# Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization

Wang, Y, Liu, H, Wei, F, Zong, T and Li, X 2018, 'Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization', Evolutionary Computation Journal, vol. 26, no. 4, pp. 569-596.

 Document type: Journal Article Journal Articles

Title Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization Wang, Y Liu, H Wei, F Zong, T Li, X 2018 Evolutionary Computation Journal 26 4 569 596 28 MIT Press For a large-scale global optimization (LSGO) problem, divide-and-conquer is usually considered an effective strategy to decompose the problem into smaller subproblems, each of which can then be solved individually. Among these decomposition methods, variable grouping is shown to be promising in recent years. Existing variable grouping methods usually assume the problem to be black-box (i.e., assuming that an analytical model of the objective function is unknown), and they attempt to learn appropriate variable grouping that would allow for a better decomposition of the problem. In such cases, these variable grouping methods do not make a direct use of the formula of the objective function. However, it can be argued that many real-world problems are white-box problems, that is, the formulas of objective functions are often known a priori. These formulas of the objective functions provide rich information which can then be used to design an effective variable group method. In this article, a formula-based grouping strategy (FBG) for white-box problems is first proposed. It groups variables directly via the formula of an objective function which usually consists of a finite number of operations (i.e., four arithmetic operations "", "", "", "" and composite operations of basic elementary functions). In FBG, the operations are classified into two classes: one resulting in nonseparable variables, and the other resulting in separable variables. In FBG, variables can be automatically grouped into a suitable number of non-interacting subcomponents, with variables in each subcomponent being interdependent. FBG can easily be applied to any white-box problem and can be integrated into a cooperative coevolution framework. Based on FBG, a novel cooperative coevolution algorithm with formula-based variable grouping (so-called CCF) is proposed in this article for decomposing a large-scale white-box problem into several smaller subproblems and optimizing them respectively. To further Optimisation Neural, Evolutionary and Fuzzy Computation large-scale global optimization cooperative coevolution local search evolutionary algorithms 10.1162/evco_a_00214 © 2017 Massachusetts Institute of Technology 1063-6560
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