Binarization of Metaheuristic Optimization Algorithm: A Comparative Analysis

Metaheuristic algorithms are a kind of optimization algorithms, which are widely used in reducing the number of variables, and choosing the most relevant, and identifiable ones in medium or high dimensional datasets. This topic, known as feature selection is widely researched and applied where binary metaheuristic algorithms are developed using as an evaluator of the quality of the feature subsets machine learning algorithms. The binary metaheuristics could be created by transforming the continuous space of the metaheuristic by using some operators named transfer function, into a binary one, since feature selection is a binary optimization problem. This paper aims to offer a comparative analysis of three distinct binary variants of metaheuristic optimization algorithms utilizing five different groups of transfer functions to assess their predictive efficacy. Four S-shaped, V-shaped, U-shaped, Q-shaped, and two X-shaped types are proposed for the binarization process. Salp Swarm Optimization, Ant Lion Optimization, and Teaching Learning-Based Optimization algorithms are chosen as the foundational algorithms for assessing each transfer function and comparing their impact on key metrics, including accuracy, F-score, sensitivity, average number of selected features, fitness, and time efficiency. The current work utilizes a medical dataset to predict the existence of gallstones. The experiment aims to compare and propose new solutions applied to the feature selection process. The optimal combinations of transfer functions and metaheuristic algorithms are produced using the combination of the Q3 transfer function together with a binary teaching-based learning method and the V2 transfer function combined with binary antlion optimization, achieving an accuracy of approximately 78%. The research emphasizes the necessity of appropriate binarization strategies and provides insights into selecting transfer functions to improve feature selection in medical data analysis.

Metaheuristic algorithm, Binary Optimization, Transfer functions, Feature selection, Gallstone prediction, Medical Analysis

1. Martí, R., Sevaux, M., & Sörensen, K. (2025) 50 years of metaheuristics, European Journal of Operational Research, 321(2), 345-362, doi: 10.1016/j.ejor.2024.04.004 [Google Scholar] [Crossref]

2. Kennedy, J. & Eberhart, C. R, (1997). A discrete binary version of the particle swarm algorithm, in 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation, Orlando, FL, USA, doi: 10.1109/ICSMC.1997.637339 [Google Scholar] [Crossref]

3. Thaher, T., Mafarja, M., Turabieh, H., Castillo, A. P., Faris, H., & Aljarah, I. (2021). Teaching Learning-Based Optimization with Evolutionary Binarization Schemes for Tackling Feature Selection Problems, IEEE Access, 9, 41082-41103, doi: 10.1109/ACCESS.2021.3064799 [Google Scholar] [Crossref]

4. Becerra-Rozas, M., Lemus-Romani, J., Cisternas-Caneo, F., Crawford, B., Soto, R., Astorga, G., Castro, C., & García, J. (2023). Continuous Metaheuristics for Binary Optimization Problems: An Updated Systematic Literature Review, Mathematics, 11(1), 1-32, [Google Scholar] [Crossref]

5. https://doi.org/10.3390/math11010129 [Google Scholar] [Crossref]

6. Mirjalili, S., & Lewis, A., (2013). S-shaped versus V-shaped transfer functions for binary Particle Swarm Optimization, Swarm and Evolutionary Computation, Swarm and Evolutionary Computation, 9, 1-14, https://doi.org/10.3390/math11010129 [Google Scholar] [Crossref]

7. Beheshti, Z. (2021), A novel x-shaped binary particle swarm optimization, Soft Computing, 25, 3013-3042, doi: 10.1007/s00500-020-05360-2 [Google Scholar] [Crossref]

8. Mirjalili, S. Z. , Zhang, H., Mirjalili, S., Chalup, S. & Noman, N. (2020). A Novel U-Shaped Transfer Function for Binary Particle Swarm Optimisation, Advances in Intelligent Systems and Computing, 1138, Singapore, Springer, 241–259, doi: 10.1007/978-981-15-3290-0_19 [Google Scholar] [Crossref]

9. Guo, Sha-sha., Wang, Jie-sheng., & Guo, Meng-wei. (2020). Z-Shaped Transfer Functions for Binary Particle Swarm Optimization Algorithm, Computational Intelligence and Neuroscience, 6502807, 1-21, https://doi.org/10.1155/2020/6502807 [Google Scholar] [Crossref]

10. Wang, L., Wang, X., Fu, J., & Zhen, L. (2008). A Novel Probability Binary Particle Swarm Optimization Algorithm and Its Application, Journal of Software, 3(9), 28-35, doi: 10.4304/jsw.3.9.28-35 [Google Scholar] [Crossref]

11. Too, J., Abdullah, R. A. & Saad, M. N. (2019). A New Quadratic Binary Harris Hawk Optimization for Feature Selection, Electronics, 8, 1-27, [Google Scholar] [Crossref]

12. https://doi.org/10.3390/electronics8101130 [Google Scholar] [Crossref]

13. Rashedi, E., Nezamabadi-Pour, H., & Saryazdi, S. (2010). BGSA: binary gravitational search algorithm”, Natural Computing, 9, 727–745, https://doi.org/10.1007/s11047-009-9175-3 [Google Scholar] [Crossref]

14. Emary, E. M., Zawbaa, M. H., & Hassanien, E. A. (2016). Binary grey wolf optimization approaches for feature selection, Neurocomputing, 172, 371-381, https://doi.org/10.1016/j.neucom.2015.06.083 [Google Scholar] [Crossref]

15. Mafarja, M., Eleyan, D., Abdullah, S., & Mirjalili, S. (2017). S-Shaped vs. V-Shaped Transfer Functions for Ant Lion Optimization Algorithm in Feature Selection Problem ,in ICFNDS '17: Proceedings of the International Conference on Future Networks and Distributed Systems, 21, 1-7, https://doi.org/10.1145/3102304.310232. [Google Scholar] [Crossref]

16. Naka, E. (2023). A Competitive Parkinson-Based Binary Volleyball Premier League Metaheuristic Algorithm for Feature Selection, Cybernetics and Information Technologies, 23(4), 91-109, https://doi.org/10.2478/cait-2023-0038 [Google Scholar] [Crossref]

17. Nadimi-Shahraki, M. H., Banaie-Dezfouli, M., Zamani, H., Taghian, S., & Mirjalili, S. (2021). B-MFO: A Binary Moth-Flame Optimization for Feature Selection from Medical Datasets, Computers, 10, 1-18, https://doi.org/10.3390/computers10110136 [Google Scholar] [Crossref]

18. Kumar, V., Kumar, D., Kaur, M., Singh, D., Idris, A. S., & Alshazly, H. (2021). A Novel Binary Seagull Optimizer and Its Application to Feature Selection Problem, IEEE Access, 9, 103481-103496, doi: 10.1109/ACCESS.2021.3098642 [Google Scholar] [Crossref]

19. Bas, E., (2024). BinDMO: a new Binary Dwarf Mongoose Optimization algorithm on based Z-shaped, U-shaped, and taper-shaped transfer functions for CEC-2017 benchmarks, Neural Computing and Applications, 36, 6903–6935, https://doi.org/10.1007/s00521-024-09436-0 [Google Scholar] [Crossref]

20. Beşkirli, A. (2025), A Transfer Function-Based Binary Version of Improved Pied Kingfisher Optimizer for Solving the Uncapacitated Facility Location Problem, Biomimetics, 10(8), 1-30, [Google Scholar] [Crossref]

21. https://doi.org/10.3390/biomimetics10080526 [Google Scholar] [Crossref]

22. Kristiyanti, D. A., Sitanggang, I. S., Annisa, Nurdiati, S. (2023). Feature Selection Using New Version of V-Shaped Transfer Function for Salp Swarm Algorithm in Sentiment Analysis, Computation, 11(3), https://doi.org/10.3390/computation11030056 [Google Scholar] [Crossref]

23. Heris, M. K. (2015), Teaching-Learning-based Optimization in MATLAB. [Online]. January 25 2021, Available: https://yarpiz.com/83/ypea111-teaching-learning-based-optimization. [Google Scholar] [Crossref]

24. Too, J. Salp Swarm Algorithm for Feature Selection, [Online]. January 21 2021, Available: [Google Scholar] [Crossref]

25. https://www.mathworks.com/matlabcentral/fileexchange/78913-salp-swarm-algorithm-for-feature-selection?s_tid=prof_contriblnk. [Google Scholar] [Crossref]

26. Emary, E., Zawbaa, H. M., & Hassanien, A. E. (2016), Binary ant lion approaches for feature selection, Neurocomputing, 213, 54-65, https://doi.org/10.1016/j.neucom.2016.03.101 [Google Scholar] [Crossref]

27. Rao, R. V., Savsani, V. J., & Vakharia, D. P. (2011), Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems, Computer-Aided Design, 43(3), 303-315, doi: 10.1016/j.cad.2010.12.015 [Google Scholar] [Crossref]

28. Mirjalili, S. (2015), The Ant Lion Optimizer, Advances in Engineering Software, 83, 80-98, doi: [Google Scholar] [Crossref]

29. 1016/j.advengsoft.2015.01.010 [Google Scholar] [Crossref]

30. Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H., & Mirjalili, S. M., (2017). Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems, Advances in Engineering Software, 114, 163-191, https://doi.org/10.1016/j.advengsoft.2017.07.002 [Google Scholar] [Crossref]

31. Lemus-Romani, J., Crawford, B., Cisternas-Caneo, F., Soto, R., & Becerra-Rozas, M., (2023). Binarization of Metaheuristics: Is the Transfer Function Really Important? Electronics, 8(5), 1-47, https://doi.org/10.3390/biomimetics8050400 [Google Scholar] [Crossref]

32. Esen, İ., Arslan, H., Esen, S. A., Gülşen, M., Kültekin, N., & Özdemir, O. (2024). Early prediction of gallstone disease with a machine learning-based method from bioimpedance and laboratory data, Medicine, 103(8), doi: 10.1097/MD.0000000000037258. [Google Scholar] [Crossref]

• Assessment of the Role of Artificial Intelligence in Repositioning TVET for Economic Development in Nigeria
• Teachers’ Use of Assure Model Instructional Design on Learners’ Problem Solving Efficacy in Secondary Schools in Bungoma County, Kenya
• “E-Booksan Ang Kaalaman”: Development, Validation, and Utilization of Electronic Book in Academic Performance of Grade 9 Students in Social Studies
• Analyzing EFL University Students’ Academic Speaking Skills Through Self-Recorded Video Presentation
• Major Findings of The Study on Total Quality Management in Teachers’ Education Institutions (TEIs) In Assam – An Evaluative Study