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Dynamic Inertia Weight Whale Optimization Algorithm for Numerical and Engineering Optimization Problems
Research Article  ·  Published: 21 June 2026
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Journal of Mathematics and Interdisciplinary Applications
Volume 2, Issue 2, 2026: 125-142
Research Article Open Access

Dynamic Inertia Weight Whale Optimization Algorithm for Numerical and Engineering Optimization Problems

by
Wen Long Wen Long 1 * ORCID
Tiantian Hu Tiantian Hu 2
1 School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
2 School of Information, Guizhou University of Finance and Economics, Guiyang 550025, China
* Corresponding Author: Wen Long, [email protected]
Volume 2, Issue 2
Volume 2, Issue 2 2026
Received: 27 April 2026 Accepted: 10 June 2026 Published: 21 June 2026 CrossMark
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DOI: 10.62762/JMIA.2026.111913
ARK: ark:/57805/jmia.2026.111913

Article Information

Published in Journal of Mathematics and Interdisciplinary Applications
Volume/Issue Volume 2, Issue 2, 2026
Pages 125-142

Abstract

Whale optimization algorithm (WOA) is a relatively new population-based metaheuristic optimization method, which has the advantage of fewer control parameters, strong global optimization ability and easy to implement. However, when being used for high-dimensional problems, WOA may be trapped in the local optimum. In this study, we propose an effective whale optimization algorithm called EWOA. Inspired by particle swarm optimization (PSO), a modified position-updated equation by introducing dynamic inertia weight parameter to guide the search of new candidate individuals is presented. In addition, in order to make full use of and balance the exploration and the exploitation of WOA, a nonlinear distance control parameter strategy is proposed. The effectiveness of EWOA is tested based on 26 traditional high-dimensional benchmark problems (D = 30, 100, and 500) and four real-world engineering applications. The experimental and statistical test results demonstrate that EWOA converges to the global optima faster and provides more accurate results than the classical WOA, variants WOA, and other considered population-based metaheuristic algorithms in most cases, especially in solving an optimization problem that has high dimensionality.

Graphical Abstract

Dynamic Inertia Weight Whale Optimization Algorithm for Numerical and Engineering Optimization Problems

Keywords

whale optimization algorithm inertia weight global optimization high-dimensional complex problem engineering application

Data Availability Statement

Data will be made available on request.

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 12361106; in part by the Guizhou Provincial Science and Technology Plan Key Projects under Grant Qiankehe Jichu ZK[2023]003; in part by the Guizhou Provincial High Level Innovative Talent Training Plan Project under Grant Qiankehe Platform Talent GCC[2023]006.

Conflicts of Interest

Wen Long served as an Associate Editor of the Journal of Mathematics and Interdisciplinary Applications at the time of manuscript submission. To ensure the integrity of the peer-review process, Wen Long was not involved in the editorial handling, peer review, or decision-making process for this manuscript, which was handled independently by another editor. The remaining authors declare no conflicts of interest.

AI Use Statement

The authors declare that no generative AI was used in the preparation of this manuscript.

Ethical Approval and Consent to Participate

Not applicable.

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APA Style
Long, W., & Hu, T. (2026). Dynamic Inertia Weight Whale Optimization Algorithm for Numerical and Engineering Optimization Problems. Journal of Mathematics and Interdisciplinary Applications, 2(2), 125-142. https://doi.org/10.62762/JMIA.2026.111913
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TY  - JOUR
AU  - Long, Wen
AU  - Hu, Tiantian
PY  - 2026
DA  - 2026/06/21
TI  - Dynamic Inertia Weight Whale Optimization Algorithm for Numerical and Engineering Optimization Problems
JO  - Journal of Mathematics and Interdisciplinary Applications
T2  - Journal of Mathematics and Interdisciplinary Applications
JF  - Journal of Mathematics and Interdisciplinary Applications
VL  - 2
IS  - 2
SP  - 125
EP  - 142
DO  - 10.62762/JMIA.2026.111913
UR  - https://www.icck.org/article/abs/JMIA.2026.111913
KW  - whale optimization algorithm
KW  - inertia weight
KW  - global optimization
KW  - high-dimensional complex problem
KW  - engineering application
AB  - Whale optimization algorithm (WOA) is a relatively new population-based metaheuristic optimization method, which has the advantage of fewer control parameters, strong global optimization ability and easy to implement. However, when being used for high-dimensional problems, WOA may be trapped in the local optimum. In this study, we propose an effective whale optimization algorithm called EWOA. Inspired by particle swarm optimization (PSO), a modified position-updated equation by introducing dynamic inertia weight parameter to guide the search of new candidate individuals is presented. In addition, in order to make full use of and balance the exploration and the exploitation of WOA, a nonlinear distance control parameter strategy is proposed. The effectiveness of EWOA is tested based on 26 traditional high-dimensional benchmark problems (D = 30, 100, and 500) and four real-world engineering applications. The experimental and statistical test results demonstrate that EWOA converges to the global optima faster and provides more accurate results than the classical WOA, variants WOA, and other considered population-based metaheuristic algorithms in most cases, especially in solving an optimization problem that has high dimensionality.
SN  - 3070-393X
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -
BibTeX Format
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@article{Long2026Dynamic,
  author = {Wen Long and Tiantian Hu},
  title = {Dynamic Inertia Weight Whale Optimization Algorithm for Numerical and Engineering Optimization Problems},
  journal = {Journal of Mathematics and Interdisciplinary Applications},
  year = {2026},
  volume = {2},
  number = {2},
  pages = {125-142},
  doi = {10.62762/JMIA.2026.111913},
  url = {https://www.icck.org/article/abs/JMIA.2026.111913},
  abstract = {Whale optimization algorithm (WOA) is a relatively new population-based metaheuristic optimization method, which has the advantage of fewer control parameters, strong global optimization ability and easy to implement. However, when being used for high-dimensional problems, WOA may be trapped in the local optimum. In this study, we propose an effective whale optimization algorithm called EWOA. Inspired by particle swarm optimization (PSO), a modified position-updated equation by introducing dynamic inertia weight parameter to guide the search of new candidate individuals is presented. In addition, in order to make full use of and balance the exploration and the exploitation of WOA, a nonlinear distance control parameter strategy is proposed. The effectiveness of EWOA is tested based on 26 traditional high-dimensional benchmark problems (D = 30, 100, and 500) and four real-world engineering applications. The experimental and statistical test results demonstrate that EWOA converges to the global optima faster and provides more accurate results than the classical WOA, variants WOA, and other considered population-based metaheuristic algorithms in most cases, especially in solving an optimization problem that has high dimensionality.},
  keywords = {whale optimization algorithm, inertia weight, global optimization, high-dimensional complex problem, engineering application},
  issn = {3070-393X},
  publisher = {Institute of Central Computation and Knowledge}
}

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