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A supercomputing method for large-scale optimization: a feedback biogeography-based optimization with steepest descent method

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Abstract

To apply biogeography-based optimization (BBO) to large scale optimization problems, this paper proposes a novel BBO variant based on feedback differential evolution mechanism and steepest descent method, referred to as FBBOSD. Firstly, the immigration refusal mechanism is proposed to eliminate the damage of inferior solutions to superior solutions. Secondly, the dynamic hybrid migration operator is designed to balance the exploration and exploitation, which makes BBO suitable for high-dimensional environment. Thirdly, the feedback differential evolution mechanism is designed to make FBBOSD can select mutation modes intelligently. Finally, the steepest descent method is creatively combined with BBO, which further improves the convergence accuracy. Meanwhile, a sequence convergence model is established to prove the convergence of FBBOSD. Quantitative evaluations: FBBOSD is compared with BBO, seven BBO variants and seven state-of-the-art evolutionary algorithms, respectively. The experimental results on 24 benchmark functions and CEC2017 show that FBBOSD outperforms all compared algorithms, and the dimension of solving optimization problems can reach 10,000. Then, FBBPOSD is applied to engineering design problems. The simulation results demonstrate that it is also effective on constrained optimization problems. In short, FBBOSD has excellent performance and outstanding stability, which is a new algorithm worthy of adoption and promotion.

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Data availability

All the data in Sect. 6 are obtained under the same experimental environment. Then, all the source programs of the compared BBO variants in Sect. 6.3 are coded according to their original references. The simulation of 24 benchmark functions in Table 3 can be downloaded from http://www.sfu.ca/~ssurjano/emulat.html. The simulation of CEC2017 test set can be downloaded from http://www5.zzu.edu.cn/cilab/Benchmark/wysyhwtcsj.htm. The simulation of GWO, WOA, MSA, HHO, AOA, AVOA and HBA in Sect. 6.5 can be downloaded from https://mianbaoduo.com/o/bread/mbd-YZaTlppv. The data cited in Sect. 6.7 are listed in references. We solemnly declare that all data in this paper are true and valid.

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Acknowledgements

This work was supported by the Key Project of Ningxia Natural Science Foundation “Several Swarm Intelligence Algorithms and Their Application” [2022AAC02043], the 2022 Graduate Innovation Project of North Minzu University [YCX22095], the National Natural Science Foundation of China under Grant [11961001], the Construction Project of First-class Subjects in Ningxia Higher Education [NXYLXK2017B09], and the Major Proprietary Funded Project of North Minzu University [ZDZX201901].

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  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

    Ziyu Zhang, Yuelin Gao & Eryang Guo

  2. Ningxia Province Key Laboratory of Intelligent Information and Data Processing, Yinchuan, 750021, China

    Ziyu Zhang & Yuelin Gao

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Zhang, Z., Gao, Y. & Guo, E. A supercomputing method for large-scale optimization: a feedback biogeography-based optimization with steepest descent method. J Supercomput 79, 1318–1373 (2023). https://doi.org/10.1007/s11227-022-04644-8

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