Cooperative coevolution for large-scale global optimization based on fuzzy decomposition
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METHODOLOGIES AND APPLICATION
Cooperative coevolution for large-scale global optimization based on fuzzy decomposition Lin Li1 · Wei Fang1
· Yi Mei2 · Quan Wang3
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Cooperative coevolution (CC) is an effective evolutionary divide-and-conquer strategy that solves large-scale global optimization (LSGO) by decomposing the problem into a set of lower-dimensional subproblems. The main challenge of CC is to find an optimal decomposition. Differential Grouping (DG) is a competitive decomposition method to identify the variable interaction with several improved versions like GDG and DG2. Although DG-based decomposition methods have shown superior performance compared to the other decomposition methods, they still have difficulty to deal with the overlapping problems since their optimal decomposition is unknown. To address this issue, instead of pursuing the high accuracy of decomposition, we propose a novel fuzzy decomposition algorithm that groups the variables according to their interaction degree. In the proposed fuzzy decomposition algorithm, the interaction structure matrix and the interactive degree for a LSGO problem are calculated at first according to the interaction among all the decision variables. Then the number of subgroups is determined based on the interactive degree. Based on the interaction structure matrix, a spectral clustering algorithm is proposed to decompose the decision variables with regard to the number of subgroups in order to achieve a better balance between high grouping accuracy and suitable group size. The proposed decomposition algorithm with DECC has been proven to outperform several state-of-the-art algorithms on the latest LSGO benchmark functions. Keywords Large-scale global optimization · Spectral clustering · Differential grouping · Cooperative co-evolution
1 Introduction In the last decades, a considerable number of large-scale global optimization (LSGO) problems have emerged in the field of science and engineering, which often have thousands or even more decision variables (Sun et al. 2020; Ge et al. 2017; Sun et al. 2019). The difficulties in solving LSGO problems mainly come from the following aspects (Omidvar et al. 2015). Firstly, as the dimension of decision variables Communicated by V. Loia.
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Wei Fang [email protected]
1
Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Department of Computer Science and Technology, Jiangnan University, Wuxi, China
2
School of Engineering and Computer Science, Victoria University of Wellington, Wellington 6012, New Zealand
3
Wuxi SensingNet Industrialization Research Institute, Wuxi, China
increases, the search space becomes extremely complex, and the number of local optimal solutions surges exponentially. Secondly, the properties of search space may change with the increasing scale of variables. Furthermore, the cost of evaluating large-scale problems is usually expensive. Finally, the interaction between deci
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