AccScience Publishing / IJOCTA / Online First / DOI: 10.36922/IJOCTA026310196
Cite this article
6
Download
48
Views
Related Info Links
More by Authors Links
Journal Browser
Volume | Year
Issue
Search
News and Announcements
View All
RESEARCH ARTICLE

Hybridization of the weighted distance method with directional bat algorithm for NMPC tuning

Misael Hernández1 ,  Luis Miguel Valenzuela1* ,  Antioco López-Molina1 ,  Carolina Conde-Mejía1 ,  Fernando Israel Gómez-Castro2 ,  Oscar Daniel Lara-Montaño3 ,  Moisés Abraham Petriz-Prieto1
Show Less
1 División Académica Multidisciplinaria de Jalpa de Méndez, UJAT, Carretera Nacajuca–Jalpa de Méndez, R/a Rivera Alta, Jalpa de Méndez, Tabasco , México
2 División de Ciencias Naturales y Exactas, Departamento de Ingeniería Química, Universidad de Guanajuato, Campus Guanajuato, Noria Alta S/N Col. Noria Alta, Guanajuato , México
3 Facultad de Ingeniería, Campus Amealco, Universidad Autónoma de Querétaro, Carretera Amealco– Atemascalcingo Km 1, Centro, Amealco de Bonfil, Querétaro , México
Received: 1 August 2026 | Revised: 16 October 2026 | Accepted: 20 October 2026 | Published online: 3 November 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

This work presents a hybrid optimization algorithm that combines the Weighted Distance Method and the Directional Bat Algorithm to improve the efficiency and robustness of solving nonlinear model predictive control problems. The proposed hybrid framework integrates the global exploration capability of the Directional Bat Algorithm with the local exploitation and adaptive refinement properties of the Weighted Distance Method. In the first stage, the Directional Bat Algorithm generates a diverse set of candidate solutions by using adaptive mechanisms for frequency, amplitude, and random movement, thereby ensuring broad coverage of the search space and preventing premature convergence to local minima. Subsequently, the Weighted Distance Method refines these solutions by computing weighted directional vectors, which are updated at each iteration based on the population mean distance and each agent’s proximity to the global best individual. The sequential combination of both strategies achieves an effective balance between exploration and exploitation, resulting in greater stability, improved convergence performance, and higher-quality optimal solutions. On a standard suite of thirty benchmark functions in dimensions 10, 30, and 50, the hybrid ranks third among five optimizers: it outperforms both of its constituent algorithms but does not surpass the Differential Evolution and Particle Swarm baselines, confirming that the sequential coupling yields a stronger optimizer than either component alone. On the tuning of a nonlinear model predictive controller for a Van de Vusse reactor, the proposed hybrid scheme achieves competitive closed-loop tracking performance compared with the standalone methods while improving convergence stability and robustness to initialization, highlighting its potential for complex nonlinear control applications.

Keywords
Directional bat algorithm
Weighted distance method
Optimization
Metaheuristic
Predictive control
Funding
None.
Conflict of interest
The authors declare they have no competing interests.
References
  1. Qin SJ, Badgwell TA. A survey of industrial model predictive control technology. Control Eng Pract. 2003;11(7):733-764. https://doi.org/10.1016/S0967-0661(02)00186-7
  2. Engell S. Feedback control for optimal process operation. J Process Control. 2007;17(3):203-219. https://doi.org/10.1016/j.jprocont.2006.10.011
  3. Wang L. Model Predictive Control System Design and Implementation Using MATLAB. London, UK: Springer; 2009. https://doi.org/10.1007/978-1-84882-331-0
  4. Rawlings JB, Mayne DQ, Diehl MM. Model Predictive Control: Theory, Computation, and Design. 2nd ed. Madison, WI: Nob Hill Publishing; 2017. Accessed January 9, 2026. https://sites.engineering.ucsb.edu/~jbraw/mpc/MPC-book-2nd-edition-1st-printing.pdf
  5. Patrón GD, Ricardez-Sandoval LA. A robust nonlinear model predictive controller for a post-combustion CO₂ capture absorber unit. Fuel. 2020;265:116932. https://doi.org/10.1016/j.fuel.2019.116932
  6. Lucia S, Finkler T, Engell S. Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty. J Process Control. 2013;23(9):1306-1319. https://doi.org/10.1016/j.jprocont.2013.08.008
  7. Vallerio M, Van Impe J, Logist F. Tuning of NMPC controllers via multi-objective optimisation. Comput Chem Eng. 2014;61:38-50. https://doi.org/10.1016/j.compchemeng.2013.10.003
  8. Flores-Tlacuahuac A, Morales P, Rivera-Toledo M. Multiobjective nonlinear model predictive control of a class of chemical reactors. Ind Eng Chem Res. 2012;51(17):5891-5899. https://doi.org/10.1021/ie201742e
  9. Giraldo SAC, Melo PA, Secchi AR. Tuning of model predictive controllers based on hybrid optimization. Processes. 2022;10(2):351. https://doi.org/10.3390/pr10020351
  10. Al Bannoud M, da Silva CAM, Martins TD. Applications of metaheuristic optimization algorithms in model predictive control for chemical engineering processes: A systematic review. Annu Rev Control. 2024;58:100973. https://doi.org/10.1016/j.arcontrol.2024.100973
  11. Ölmez Y, Koca GÖ, Akpolat ZH. Recent metaheuristics on control parameter determination. Int J Optim Control Theor Appl. 2025;15(1):166-182. https://doi.org/10.36922/ijocta.1620
  12. Joseph SB, Dada EG, Abidemi A, Oyewola DO, Khammas BM. Metaheuristic algorithms for PID controller parameters tuning: Review, approaches and open problems. Heliyon. 2022;8(5):e09399. https://doi.org/10.1016/j.heliyon.2022.e09399
  13. Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of ICNN'95 - International Conference on Neural Networks. Vol 4. Piscataway, NJ: IEEE; 1995:1942-1948. https://doi.org/10.1109/ICNN.1995.488968
  14. Storn R, Price K. Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim. 1997;11(4):341-359. https://doi.org/10.1023/A:1008202821328
  15. Yang XS. A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010). Studies in Computational Intelligence, Vol 284. Berlin, Germany: Springer; 2010:65-74. https://doi.org/10.1007/978-3-642-12538-6_6
  16. Mirjalili S, Lewis A. The whale optimization algorithm. Adv Eng Softw. 2016;95:51-67. https://doi.org/10.1016/j.advengsoft.2016.01.008
  17. Benaissa B, Kobayashi M, Al Ali M, Khatir T, Elaissaoui Elmeliani MEA. Metaheuristic optimization algorithms: An overview. HCMCOU J Sci Adv Comput Struct. 2024;14(1):33-61. https://doi.org/10.46223/hcmcoujs.acs.en.14.1.47.2024
  18. Houssein EH, Saeed MK, Hu G, Al-Sayed MM. Metaheuristics for solving global and engineering optimization problems: Review, applications, open issues and challenges. Arch Comput Methods Eng. 2024;31:4485-4519. https://doi.org/10.1007/s11831-024-10168-6
  19. Delgarm Z, Mostafa Gharebaghi AR, Emami A. Comparison of metaheuristic algorithms for weight optimization of a semi-submersible VAWT substructure with hexagonal pontoons. Int J Marit Technol. 2026;22(1):66-80. https://doi.org/10.66224/ijmt.22.1.66
  20. Tomar V, Bansal M, Singh P. Metaheuristic algorithms for optimization: A brief review. In: Engineering Proceedings (RAiSE-2023). Vol 59. Basel, Switzerland: MDPI; 2024:238. https://doi.org/10.3390/engproc2023059238
  21. Wolpert DH, Macready WG. No free lunch theorems for optimization. IEEE Trans Evol Comput. 1997;1(1):67-82. https://doi.org/10.1109/4235.585893
  22. Kusznir T, Smoczek J. Nonlinear model predictive control with evolutionary data-driven prediction model and particle swarm optimization optimizer for an overhead crane. Appl Sci. 2024;14(12):5112. https://doi.org/10.3390/app14125112
  23. Devanathan B, Selvaraj P, Suyampulingam A. Nonlinear model predictive control for Internet of Things using particle swarm optimization and cloud computing. IEEE Access. 2025;99:1. https://doi.org/10.1109/ACCESS.2025.3554719
  24. Essa MESM, Elsisi M, Saleh Elsayed M, Fawzy Ahmed M, Elshafeey AM. An improvement of model predictive for aircraft longitudinal flight control based on intelligent technique. Mathematics. 2022;10(19):3510. https://doi.org/10.3390/math10193510
  25. Liu L, Liu H, Wang X,  et al. Application of path planning and tracking control technology in mower robots. Agronomy. 2024;14(11):2473. https://doi.org/10.3390/agronomy14112473
  26. Ewias AM, Hakmi SH, Mohamed TH,  et al. Advanced load frequency control of microgrid using a bat algorithm supported by a balloon effect identifier in the presence of photovoltaic power source. PLoS One. 2023;18(10). https://doi.org/10.1371/journal.pone.0293246
  27. Zhao J, Chang G, Sun Y,  et al. Real-time nonlinear model predictive control for optimizing the ammonia coverage ratio of an SCR system based on TC-QPSO. Control Eng Pract. 2023;132:105409. https://doi.org/10.1016/j.conengprac.2022.105409
  28. Zhang L, Xie L, Su H, Liu J. Data-driven auto-tuning strategy for RTO-MPC based on Bayesian optimization. Comput Chem Eng. 2024;187:108743. https://doi.org/10.1016/j.compchemeng.2024.108743
  29. Meng Z, Xiao Y, Xu X, Luo B, Du Y, Gui W. Auto-tuning strategy for deep Koopman robust model predictive control design based on advanced metaheuristics. Neurocomputing. 2025;638:130197. https://doi.org/10.1016/j.neucom.2025.130197
  30. Ławryńczuk M. Koopman operator-based multi-model for predictive control. Nonlinear Dyn. 2024;116:19085-19110. https://doi.org/10.1007/s11071-024-09615-7
  31. Dahak A, Boutaghane H, Boulmaiz T. Machine and deep learning-based prediction of infiltration parameters: insights from field data in Northern Algeria. Euro-Mediterr J Environ Integr. 2026;11(4):58. https://doi.org/10.1007/s41207-026-01103-1
  32. Ankalugari S, Abuthahir MU, Jan NM, Joseph AG. Control of van de Vusse reactor using deep reinforcement learning. In: 2024 29th International Conference on Automation and Computing (ICARCV). Piscataway, NJ: IEEE; 2024:1-6. https://doi.org/10.1109/ICARCV63323.2024.10821642
  33. Wang Y, Wang P, Zhang J,  et al. A novel bat algorithm with multiple strategies coupling for numerical optimization. Mathematics. 2019;7(2):135. https://doi.org/10.3390/math7020135
  34. Yu H, Song J, Chen C,  et al. Optimal performance design of bat algorithm: An adaptive multi-stage structure. CAAI Trans Intell Technol. 2025;10(3):755-814. https://doi.org/10.1049/cit2.12377
  35. Qin F, Zain AM, Zhou KQ,  et al. Hybrid harmony search algorithm integrating differential evolution and Lévy flight for engineering optimization. IEEE Access. 2025;13:13534-13572. https://doi.org/10.1109/ACCESS.2025.3529714
  36. Bansal S, Bhattacharjee S. An improved quantum-inspired evolutionary algorithm framework implemented to solve minimum vertex cover problem. Struct Multidisc Optim. 2025;68(7):145. https://doi.org/10.1007/s00158-025-04078-9
  37. Bindu MG, Malathi S. Explainable feature selection using improved firefly algorithm with population diversification and stagnation-aware exploration. Discov Comput. 2026;29:149. https://doi.org/10.1007/s10791-026-10041-z
  38. Zhang K, Zhao H, Li X, Fu C, Jin J. Gekko japonicus algorithm: A novel nature-inspired algorithm for engineering problems and path planning. J Bionic Eng. 2026;23(1):431-471. https://doi.org/10.1007/s42235-025-00805-6
  39. Yahaya MS, Hashim ASB, Balogun AO,  et al. Exploration and exploitation mechanism in pairwise test case generation: A systematic literature review. IEEE Access. 2025;13:82342-82377. https://doi.org/10.1109/ACCESS.2025.3566163
  40. Chakri A, Khelif R, Benouaret M, Yang XS. New directional bat algorithm for continuous optimization problems. Expert Syst Appl. 2017;69:159-175. https://doi.org/10.1016/j.eswa.2016.10.050
  41. Trierweiler JO, Engell S. Controllability analysis via the robust performance number for a CSTR with Van de Vusse reaction. In: Proceedings of the 1997 European Control Conference (ECC). Piscataway, NJ: IEEE; 1997:3083-3088. https://doi.org/10.23919/ECC.1997.7082582
  42. Klatt KU, Engell S. Gain-scheduling trajectory control of a continuous stirred tank reactor. Comput Chem Eng. 1998;22(4-5):491-502. https://doi.org/10.1016/S0098-1354(97)00261-5
Share
Back to top
An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing