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Solving large-scale global optimization problems and engineering design problems using a novel biogeography-based optimization with Lévy and Brownian movements

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Abstract

To make biogeography-based optimization (BBO) suitable for large-scale optimization problems, this paper proposes a novel BBO variant based on marine predators algorithm (MPA) and steepest descent (SD) method, named BBOMPSD. Firstly, the example learning strategy is used to eliminate the damage of inferior solutions to superior solutions. Secondly, the hybrid migration operator is designed to make the population move rapidly to the global optimal solution, which improves the convergence speed and accuracy. Then, the Lévy and Brownian movements in MPA is combined with BBO to make the algorithm effectively balance the exploitation and exploration. BBOMPSD realizes free switching between local search and global search through the two movements. Finally, the SD method is merged with BBO, which further improves the convergence accuracy. Meanwhile, the sequence convergence model is established to prove the convergence of BBOMPSD. Comparing BBOMPSD with standard BBO, seven advanced BBO variants and seven state-of-the-art evolutionary algorithms on 24 benchmark functions and CEC2017 test set, the experimental results show that BBOMPSD outperforms all compared algorithms, and the dimension of solving global optimization problems can reach 5000. Applying it to engineering design problems, the results demonstrate that the proposed algorithm is also effective on real-world constrained optimization problems.

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Data Availability

All the data in Sect. 5 is obtained under the same experimental environment. Then, all the source programs of the compared BBO variants in Sect. 5.2 are coded according to their original references. The simulation of 24 benchmark functions in Table 2 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 WOA, MSA, HHO, SSA, AOA, ChOA and RSO in Sect. 5.4 can be downloaded from https://mianbaoduo.com/o/bread/mbd-YZaTlppv. We solemnly declare that all data in this paper are true and valid.

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Acknowledgements

The authors wish to thank the editors and anonymous reviewers whose kind assistance and constructive comments helped to signifcantly improve this paper. 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

  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. Solving large-scale global optimization problems and engineering design problems using a novel biogeography-based optimization with Lévy and Brownian movements. Int. J. Mach. Learn. & Cyber. 14, 313–346 (2023). https://doi.org/10.1007/s13042-022-01642-3

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