A Hybrid Grey Wolf Optimizer–Zebra Optimization Algorithm for Solving Optimization Problems
Abstract
Keywords
Full Text:
PDFReferences
O. Altay and E. V. Altay, “A novel chaotic transient search optimization algorithm for global optimization, real-world engineering problems and feature selection,” PeerJ Comput. Sci., vol. 9, p. e1526, 2023, doi: 10.7717/peerj-cs.1526.
B. F. Azevedo, A. M. A. C. Rocha, and A. I. Pereira, “Hybrid approaches to optimization and machine learning methods: a systematic literature review,” Mach. Learn., vol. 113, no. 7, pp. 4055–4097, 2024, doi: 10.1007/s10994-023-06467-x.
S. M. Almufti, A. A. Shaban, Z. A. Ali, R. I. Ali, and J. A. Dela Fuente, “Overview of metaheuristic algorithms,” Polaris Glob. J. Sch. Res. Trends, vol. 2, no. 2, pp. 10–32, 2023, doi: 10.58429/pgjsrt.v2n2a144.
S. Voß, S. Martello, I. H. Osman, and C. Roucairol, “Meta-heuristics: Advances and trends in local search paradigms for optimization,” 2012, doi: 10.1007/978-1-4615-5775-3.
V. C. SS and A. HS, “Nature inspired meta heuristic algorithms for optimization problems,” Computing, vol. 104, no. 2, pp. 251–269, 2022, doi: 10.1007/s00607-021-00955-5.
J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95-international conference on neural networks, ieee, 1995, pp. 1942–1948, doi: 10.1109/icnn.1995.488968.
J. H. Holland, “Genetic algorithms,” Sci. Am., vol. 267, no. 1, pp. 66–73, 1992, doi: 10.1038/scientificamerican0792-66.
R. Storn and K. Price, “Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces,” J. Glob. Optim., vol. 11, pp. 341–359, 1997, doi: 10.1023/a:1008202821328.
X. Yang and A. Hossein Gandomi, “Bat algorithm: a novel approach for global engineering optimization,” Eng. Comput., vol. 29, no. 5, pp. 464–483, 2012, doi: 10.1108/02644401211235834.
S.-E. K. Fateen and A. Bonilla-Petriciolet, “Intelligent firefly algorithm for global optimization,” Cuckoo Search Firefly Algorithm Theory Appl., pp. 315–330, 2014, doi: 10.1007/978-3-319-02141-6_15.
X.-S. Yang, Cuckoo search and firefly algorithm: theory and applications, vol. 516. Springer, 2013, doi: 10.1007/978-3-319-02141-6.
S. Arora and S. Singh, “Butterfly optimization algorithm: a novel approach for global optimization,” Soft Comput., vol. 23, no. 3, pp. 715–734, 2019, doi: 10.1007/s00500-018-3102-4.
S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Adv. Eng. Softw., vol. 69, pp. 46–61, 2014, doi: 10.1016/j.advengsoft.2013.12.007.
A. Askarzadeh, “A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm,” Comput. Struct., vol. 169, pp. 1–12, 2016, doi: 10.1016/j.compstruc.2016.03.001.
A. Ali, “A NOVEL APPROACH: THREE-GROUP EXPLORATION STRATEGY ALGORITHM FOR SOLVING OPTIMIZATION PROBLEMS,” IJISCS (International J. Inf. Syst. Comput. Sci., vol. 9, no. 2, pp. 57–78, 2025, doi: 10.56327/ijiscs.v9i2.1774.
E. Trojovská, M. Dehghani, and P. Trojovský, “Zebra optimization algorithm: A new bio-inspired optimization algorithm for solving optimization algorithm,” Ieee Access, vol. 10, pp. 49445–49473, 2022, doi: 10.1109/access.2022.3172789.
M. Kohli and S. Arora, “Chaotic grey wolf optimization algorithm for constrained optimization problems,” J. Comput. Des. Eng., vol. 5, no. 4, pp. 458–472, 2018, doi: 10.1016/j.jcde.2017.02.005.
E. Emary, H. M. Zawbaa, and A. E. Hassanien, “Binary grey wolf optimization approaches for feature selection,” Neurocomputing, vol. 172, pp. 371–381, 201, doi: 10.1016/j.neucom.2015.06.083.
M. A. Tawhid and A. M. Ibrahim, “A hybridization of grey wolf optimizer and differential evolution for solving nonlinear systems,” Evol. Syst., vol. 11, no. 1, pp. 65–87, 2020, doi: 10.1007/s12530-019-09291-8.
W. Lei, W. Jiawei, and M. Zezhou, “Enhancing grey wolf optimizer with levy flight for engineering applications,” IEEE Access, vol. 11, pp. 74865–74897, 2023, doi: 10.1109/access.2023.3295242.
K. Meidani, A. Hemmasian, S. Mirjalili, and A. Barati Farimani, “Adaptive grey wolf optimizer,” Neural Comput. Appl., vol. 34, no. 10, pp. 7711–7731, 2022, doi: 10.1007/s00521-021-06885-9.
X. Zhang and Z. Ming, “An optimized grey wolf optimizer based on a mutation operator and eliminating-reconstructing mechanism and its application,” Front. Inf. Technol. Electron. Eng., vol. 18, no. 11, pp. 1705–1719, 2017, doi: 10.1631/fitee.1601555.
P. Punia, A. Raj, and P. Kumar, “Enhanced zebra optimization algorithm for reliability redundancy allocation and engineering optimization problems,” Cluster Comput., vol. 28, no. 4, p. 267, 2025, doi: 10.1007/s10586-024-04931-4.
H. M. El-Hageen et al., “Chaotic zebra optimization algorithm for increasing the lifetime of wireless sensor network,” J. Netw. Syst. Manag., vol. 32, no. 4, p. 85, 2024, doi: 10.1007/s10922-024-09860-6.
J. J. Al-zamili, “Mathematical modeling and optimization of intelligent systems using a hybrid PSO-GWO algorithm: A minx J(x) approach,” Results in Nonlinear Analysis, vol. 8, no. 2, pp. 133–147, 2025, doi: 10.31838/rna/2025.08.02.012.
N. A. Aris et al., “A Hybrid Chaotic Zebra Optimization Algorithm for Cost-Effective Healthcare Team Formation,” Int. J. Online Biomed. Eng. (iJOE), vol. 21, no. 8, pp. 56–74, 2025, doi: 10.3991/ijoe.v21i08.54697.
X. Yu, Y. Li, and J. Wang, “A hybrid algorithm based on Grey Wolf Optimizer and Differential Evolution (HGWODE),” Expert Systems with Applications, vol. 213, p. 119327, 2023, doi: 10.1016/j.eswa.2022.119327.
H. M. Mohammed and T. A. Rashid, “A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design,” Neural Computing and Applications, doi: 10.36227/techrxiv.11916369.v1.
S. Mirjalili, “SCA: a sine cosine algorithm for solving optimization problems,” Knowledge-based Syst., vol. 96, pp. 120–133, 2016, doi: 10.1016/j.knosys.2015.12.022.
S. Mirjalili, “Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm,” Knowledge-based Syst., vol. 89, pp. 228–249, 2015, doi: 10.1016/j.knosys.2015.07.006.
A. A. Heidari, S. Mirjalili, H. Faris, I. Aljarah, M. Mafarja, and H. Chen, “Harris hawks optimization: Algorithm and applications,” Futur. Gener. Comput. Syst., vol. 97, pp. 849–872, 2019, doi: 10.1016/j.future.2019.02.028.
S. Mirjalili and A. Lewis, “The whale optimization algorithm,” Adv. Eng. Softw., vol. 95, pp. 51–67, 2016, doi: 10.1016/j.advengsoft.2016.01.008.
G. Wu, R. Mallipeddi, and P. N. Suganthan, “Problem definitions and evaluation criteria for the CEC 2017 competition on constrained real-parameter optimization,” Natl. Univ. Def. Technol. Chang. Hunan, PR China Kyungpook Natl. Univ. Daegu, South Korea Nanyang Technol. Univ. Singapore, Tech. Rep., 2017, https://www.researchgate.net/publication/317228117_Problem_Definitions_and_Evaluation_Criteria_for_the_CEC_2017_Competition_and_Special_Session_on_Constrained_Single_Objective_Real-Parameter_Optimization.
C. T. Yue et al., “Biswas Problem Definitions and Evaluation Criteria for the CEC 2020 Special Session and Competition on Single Objective Bound Constrained Numerical Optimization,” Technical Report, Computational Intelligence Laboratory, Zhengzhou …, 2020, https://www.researchgate.net/publication/338711283_Problem_Definitions_and_Evaluation_Criteria_for_the_CEC_2020_Special_Session_on_Multimodal_Multiobjective_Optimization.
Y. Li, X. Liang, J. Liu, and H. Zhou, “Multi-strategy Equilibrium Optimizer: An improved meta-heuristic tested on numerical optimization and engineering problems,” PLoS One, vol. 17, no. 10 October, p. e0276210, 2022, doi: 10.1371/journal.pone.0276210.
X. Li, Y. Qi, Q. Xing, and Y. Hu, “IMSCSO: an intensified sand cat swarm optimization with multi-strategy for solving global and engineering optimization problems,” IEEE Access, vol. 11, pp. 122315–122344, 2023, doi: 10.1109/access.2023.3327732.
Y. Liu, Z. Fang, M. H. Cheung, W. Cai, and J. Huang, “Economics of blockchain storage,” in ICC 2020-2020 IEEE International Conference on Communications (ICC), IEEE, 2020, pp. 1–6, doi: 10.1109/icc40277.2020.9148934.
DOI: https://doi.org/10.37905/jjom.v8i1.34499
Copyright (c) 2026 Ayad Ali

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Jambura Journal of Mathematics has been indexed by
Jambura Journal of Mathematics (e-ISSN: 2656-1344) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Powered by Public Knowledge Project OJS.
Editorial Office
Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo, Indonesia
Email: [email protected].


















