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MSBES: an improved bald eagle search algorithm with multi- strategy fusion for engineering design and water management problems

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Abstract

The Bald Eagle Search algorithm is prone to falling into local optimums and having poor convergence accuracy when solving complex optimization problems. This paper proposes a multi-strategy modified Bald Eagle Search (MSBES) algorithm to solve these problems. Firstly, adaptive control factors are used to replace key control parameters, and the adaptive characteristics are brought into play in the algorithm search process to enrich the search mechanism and effectively balance the ability of algorithm exploitation and exploration. The Cauchy operator and the strategy of fusing Levy flight and adaptive weights are introduced to update the position equation, expand the search range, avoid excessive population assimilation at the end of the iteration, and strengthen the algorithm’s ability of anti-prematurity. Finally, adaptive variance probabilities are employed to strengthen the exploration ability and the ability to escape local extremes and maintain population diversity. The performance of this algorithm was evaluated on 59 test functions from CEC2014 and CEC2017, eight engineering optimization problems, one reservoir flood control optimal scheduling problem, and one Muskingum flood evolution problem. Experimental results show that MSBES has the advantages of strong merit-seeking ability, high convergence accuracy, and fast convergence speed compared to other advanced optimization algorithms. It also has better robustness, which can effectively deal with complex engineering problems.

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Acknowledgements

The authors are grateful for the support of the doctoral innovation fund of North China University of Water Resources and Electric Power (No: 202220902), the special project for collaborative innovation of science and technology in 2021 (No: 202121206), and Henan Province university scientific and technological innovation team (No: 18IRTSTHN009).

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Authors and Affiliations

  1. College of Water Resources, North China University of Water Resources and Electric Power, Zhengzhou, 450046, People’s Republic of China

    Wen-Chuan Wang, Wei-Can Tian & Hongfei Zang

  2. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China

    Kwok-Wing Chau

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Contributions

Wen-chuan Wang: Conceptualization, Methodology, Writing—original draft, Formal analysis. Wei-can Tian：Investigation, Writing—original draft, Methodology, Data curation. Kwok-wing Chau: Writing—original draft, Formal analysis. Hong-fei Zang: Formal analysis, Investigation, Investigation.

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Correspondence to Wen-Chuan Wang.

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Appendix

Appendix

The detailed experimental results for sensitivity analysis of the parameter a are shown in Tables 4 and 5. The detailed experimental results for sensitivity analysis of the parameter R are shown in Tables 6 and 7.

The detailed experimental results comparing each improvement strategy are shown in Tables 8 and 9.

The detailed experimental results of comparison on CEC2014 and CEC2017 are shown in Tables 11, 12, 13, and 14.

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Wang, WC., Tian, WC., Chau, KW. et al. MSBES: an improved bald eagle search algorithm with multi- strategy fusion for engineering design and water management problems. J Supercomput 81, 251 (2025). https://doi.org/10.1007/s11227-024-06727-0

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