Improved Whale Optimization Algorithm Based On π Number

Abstract

In this study, an improved version is presented as a result of experiments performed on the whale optimization algorithm (WOA) in the literature. As a result of the experiments, number was added to the coefficient vector of the algorithm. The developed WOA algorithm based on the number of was adapted to test problems. The 23 most common Benchmark functions have been selected as test problems. In line with the results, it was observed that the exploitation and exploration phases of the WOA developed. The success of the results has proven itself in comparison with other algorithms.

Keywords

• Whale Optimization Algorithm
• Benchmark Functions
• optimization

References

1. [1] Alatas, B. “ACROA: Artificial Chemical Reaction Optimization Algorithm for global optimization.” Expert Systems with Applications 38, 13170–13180, 2011.
2. [2] Hatamlou A. “Black hole: a new heuristic optimization approach for data clustering,” Inf Sci, 222:175–184. 2013.
3. [3] Huang F, Wang L, He Q. “An effective co-evolutionary differential evolution for constrained optimization,” Appl Math Computation, 186(1), 340–356, 2007.
4. [4] Kirkpatrick S, Gelatt CD, Vecchi MP. “Optimization by simulated annealing,” Science, 220(4598), 671–680. 1983.
5. [5] CernýV. “Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm,” Journal of Optimization Theory and Applications, 45(1), 41–51, 1985.
6. [6] Rashedi E, Nezamabadi-Pour H, Saryazdi S. “GSA: a gravitational search algorithm,” Inf Sci, 179,2232–2248,2009.
7. [7] Mirjalili, S., Mirjalili, S. M., & Hatamlou, “A. Multi-verse optimizer: a nature-inspired algorithm for global optimization” Neural Computing and Applications, 27(2), 495-513. 2016.
8. [8] Dorigo M, Birattari M, Stutzle T. “Ant colony optimization,” IEEE Comput Intell, 1(4), 28–39. 2006.

9. [9] Kennedy J, Eberhart R. “Particle swarm optimization,” In: Proceedings of the 1995 IEEE international conference on neural networks, Australia, 1942–1948, 1995.
10. [10] Basturk B, Karaboga D. “An artificial bee colony (ABC) algorithm for numeric function optimization,” In: Proceedings of the IEEE swarm intelligence symposium, Indianapolis, USA, 12–14 May 2006.
11. [11] Tan Y, Zhu Y. “Fireworks algorithm for optimization.” Advances in swarm intelligence, Berlin: Springer-Verlag; 355–364. 2010.
12. [12] Fogel D. Artificial intelligence through simulated evolution. Wiley-IEEE Press; 2009.
13. [13] Glover F. Tabu search –Part I. ORSA J Comput 1989; 1:190–206.
14. [14] Glover F. Tabu search –Part II. ORSA J Comput 1990; 2:4–32.
15. [15] Geem Z,W. Kim J,H., Loganathan G., “A new heuristic optimization algorithm: harmony search,” Simulation,76(2),60–68, 2001.
16. [16] Mirjalili S., “SCA: A Sine Cosine Algorithm for solving optimization problems,” Knowledge-Based Sys,96,120-133, 2016.
17. [17] Salimi H., “Stochastic fractal search: a powerful metaheuristic algorithm,” Knowledge-Based Sys,75,1-18, 2015.
18. [18] Eskandar H, Sadollah A, Bahreininejad A, Hamdi M., “Water cycle algorithm–A novel metaheuristic optimization method for solving constrained engineering optimization problems,” Comp & Struct, 110,151-166, 2012.
19. [19] Wolpert DH, Macready WG., “No free lunch theorems for optimization,” Evolut Comput, IEEE Trans, 1:67–82, 1997.
20. [20] Ateş, V., & Barışçı, N. “Short-Term Load Forecasting Model Using Flower Pollination Algorithm,” International Scientific and Vocational Studies Journal, 1(1), 22-29, 2017.
21. [21] Koç, İ. B., Al Janadi, A., & Ateş, V. “Interlock Optimization Of An Accelerator Using Genetic Algorithm,” International Scientific and Vocational Studies Journal, 1(1), 30-41. 2017.
22. [22] Trivedi, I. N., Pradeep, J., Narottam, J., Arvind, K., & Dilip, L. “Novel adaptive whale optimization algorithm for global optimization,” Indian Journal of Science and Technology, 9(38), 319-326, 2016.
23. [23] Hu, H., Bai, Y., & Xu, T., “A whale optimization algorithm with inertia weight,” WSEAS Trans. Comput, 15, 319-326, 2016.
24. [24] Kaveh, A, Ghazaan, M. I., “Enhanced whale optimization algorithm for sizing optimization of skeletal structures,” Mechanics Based design of structures and Machines, 45(3), 345-362, 2017.
25. [25] Hu, H, Bai, Y, Xu, “Improved whale optimization algorithms based on inertia weights and theirs applications,” International journal of circuits, systems and signal processing, 11, 12-26. 2017.
26. [26] Ling, Y., Zhou, Y., Luo, Q. Lévy, “flight trajectory-based whale optimization algorithm for global optimization.,” IEEE access,5, 6168-6186, 2017.
27. [27] Oliva, D., El Aziz, M. A., “Hassanien, A. E. Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm,” Applied Energy, 200, 141-154. 2017.
28. [28] Wang, J., Du, P., Niu, T., Yang, W., “A novel hybrid system based on a new proposed algorithm—Multi-Objective Whale Optimization Algorithm for wind speed forecasting,” Applied energy, 208, 344-360, 2017.
29. [29] Abdel-Basset, M., Abdle-Fatah, L., Sangaiah, A. K. “An improved Lévy based whale optimization algorithm for bandwidth-efficient virtual machine placement in cloud computing environment,” Cluster Computing, 1-16, 2018.
30. [30] Kaur, G., Arora, S. “Chaotic whale optimization algorithm,” Journal of Computational Design and Engineering, 5(3), 275-284, 2018.
31. [31] Saidala, R. K., Devarakonda, N. “Improved whale optimization algorithm case study: clinical data of anaemic pregnant woman,” In Data engineering and intelligent computing, Springer, Singapore. 271-281, 2018.
32. [32] Mirjalili S, Lewis A., “The whale optimization algorithm,” Adv Eng Softw, 95:51–67, 2016.
33. [33] El Aziz, M. A, Ewees, A. A, Hassanien, A. E., “Multi-objective whale optimization algorithm for content-based image retrieval,” Multimedia Tools and Applications, 77(19), 26135-26172, 2018.
34. [34] Xiong, G., Zhang, J., Shi, D., He, Y. “Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm,” Energy conversion and management, 174(1), 388-405, 2018.
35. [35] Abdel-Basset, M. El-Shahat, D, Sangaiah, A. K. A, “modified nature inspired meta-heuristic whale optimization algorithm for solving 0–1 knapsack problem,” International Journal of Machine Learning and Cybernetics, 10(3), 495-514, 2019.
36. [36] Danacı, M., & Alızada, B., “An Improvement Of Hybrid Whale Optimization Algorithm,” Euroasia Journal of Mathematics-Engineering Natural & Medical Sciences, vol.2, 60-68, 2019. [37] Yao X, Liu Y, Lin G. “Evolutionary programming made faster,” IEEE Trans Evol Comput,3:82–102, 1999.
37. [38] Digalakis J, “Margaritis K. On benchmarking functions for genetic algorithms,” Int J Comput Math, 77:481–506, 2001.
38. [39] Molga M, Smutnicki C. Test functions for optimization needs. 2005; https://www.robertmarks.org/Classes/ENGR5358/Papers/functions.pdf
39. [40] Yang X-S. “Firefly algorithm, stochastic test functions and design optimization,” Int J Bio-Inspired Comput, 2(2):78–84. 2010.