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An improved decomposition method for large-scale global optimization: bidirectional-detection differential grouping

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Abstract

Differential grouping (DG) is an efficient decomposition method that is used to solve large-scale global optimization (LSGO) problems. To further reduce the computational cost, a bidirectional-detection differential grouping (BDDG) method is proposed in this paper. By exploiting the bidirectional detection structure (BDS), BDDG is able to spend less computation than other DG-based methods. An adaptive perturbation strategy (APS) is proposed to improve the problem with the BDS decomposition accuracy. Analytical methods are used to demonstrate that the complexity of BDDG is lower than that of other state-of-the-art DG-based methods. Experiments showed that BDDG substantially reduced the computational cost for problem decomposition and that the computational cost used by BDDG grew slowly, as the problem dimension grew compared to other DG-based methods. When BDDG was embedded in the cooperative coevolution (CC) framework, it improved the performance of the CC for solving LSGO problems.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61763002 and 62072124), Guangxi Major projects of science and technology (Grants No.2020AA21077021), Foundation of Guangxi Experiment Center of Infor mation Science (Grant No. KF1401).

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  1. School of Computer and Electronics and Information, Guangxi University, Nanning, Guangxi, China

    Yu Sun & Hongda Yue

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  1. Yu Sun
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  2. Hongda Yue
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Correspondence to Hongda Yue.

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Appendix:

Appendix:

Table 10 depicts the decomposition results of the ERDG on the high-dimensional CEC2010. The numbers in each column indicate the number of function evaluations used in decomposing problem in that dimension. Table 10 is used for the calculation of the results in Fig. 7 and for the analysis of the optimization results in Tables 8 and 9 in the experimental part of the main text.

Tables 11 and 12 depict the change in the growth rate of the function evaluation used in problem decomposition for DG, DG2, RDG, RDG2, ERDG and BDDG during the dimensional change from 1000 to 5000 dimensions on CEC’2010, each calculated by (15) in the main text, and the percentages indicate the growth rate of the function evaluations used by the decomposition methods.

Table 10 The decomposition results of the ERDG on high-dimensional CEC’2010
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Table 11 The growth rate of DG, DG2, RDG, RDG2, ERDG and BDDG on CEC’2010, D from 1000 to 2000
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Table 12 The growth rate of DG, DG2, RDG, RDG2, ERDG and BDDG on CEC’2010, D from 2000 to 5000
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Sun, Y., Yue, H. An improved decomposition method for large-scale global optimization: bidirectional-detection differential grouping. Appl Intell 52, 11569–11591 (2022). https://doi.org/10.1007/s10489-021-03023-9

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