Bin_MRFOA: A NOVEL MANTA RAY FORAGING OPTIMIZATION ALGORITHM FOR BINARY OPTIMIZATION

Abstract

Optimization problems occur in three different structures: continuous, discrete, and hybrid. Metaheuristic algorithms, which are frequently preferred in the solution of optimization problems today, are mostly proposed for continuous problems and are discretized with subsequent modifications. In this study, a novel binary version (Bin_MRFOA) of the manta ray foraging optimization algorithm, which was frequently used in the solution of continuous optimization problems before, was proposed to be used in the solution of binary optimization problems. The Bin_MRFOA was first tested on ten classical benchmark functions, and the effect of the transfer function on performance was examined by comparing the variants obtained using eight different transfer functions. Then the most successful Bin_MRFOA variant was run on the eighteen CEC2005 benchmark functions. The results were compared with the algorithms in the literature and interpreted with Wilcoxon signed-rank and Friedman tests, which are nonparametric tests. The results revealed that Bin_MRFOA is a successful, competitive, and preferable algorithm compared to the literature.

Keywords

• Binary Optimization
• Manta Ray Foraging Optimization
• S-shaped and V-shaped Transfer Functions

BIN_MRFOA: İkili Optimizasyon İçin Yeni Bir Manta Vatozu Beslenme Optimizasyonu Algoritması

Abstract

Optimizasyon problemleri üç farklı yapıda ortaya çıkar: sürekli, ayrık ve hibrit. Günümüzde optimizasyon problemlerinin çözümünde sıklıkla tercih edilen metasezgisel algoritmalar daha çok sürekli problemler için önerilmiş ve sonraki modifikasyonlarla ayrıklaştırılmıştır. Bu çalışmada, daha önce sürekli optimizasyon problemlerinin çözümünde sıklıkla kullanılan manta vatozu beslenme optimizasyon algoritmasının yeni bir ikili versiyonu (Bin_MRFOA), ikili optimizasyon problemlerinin çözümünde kullanılmak üzere önerilmiştir. Bin_MRFOA ilk olarak on tane klasik kıyaslama fonksiyon üzerinde test edilmiş ve sekiz farklı transfer fonksiyonu kullanılarak elde edilen varyantlar karşılaştırılarak transfer fonksiyonunun performans üzerindeki etkisi incelenmiştir. Ardından en başarılı Bin_MRFOA varyantı, on sekiz CEC2005 kıyaslama fonksiyonu üzerinde çalıştırılmıştır. Sonuçlar literatürdeki algoritmalar ile karşılaştırılmış ve parametrik olmayan Friedman testi ile yorumlanmıştır. Sonuçlar, Bin_MRFOA'nın literatüre kıyasla başarılı, rekabetçi ve tercih edilebilir bir algoritma olduğunu ortaya koymuştur.

Keywords

• İkili optimizasyon
• Manta vatozu beslenme optimizasyonu
• S-şekilli ve V-şekilli transfer fonksiyonları

References

1. [1] R. M. Rizk-Allah, "Hybridizing sine cosine algorithm with multi-orthogonal search strategy for engineering design problems," Journal of Computational Design and Engineering, vol. 5, no. 2, pp. 249-273, 2018.
2. [2] S. Korkmaz, A. Babalik, and M. S. Kiran, "An artificial algae algorithm for solving binary optimization problems," International Journal of Machine Learning and Cybernetics, vol. 9, no. 7, pp. 1233-1247, 2018.
3. [3] J. Wang, M. Khishe, M. Kaveh, and H. Mohammadi, "Binary Chimp Optimization Algorithm (BChOA): a New Binary Meta-heuristic for Solving Optimization Problems," Cognitive Computation, vol. 13, no. 5, pp. 1297-1316, 2021.
4. [4] Q. Al-Tashi, S. J. A. Kadir, H. M. Rais, S. Mirjalili, and H. Alhussian, "Binary optimization using hybrid grey wolf optimization for feature selection," Ieee Access, vol. 7, pp. 39496-39508, 2019.
5. [5] E. Baş and E. Ülker, "A binary social spider algorithm for continuous optimization task," Soft Computing, vol. 24, no. 17, pp. 12953-12979, 2020.
6. [6] M. Aslan, M. Gunduz, and M. S. Kiran, "JayaX: Jaya algorithm with xor operator for binary optimization," Applied Soft Computing, vol. 82, p. 105576, 2019.
7. [7] A. G. Hussien, A. E. Hassanien, E. H. Houssein, M. Amin, and A. T. Azar, "New binary whale optimization algorithm for discrete optimization problems," Engineering Optimization, vol. 52, no. 6, pp. 945-959, 2020.
8. [8] A. C. Cinar and M. S. Kiran, "Similarity and logic gate-based tree-seed algorithms for binary optimization," Computers & Industrial Engineering, vol. 115, pp. 631-646, 2018.

9. [9] R. M. Rizk-Allah, A. E. Hassanien, M. Elhoseny, and M. Gunasekaran, "A new binary salp swarm algorithm: development and application for optimization tasks," Neural Computing and Applications, vol. 31, no. 5, pp. 1641-1663, 2019.
10. [10] S. Arora and P. Anand, "Binary butterfly optimization approaches for feature selection," Expert Systems with Applications, vol. 116, pp. 147-160, 2019.
11. [11] M. Mafarja et al., "Binary dragonfly optimization for feature selection using time-varying transfer functions," Knowledge-Based Systems, vol. 161, pp. 185-204, 2018.
12. [12] T. Akan, S. Agahian, and R. Dehkharghani, "Binbro: Binary battle royale optimizer algorithm," Expert Systems with Applications, vol. 195, p. 116599, 2022.
13. [13] M. Abdel-Basset, R. Mohamed, R. K. Chakrabortty, M. Ryan, and S. Mirjalili, "New binary marine predators optimization algorithms for 0–1 knapsack problems," Computers & Industrial Engineering, vol. 151, p. 106949, 2021.
14. [14] E. Kaya, "BinGSO: galactic swarm optimization powered by binary artificial algae algorithm for solving uncapacitated facility location problems," Neural Computing and Applications, pp. 1-20, 2022.
15. [15] D. Chauhan and A. Yadav, "Binary Artificial Electric Field Algorithm," Evolutionary Intelligence, pp. 1-29, 2022.
16. [16] M. A. Sahman and A. C. Cinar, "Binary tree-seed algorithms with S-shaped and V-shaped transfer functions," International Journal of Intelligent Systems and Applications in Engineering, vol. 7, no. 2, pp. 111-117, 2019.
17. [17] M. Dehghani et al., "Binary Spring Search Algorithm for Solving Various Optimization Problems," Applied Sciences, vol. 11, no. 3, p. 1286, 2021. [Online]. Available: https://www.mdpi.com/2076-3417/11/3/1286.
18. [18] Z. Beheshti, "A novel x-shaped binary particle swarm optimization," Soft Computing, vol. 25, no. 4, pp. 3013-3042, 2021/02/01 2021, doi: 10.1007/s00500-020-05360-2.
19. [19] M. Kalra, V. Kumar, M. Kaur, S. A. Idris, Ş. Öztürk, and H. Alshazly, "A Novel Binary Emperor Penguin Optimizer for Feature Selection Tasks," Comput. Mater. Contin, vol. 70, pp. 6239-6255, 2022.
20. [20] H. Chantar, M. Mafarja, H. Alsawalqah, A. A. Heidari, I. Aljarah, and H. Faris, "Feature selection using binary grey wolf optimizer with elite-based crossover for Arabic text classification," Neural Computing and Applications, vol. 32, no. 16, pp. 12201-12220, 2020/08/01 2020, doi: 10.1007/s00521-019-04368-6.
21. [21] M. H. Nadimi-Shahraki, S. Taghian, S. Mirjalili, and L. Abualigah, "Binary Aquila Optimizer for Selecting Effective Features from Medical Data: A COVID-19 Case Study," Mathematics, vol. 10, no. 11, p. 1929, 2022. [Online]. Available: https://www.mdpi.com/2227-7390/10/11/1929.
22. [22] Y. He, F. Zhang, S. Mirjalili, and T. Zhang, "Novel binary differential evolution algorithm based on Taper-shaped transfer functions for binary optimization problems," Swarm and Evolutionary Computation, vol. 69, p. 101022, 2022/03/01/ 2022, doi: https://doi.org/10.1016/j.swevo.2021.101022.
23. [23] H. Hakli, "BinEHO: a new binary variant based on elephant herding optimization algorithm," Neural Computing and Applications, vol. 32, no. 22, pp. 16971-16991, 2020/11/01 2020, doi: 10.1007/s00521-020-04917-4.
24. [24] A. Pourrajabian, M. Dehghan, and S. Rahgozar, "Genetic algorithms for the design and optimization of horizontal axis wind turbine (HAWT) blades: A continuous approach or a binary one?," Sustainable Energy Technologies and Assessments, vol. 44, p. 101022, 2021/04/01/ 2021, doi: https://doi.org/10.1016/j.seta.2021.101022.
25. [25] H. Mohammadzadeh and F. S. Gharehchopogh, "Feature selection with binary symbiotic organisms search algorithm for email spam detection," International Journal of Information Technology & Decision Making, vol. 20, no. 01, pp. 469-515, 2021.
26. [26] K. K. Ghosh, R. Guha, S. K. Bera, N. Kumar, and R. Sarkar, "S-shaped versus V-shaped transfer functions for binary Manta ray foraging optimization in feature selection problem," Neural Computing and Applications, vol. 33, no. 17, pp. 11027-11041, 2021/09/01 2021, doi: 10.1007/s00521-020-05560-9.
27. [27] Y. Feng and G.-G. Wang, "A binary moth search algorithm based on self-learning for multidimensional knapsack problems," Future Generation Computer Systems, vol. 126, pp. 48- 64, 2022/01/01/ 2022, doi: https://doi.org/10.1016/j.future.2021.07.033.
28. [28] M. Xi, Q. Song, M. Xu, and Z. Zhou, "Binary African vultures optimization algorithm for various optimization problems," International Journal of Machine Learning and Cybernetics, 2022/11/16 2022, doi: 10.1007/s13042-022-01703-7.
29. [29] P. Hu, J.-S. Pan, S.-C. Chu, and C. Sun, "Multi-surrogate assisted binary particle swarm optimization algorithm and its application for feature selection," Applied Soft Computing, vol. 121, p. 108736, 2022/05/01/ 2022, doi: https://doi.org/10.1016/j.asoc.2022.108736.
30. [30] A. Banitalebi, M. I. Abd Aziz, and Z. A. Aziz, "A self-adaptive binary differential evolution algorithm for large scale binary optimization problems," Information Sciences, vol. 367, pp. 487- 511, 2016.
31. [31] A. Mohammadzadeh, M. Masdari, F. S. Gharehchopogh, and A. Jafarian, "Improved chaotic binary grey wolf optimization algorithm for workflow scheduling in green cloud computing," Evolutionary Intelligence, vol. 14, no. 4, pp. 1997-2025, 2021/12/01 2021, doi: 10.1007/s12065-020- 00479-5.
32. [32] S. Korkmaz, "İkili optimizasyon problemlerinin çözümü için yapay alg algoritması tabanlı yeni yaklaşımlar," Doktora Tezi Doktora Tezi, Konya Teknik Üniversitesi, Konya, 2019.
33. [33] W. Zhao, Z. Zhang, and L. Wang, "Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications," Engineering Applications of Artificial Intelligence, vol. 87, p. 103300, 2020.
34. [34] G. Hu, M. Li, X. Wang, G. Wei, and C.-T. Chang, "An enhanced manta ray foraging optimization algorithm for shape optimization of complex CCG-Ball curves," Knowledge-Based Systems, vol. 240, p. 108071, 2022/03/15/ 2022, doi: https://doi.org/10.1016/j.knosys.2021.108071.
35. [35] M. Beşkirli, İ. Koç, H. Haklı, and H. Kodaz, "A new optimization algorithm for solving wind turbine placement problem: Binary artificial algae algorithm," Renewable Energy, vol. 121, pp. 301-308, 2018/06/01/ 2018, doi: https://doi.org/10.1016/j.renene.2017.12.087.
36. [36] M. Beşkirli, I. Koc, and H. Kodaz, "Optimal placement of wind turbines using novel binary invasive weed optimization," Tehnički vjesnik, vol. 26, no. 1, pp. 56-63, 2019.
37. [37] A. Beşkirli and İ. Dağ, "A new binary variant with transfer functions of Harris Hawks Optimization for binary wind turbine micrositing," Energy Reports, vol. 6, pp. 668-673, 2020/12/01/ 2020, doi: https://doi.org/10.1016/j.egyr.2020.11.154.
38. [38] S. García, D. Molina, M. Lozano, and F. Herrera, "A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization," Journal of Heuristics, vol. 15, no. 6, pp. 617-644, 2009.
39. [39] T. Eftimov, P. Korošec, and B. Koroušić Seljak, "A Novel Approach to statistical comparison of meta-heuristic stochastic optimization algorithms using deep statistics," Information Sciences, vol. 417, pp. 186-215, 2017/11/01/ 2017, doi: https://doi.org/10.1016/j.ins.2017.07.015.
40. [40] J. Derrac, S. García, D. Molina, and F. Herrera, "A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms," Swarm and Evolutionary Computation, vol. 1, no. 1, pp. 3-18, 2011.
41. [41] Z. Beheshti, "A time-varying mirrored S-shaped transfer function for binary particle swarm optimization," Information Sciences, vol. 512, pp. 1503-1542, 2020.
42. [42] E. Baş and E. Ülker, "A binary social spider algorithm for uncapacitated facility location problem," Expert Systems with Applications, vol. 161, p. 113618, 2020.
43. [43] I. Tariq et al., "MOGSABAT: a metaheuristic hybrid algorithm for solving multi-objective optimisation problems," Neural Computing and Applications, vol. 32, no. 8, pp. 3101-3115, 2020/04/01 2020, doi: 10.1007/s00521-018-3808-3.