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Bto: a barrel theory-based optimizer for engineering design problems
Authors:
Van Tai Tran1,2
, Quynh T.T Nhu1,2
, Chitsutha Soomlek1
, Punyaphol Horata1
,
Khamron Sunat1
1College of Computing, Khon Kaen University, Khon Kaen, Thailand
2School of Computing and Information Technology, Eastern International University, Ho Chi Minh, Vietnam
Received: 11 September 2025
Revised: 1 November 2025
Accepted: 20 November 2025
Published: 15 December 2025
Abstract:
This study introduces the Barrel Theory-based Optimizer (BTO), a novel metaheuristic algorithm inspired by the wooden barrel theory, where the weakest component constrains overall performance. In BTO, each solution is viewed as a barrel and each variable as a plank. Low-fitness solutions, which can be seen as the limiting planks, are updated frequently via a population-level adjustment strategy called Barrel Adjustment. As a result, the overall search capability improves. Besides, BTO uses an adaptive elite selection mechanism that gradually adjusts the number of elite solutions. It enables a smooth transition from exploration to exploitation. The elite set further guides directional updates with a gradually decreasing disturbance factor. The performance of BTO was tested on three groups of problems, including CEC2022 benchmark functions, classical benchmarks, and eight well-known engineering design problems from mechanical and structural engineering. Experimental results show that it achieves higher solution quality, faster convergence, and more stable performance than well-known algorithms, including Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO). These findings establish BTO as a reliable and effective algorithm for complex and real-world engineering optimization tasks.
Keywords:
Metaheuristic optimization, Barrel theory, Adaptive strategy, Engineering design problems, Mechanical and structural design problems
References:
[1] W. Wang, H. Dong, X. Wang, P. Wang, J. Shen, Y. Jiang, Z. Wen, H. Zhu, Knowledge-guided global optimization for expensive and black-box constrained multi-objective engineering design problems. Applied Soft Computing, 177, 2025: 113216. https://doi.org/10.1016/j.asoc.2025.113216
[2] N.E. Chalabi, A. Attia, A.S. Almazayd, A.W. Mohamed, F. Werner, P. Jangir, M. Shokouhifar, MO-CBOA: Multi-objective chef-based optimization algorithm using hybrid dominance relations for solving engineering design problems. Computer Modeling in Engineering and Sciences, 143(1), 2025: 967–1008. https://doi.org/10.32604/cmes.2025.062332
[3] F. Wu, S. Li, J. Zhang, L. Yu, X. Xiong, L. Wu, Q-learning-based exponential distribution optimizer with multi-strategy guidance for solving engineering design problems and robot path planning. Results in Engineering, 27, 2025: 105705. https://doi.org/10.1016/j.rineng.2025.105705
[4] H. Bayzidi, S. Talatahari, M. Saraee, C.P. Lamarche, Social network search for solving engineering optimization problems. Computational Intelligence and Neuroscience, 2021(1), 2021: 8548639. https://doi.org/10.1155/2021/8548639
[5] S. Mohapatra, P. Mohapatra, An improved Golden Jackal Optimization algorithm using opposition-based learning for global optimization and engineering problems. International Journal of Computational Intelligence Systems, 16(1), 2023: 147. https://doi.org/10.1007/S44196-023-00320-8
[6] M.O. Okwu, L.K. Tartibu, Metaheuristic Optimization: Nature-Inspired Algorithms, Swarm and Computational Intelligence – Theory and Applications. Springer Cham, 2021. https://doi.org/10.1007/978-3-030-61111-8
[7] N. Hansen, D.V. Arnold, A. Auger, Evolution strategies. In: Springer Handbook of Computational Intelligence, Springer Handbooks, 2015: 871–898. https://doi.org/10.1007/978-3-662-43505-2_44
[8] S. Forrest, Genetic algorithms. ACM Computing Surveys (CSUR), 28(1), 1996: 77–80. https://doi.org/10.1145/234313.234350
[9] R. Storn, K. Price, Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11, 1997: 341–359. https://doi.org/10.1023/A:1008202821328
[10] S. Kamel, H. Hamour, M.H. Ahmed, L. Nasrat, Atom search optimization algorithm for optimal radial distribution system reconfiguration. Proceedings of ICCCEEE, 21–23 September 2019, Khartoum, Sudan.
[11] C. Yuan, D. Zhao, A.A. Heidari, L. Liu, Y. Chen, Z. Wu, H. Chen, Artemisinin optimization based on malaria therapy: algorithm and applications to medical image segmentation. Displays, 84, 2024: 102740. https://doi.org/10.1016/j.displa.2024.102740
[12] P. Duankhan, K. Sunat, S. Chiewchanwattana, P. Nasa-ngium, The differentiated creative search (DCS): leveraging differentiated knowledge-acquisition and creative realism to address complex optimization problems. Expert Systems with Applications, 252(Part A), 2024: 123734. https://doi.org/10.1016/j.eswa.2024.123734
[13] J. Kennedy, R. Eberhart, Particle swarm optimization. ICNN’95 – International Conference on Neural Networks, 27 Nov–1 Dec 1995, Perth, Australia, 1942–1948.
[14] C. Blum, Ant colony optimization: introduction and recent trends. Physics of Life Reviews, 2(4), 2005: 353–373. https://doi.org/10.1016/j.plrev.2005.10.001
[15] S. Mirjalili, S.M. Mirjalili, A. Lewis, Grey wolf optimizer. Advances in Engineering Software, 69, 2014: 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007
[16] S. Mirjalili, SCA: a sine cosine algorithm for solving optimization problems. Knowledge-Based Systems, 96, 2016: 120–133. https://doi.org/10.1016/j.knosys.2015.12.022
[17] M.H. Nadimi-Shahraki, H. Zamani, Z. Asghari Varzaneh, S. Mirjalili, A systematic review of the Whale Optimization Algorithm. Archives of Computational Methods in Engineering, 30, 2023: 4113–4159. https://doi.org/10.1007/S11831-023-09928-7
[18] S. Li, H. Chen, M. Wang, A.A. Heidari, S. Mirjalili, Slime mould algorithm: a new method for stochastic optimization. Future Generation Computer Systems, 111, 2020: 300–323. https://doi.org/10.1016/j.future.2020.03.055
[19] Y. Fu, D. Liu, J. Chen, L. He, Secretary bird optimization algorithm. Artificial Intelligence Review, 57, 2024: 123. https://doi.org/10.1007/s10462-024-10729-y
[20] P.J.M. Van Laarhoven, E.H.L. Aarts, Simulated annealing. In: Simulated Annealing: Theory and Applications. Springer Dordrecht, 1987: 7–15. https://doi.org/10.1007/978-94-015-7744-1
[21] H. Su, D. Zhao, A.A. Heidari, L. Liu, X. Zhang, M. Mafarja, H. Chen, RIME: a physics-based optimization. Neurocomputing, 532, 2023: 183–214. https://doi.org/10.1016/j.neucom.2023.02.010
[22] D. Zhu, S. Wang, C. Zhou, R. Tian, H. Zhang, J. Mao, Human memory optimization algorithm. Expert Systems with Applications, 237(Part C), 2024: 121597. https://doi.org/10.1016/j.eswa.2023.121597
[23] K. Ouyang, S. Fu, Y. Chen, Q. Cai, A.A. Heidari, H. Chen, Escape: an optimization method based on crowd evacuation behaviors. Artificial Intelligence Review, 58, 2025: 19. https://doi.org/10.1007/s10462-024-11008-6
[24] H.J.W. de Baar, von Liebig’s law of the minimum and plankton ecology (1899–1991). Progress in Oceanography, 33(4), 1994: 347–386. https://doi.org/10.1016/0079-6611(94)90022-1
[25] E.M. Goldratt, J. Cox, The Goal: A Process of Ongoing Improvement. Routledge, 2016.
[26] D. Meadows, Leverage Points – Places to Intervene in a System. Sustainability Institute, 2015.
[27] J.P. Womack, D.T. Jones, D. Roos, The Machine that Changed the World. Free Press, New York, 1990.
[28] R.D. Snee, R.W. Horerll, Leading Six Sigma: A Step-by-Step Guide Based on Experience with GE and Other Six Sigma Companies. Prentice-Hall, 2003.
[29] E.L. Charnov, Optimal foraging, the marginal value theorem. Theoretical Population Biology, 9(2), 1976: 129–136. https://doi.org/10.1016/0040-5809(76)90040-x
[30] R.S. Sutton, A.G. Barto, Reinforcement Learning: An Introduction. MIT Press, Cambridge, 2014.
[31] A. Kumar, K.V. Price, A.W. Mohamed, Problem definitions and evaluation criteria for the CEC 2022 competition, Technical Report. NTU Singapore, 2022.
[32] C.-Y. Lee, X. Yao, Evolutionary programming using mutations based on the Lévy probability distribution. IEEE Transactions on Evolutionary Computation, 8(1), 2004: 1–13. https://doi.org/10.1109/TEVC.2003.816583
[33] S. Mirjalili, Moth-flame optimization algorithm. Knowledge-Based Systems, 89, 2015: 228–249. https://doi.org/10.1016/j.knosys.2015.07.006
[34] H. Liu, Z. Chen, X. Zhang, C.-C. Wu, J.N.D. Gupta, An improved arithmetic optimization algorithm based on reinforcement learning. Swarm and Evolutionary Computation, 96, 2025: 101985. https://doi.org/10.1016/j.swevo.2025.101985
[35] K. Hussain, M.N.M. Salleh, S. Cheng, Y. Shi, On exploration and exploitation in swarm algorithms. Neural Computing and Applications, 31, 2019: 7665–7683. https://doi.org/10.1007/s00521-018-3592-0
© 2025 by the authors. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0)
Volume 10
Number 4
December 2025
Last Edition
Volume 10
Number 4
December 2025
How to Cite
V.T. Tran, Q.T.T. Nhu, C. Soomlek, P. Horata, K. Sunat, BTO: A Barrel Theory-Based Optimizer for Engineering Design Problems. Applied Engineering Letters, 10(4), 2025: 193-210.
https://doi.org/10.46793/aeletters.2025.10.4.2
More Citation Formats
Tran, V.T., Nhu, Q.T.T., Soomlek, C., Horata, P., & Sunat, K. (2025). BTO: A Barrel Theory-Based Optimizer for Engineering Design Problems. Applied Engineering Letters, 10(4), 193-210.
https://doi.org/10.46793/aeletters.2025.10.4.2
Tran, Van Tai, et al. “BTO: A Barrel Theory-Based Optimizer for Engineering Design Problems.“ Applied Engineering Letters, vol. 10, no. 4, 2025, pp. 193-210.
https://doi.org/10.46793/aeletters.2025.10.4.2
Tran, Van Tai, Quynh T.T Nhu, Chitsutha Soomlek, Punyaphol Horata, and Khamron Sunat. 2025. “BTO: A Barrel Theory-Based Optimizer for Engineering Design Problems.“ Applied Engineering Letters, 10(4): 193-210.
https://doi.org/10.46793/aeletters.2025.10.4.2
Tran, V.T., Nhu, Q.T.T., Soomlek, C., Horata, P. and Sunat, K. (2025). BTO: A Barrel Theory-Based Optimizer for Engineering Design Problems. Applied Engineering Letters, 10(4), pp. 193-210.
doi: 10.46793/aeletters.2025.10.4.2.