Utilizing Walrus Optimizer with Chaotic Maps for Solving Engineering Design Optimization Problems
Corresponding author: Lakkana Ruekkasaem
Abstract
Modern manufacturing is significantly influenced by machining optimization, which enhances surface quality, reduces production costs, and improves material removal efficiency. However, conventional optimization methods often struggle with the nonlinear, multi-constrained nature of machining problems. Metaheuristic algorithms have emerged as effective alternatives, and the Walrus Optimizer (WO) is a recent bio-inspired method that models walrus behaviors, such as migration, breeding, and foraging. Despite its promising structure, the original WO suffers from premature convergence and limited search diversity due to its reliance on uniform random numbers. To address these shortcomings, this study proposes a hybrid framework that integrates the chaos theory into WO by embedding three chaotic maps—Logistic, Chebyshev, and Iterative Chaotic Map with Infinite Collapses (ICMIC)—into the initialization, migration, reproduction, and foraging phases. These chaos-enhanced variants, namely WO-Logistic, WO-Chebyshev, and WO-ICMIC, are applied to four benchmark machining optimization problems: (1) surface roughness minimization, (2) Material Removal Rate (MRR) maximization, (3) multi-pass turning cost minimization, and (4) a multi-objective model combining time, cost, and roughness. Comparative experiments demonstrate that the chaotic WO algorithms consistently outperform the standard WO and several state-of-the-art metaheuristics in terms of solution accuracy, convergence speed, and stability. The main contribution of this work lies in establishing a robust hybrid optimization framework that leverages the chaos theory to improve the exploration–exploitation balance. The findings highlight the potential of Chaos-enhanced Walrus Optimizer (CWO) as a reliable and generalizable tool for solving complex machining optimization problems and advancing intelligent manufacturing.
Keywords:
Walrus Optimizer, chaotic map integration, hybrid metaheuristic algorithm, machining optimization, surface roughness minimizationDownloads
References
K. S. Sangwan and G. Kant, "Optimization of Machining Parameters for Improving Energy Efficiency using Integrated Response Surface Methodology and Genetic Algorithm Approach," Procedia CIRP, vol. 61, pp. 517–522, 2017. DOI: https://doi.org/10.1016/j.procir.2016.11.162
M. Han, Z. Du, K. F. Yuen, H. Zhu, Y. Li, and Q. Yuan, "Walrus Optimizer: A Novel Nature-inspired Metaheuristic Algorithm," Expert Systems with Applications, vol. 239, Apr. 2024, Art. no. 122413. DOI: https://doi.org/10.1016/j.eswa.2023.122413
S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, and S. M. Mirjalili, "Salp Swarm Algorithm: A Bio-inspired Optimizer for Engineering Design Problems," Advances in Engineering Software, vol. 114, pp. 163–191, Dec. 2017. DOI: https://doi.org/10.1016/j.advengsoft.2017.07.002
S. Mirjalili, S. M. Mirjalili, and A. Lewis, "Grey Wolf Optimizer," Advances in Engineering Software, vol. 69, pp. 46–61, Mar. 2014. DOI: https://doi.org/10.1016/j.advengsoft.2013.12.007
T. M. Shami, A. A. El-Saleh, M. Alswaitti, Q. Al-Tashi, M. A. Summakieh, and S. Mirjalili, "Particle Swarm Optimization: A Comprehensive Survey," IEEE Access, vol. 10, pp. 10031–10061, 2022. DOI: https://doi.org/10.1109/ACCESS.2022.3142859
T. V. Dua, H. X. Thinh, N. C. Bao, D. V. Duc, and T. M. Hoang, "Multi-objective Optimization of the Turning Process using the Probability Method," Engineering, Technology and Applied Science Research, vol. 15, no. 1, pp. 19865–19870, Feb. 2025. DOI: https://doi.org/10.48084/etasr.9472
V. B. Pansare and M. V. Kavade, "Optimization of Cutting Parameters in Multipass Turning Operation using Ant Colony Algorithm," International Journal of Engineering Science and Advanced Technology, vol. 2, no. 4, pp. 955–960, Jul. 2012.
I. Shivakoti, S. Diyaley, G. Kibria, and B. B. Pradhan, "Analysis of Material Removal Rate using Genetic Algorithm Approach," International Journal of Scientific and Engineering Research, vol. 3, no. 5, pp. 1–6, May 2012.
K.-M. Lee, M.-R. Hsu, J.-H. Chou, and C.-Y. Guo, "Improved Differential Evolution Approach for Optimization of Surface Grinding Process," Expert Systems with Applications, vol. 38, no. 5, pp. 5680–5686, May 2011. DOI: https://doi.org/10.1016/j.eswa.2010.10.067
M.-C. Chen and D.-M. Tsai, "A Simulated Annealing Approach for Optimization of Multi-pass Turning Operations," International Journal of Production Research, vol. 34, no. 10, pp. 2803–2825, Oct. 1996. DOI: https://doi.org/10.1080/00207549608905060
Z. G. Wang, M. Rahman, Y. S. Wong, and J. Sun, "Optimization of Multi-pass Milling using Parallel Genetic Algorithm And Parallel Genetic Simulated Annealing," International Journal of Machine Tools and Manufacture, vol. 45, no. 15, pp. 1726–1734, Dec. 2005. DOI: https://doi.org/10.1016/j.ijmachtools.2005.03.009
G. Atali, İh. Pehli̇Van, B. Gürevi̇N, and H. İb. Şeker, "Chaos In Metaheuristic Based Artificial Intelligence Algorithms: A Short Review," Turkish Journal of Electrical Engineering and Computer Sciences, vol. 29, no. 3, pp. 1354–1367, May 2021. DOI: https://doi.org/10.3906/elk-2102-5
B. S. Yıldız, N. Pholdee, N. Panagant, S. Bureerat, A. R. Yildiz, and S. M. Sait, "A Novel Chaotic Henry Gas Solubility Optimization Algorithm for Solving Real-world Engineering Problems," Engineering with Computers, vol. 38, no. S2, pp. 871–883, Jun. 2022. DOI: https://doi.org/10.1007/s00366-020-01268-5
S. Kumar et al., "Chaotic Marine Predators Algorithm for Global Optimization of Real-world Engineering Problems," Knowledge-Based Systems, vol. 261, Feb. 2023, Art. no. 110192. DOI: https://doi.org/10.1016/j.knosys.2022.110192
M. W. Ouertani, G. Manita, and O. Korbaa, "Chaotic Lightning Search Algorithm," Soft Computing, vol. 25, no. 3, pp. 2039–2055, Feb. 2021. DOI: https://doi.org/10.1007/s00500-020-05273-0
A. Kaveh and H. Yousefpoor, "Chaotic Optimization of Trusses with Frequency Constraints with Three Metaheuristic Algorithms," Iranian Journal of Science and Technology, Transactions of Civil Engineering, vol. 48, no. 1, pp. 271–293, Feb. 2024. DOI: https://doi.org/10.1007/s40996-023-01223-6
P. Trojovský and M. Dehghani, "A New Bio-inspired Metaheuristic Algorithm for Solving Optimization Problems Based on Walruses Behavior," Scientific Reports, vol. 13, no. 1, May 2023, Art. no. 8775. DOI: https://doi.org/10.1038/s41598-023-35863-5
Y. T. Bozkurt and M. Şimşek, "Channel Estimation in OFDM System using Walrus Optimization Algorithm," in 9th International Symposium on Innovative Approaches in Smart Technologies (ISAS), Gaziantep, Turkiye, Jun. 2025, pp. 1–6. DOI: https://doi.org/10.1109/ISAS66241.2025.11101734
R. Tang, S. Fong, and N. Dey, "Metaheuristics and Chaos Theory," in Chaos Theory, K. A. M. A. Naimee, Ed. London, United Kingdom: InTech, 2018. DOI: https://doi.org/10.5772/intechopen.72103
A. Limane et al., "Chaos-enhanced Metaheuristics: Classification, Comparison, and Convergence Analysis," Complex and Intelligent Systems, vol. 11, no. 3, Mar. 2025, Art. no. 177. DOI: https://doi.org/10.1007/s40747-025-01791-2
I. Zelinka et al., "Impact of Chaotic Dynamics on the Performance of Metaheuristic Optimization Algorithms: An Experimental Analysis," Information Sciences, vol. 587, pp. 692–719, Mar. 2022. DOI: https://doi.org/10.1016/j.ins.2021.10.076
H. Zhang, B. Buchmeister, X. Li, and R. Ojstersek, "An Efficient Metaheuristic Algorithm for Job Shop Scheduling in a Dynamic Environment," Mathematics, vol. 11, no. 10, May 2023, Art. no. 2336. DOI: https://doi.org/10.3390/math11102336
M. Bezoui, A. T. Almaktoom, A. Bounceur, S. M. Qaisar, and M. Chouman, "Hybrid Metaheuristics for Industry 5.0 Multi-Objective Manufacturing and Supply Chain Optimization," in 21st Learning and Technology Conference, Jeddah, Saudi Arabia, Jan. 2024, pp. 245–249. DOI: https://doi.org/10.1109/LT60077.2024.10469011
E. Ficarella, L. Lamberti, and S. O. Degertekin, "Comparison of Three Novel Hybrid Metaheuristic Algorithms for Structural Optimization Problems," Computers and Structures, vol. 244, Feb. 2021, Art. no. 106395. DOI: https://doi.org/10.1016/j.compstruc.2020.106395
Z. Khan, B. Prasad, and T. Singh, "Machining Condition Optimization by Genetic Algorithms and Simulated Annealing," Computers and Operations Research, vol. 24, no. 7, pp. 647–657, Jul. 1997. DOI: https://doi.org/10.1016/S0305-0548(96)00077-9
Downloads
How to Cite
License
Copyright (c) 2025 Pasura Aungkulanon, Lakkana Ruekkasaem, Pongchanun Luangpaiboon
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
