An enhanced whale migration algorithm for its application in engineering problems

Shirong Li; Nan Xiang; Mengya Chen; Yangyang Liu; Xuemei Zhu; Yu Liu; Shirong Li; Nan Xiang; Mengya Chen; Yangyang Liu; Xuemei Zhu; Yu Liu

doi:10.3934/era.2025261

Electronic Research Archive

2025, Volume 33, Issue 9: 5865-5896. doi: 10.3934/era.2025261

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Research article

An enhanced whale migration algorithm for its application in engineering problems

1.
Automotive Technology College, Anhui Vocational College of Defense Technology, Lu'an 237011, China
2.
Experimental and Practical Training Teaching Management Department, West Anhui University, Lu'an 237012, China
3.
School of Electronics and Information Engineering, West Anhui University, Lu'an 237012, China

Received: 22 June 2025 Revised: 07 August 2025 Accepted: 20 August 2025 Published: 26 September 2025

In this paper, we proposed an enhanced whale migration algorithm (EWMA) that integrates two novel strategies: Normal cloud model mutation (NCMM) and Fast Random Opposition-Based Learning. NCMM enables adaptive uncertainty management through expectation-entropy-hyperentropy mechanisms to balance exploration and exploitation. FROBL improves population diversity and convergence speed via oscillatory perturbations and nonlinear scaling. EWMA outperformed eight competing algorithms when evaluated on 23 benchmark functions and the CEC 2019, achieving optimal results on 18 of the 23 benchmark functions and all 10 CEC 2019 functions. It ranked first overall, significantly surpassing the other algorithms. Statistical analysis confirmed notable improvements in solution accuracy, convergence speed, and stability, with standard deviations 2–4 orders of magnitude lower than those of competitors. Engineering applications, including pressure vessel design, cantilever beams, and reinforced concrete beams, further demonstrated EWMA's practical effectiveness, yielding optimal designs with improved constraint handling. EWMA offers a robust optimization tool for complex engineering problems requiring global search capability and precise local refinement.
- whale migration algorithm,
- normal cloud model,
- opposition-based learning,
- engineering optimization,
- metaheuristic algorithms
Citation: Shirong Li, Nan Xiang, Mengya Chen, Yangyang Liu, Xuemei Zhu, Yu Liu. An enhanced whale migration algorithm for its application in engineering problems[J]. Electronic Research Archive, 2025, 33(9): 5865-5896. doi: 10.3934/era.2025261

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Abstract

In this paper, we proposed an enhanced whale migration algorithm (EWMA) that integrates two novel strategies: Normal cloud model mutation (NCMM) and Fast Random Opposition-Based Learning. NCMM enables adaptive uncertainty management through expectation-entropy-hyperentropy mechanisms to balance exploration and exploitation. FROBL improves population diversity and convergence speed via oscillatory perturbations and nonlinear scaling. EWMA outperformed eight competing algorithms when evaluated on 23 benchmark functions and the CEC 2019, achieving optimal results on 18 of the 23 benchmark functions and all 10 CEC 2019 functions. It ranked first overall, significantly surpassing the other algorithms. Statistical analysis confirmed notable improvements in solution accuracy, convergence speed, and stability, with standard deviations 2–4 orders of magnitude lower than those of competitors. Engineering applications, including pressure vessel design, cantilever beams, and reinforced concrete beams, further demonstrated EWMA's practical effectiveness, yielding optimal designs with improved constraint handling. EWMA offers a robust optimization tool for complex engineering problems requiring global search capability and precise local refinement.

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