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Cooperative coevolution for large-scale global optimization based on fuzzy decomposition

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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.

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Acknowledgements

This work was supported in part by the National Key R&D Program of China under Grants 2017YFC1601800 and 2017YFC1601000, in part by the National Natural Science foundation of China, under Grants 61673194 and Grant 61672263, in part by the Key Research and Development Program of Jiangsu Province, China, under Grant BE2017630, in part by “Blue Project” in Jiangsu Universities, in part by the Postdoctoral Science Foundation of China under Grant 2014M560390.

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Authors and Affiliations

  1. Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Department of Computer Science and Technology, Jiangnan University, Wuxi, China

    Lin Li & Wei Fang

  2. School of Engineering and Computer Science, Victoria University of Wellington, Wellington, 6012, New Zealand

    Yi Mei

  3. Wuxi SensingNet Industrialization Research Institute, Wuxi, China

    Quan Wang

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  1. Lin Li
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  2. Wei Fang
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  3. Yi Mei
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  4. Quan Wang
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Correspondence to Wei Fang.

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Li, L., Fang, W., Mei, Y. et al. Cooperative coevolution for large-scale global optimization based on fuzzy decomposition. Soft Comput 25, 3593–3608 (2021). https://doi.org/10.1007/s00500-020-05389-3

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