieves high grouping accuracy on both new and CEC series benchmark problems, especially on non-additively separable problems Finally, we verify that the proposed GSG can effectively improve the optimization performance of non-additively separable problems through optimization experiments.