A Modified Variant of Grey Wolf Optimizer

Document Type : Article

Author

Department of Mathematics, Punjabi University, Patiala-147002, Punjab, India

Abstract

The original version of Grey Wolf Optimization (GWO) algorithm has small number of disadvantages of low solving accuracy, bad local searching ability and slow convergence rate. In order to overcome these disadvantages of Grey Wolf Optimizer, a new version of Grey Wolf Optimizer algorithm has been proposed by modifying the encircling behavior and position update equations of Grey Wolf Optimization Algorithm. The accuracy and convergence performance of modified variant is tested on several well known classical further more like sine dataset and cantilever beam design functions. For verification, the results are compared with some of the most powerful well known algorithms i.e. Particle Swarm Optimization, Grey Wolf Optimizer and Mean Grey Wolf Optimization. The experimental solutions demonstrate that the modified variant is able to provide very competitive solutions in terms of improved minimum objective function value, maximum objective function value, mean, standard deviation and convergence rate.

Keywords


References:
1. Holland, J.H. "Genetic algorithms", Scientific American, 267(1), pp. 66-72 (1992).
2. Kennedy, J. and Eberhart, R. "Particle swarm optimization", in Proceedings of the IEEE International Conference on Neural Networks, 4(1), pp. 1942-1948 (1995).
3. Price, K. and Storn, R. "Differential evolution", Dr. Dobb's Journal, 22(2), pp. 18-20 (1997).
4. Price, K.V., Storn, R.M., and Lampinen, J.A., Differential Evolution: A Practical Approach to Global Optimization, Book, Springer, New York, NY, USA (2005).
5. Wolpert, D.H. and Macready, W.G. "No free lunch theorems for optimization", IEEE Transactions on Evolutionary Computation, 1(1), pp. 67-82 (1997).
6. Karaboga, D. and Basturk, B. "A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm", Journal of Global Optimization, 39(3), pp. 459-471 (2007).
7. Yang, X.S. and Deb, S. "Cuckoo Search via Levy  flights", In Proceedings of the World Congress on Nature & Biologically Inspired Computing (NaBIC '09), IEEE, Coimbatore, India, pp. 210-214 (2009).
8. Rashedi, E., Nezamabadi-Pour, H., and Saryazdi, S. "GSA: a gravitational search algorithm", Information Sciences, 179(13), pp. 2232-2248 (2009).
9. Yang, X.S. "Fire y algorithm, levy  flights and global optimization", In Research and Development in Intelligent Systems XXVI, Springer, London, UK, pp. 209- 218 (2010).
10. Rajabioun, R. "Cuckoo optimization algorithm", Applied Soft Computing, 11(8), pp. 5508-5518 (2011).
11. Mirjalili S. and Lewis, A. "Adaptive gbest-guided gravitational search algorithm", Neural Computing and Applications, 25(7), pp. 1569-1584 (2014).
12. Mirjalili, S., Mirjalili, S.M., and Lewis, A. "Grey wolf optimizer", Advances in Engineering Software, 69(2), pp. 46-61 (2014).
13. Mirjalili, S. "The ant lion optimizer", Advances in Engineering Software, 83(1), pp. 80-98 (2015).
14. Mirjalili, S., Mirjalili, S.M., and Hatamlou, A. "Multiverse optimizer: a nature-inspired algorithm for global optimization", Neural Computing and Applications, 27(2) (2015).
15. Eusuff, M.M. and Lansey, K.E. "Optimization of water distribution network design using the shuffled frog leaping algorithm", Journal of Water Resources Planning and Management, 129(3), pp. 210-225 (2003).
16. Das, S., Biswas, A., Gupta, S.D., and Abraham, A. "Bacterial foraging optimization algorithm: Theoretical foundations, analysis, and applications", In Foundations of Computational Intelligence, Global Optimization, 3(1), pp. 23-55 (2009).
17. Raj, S. and Bhattacharyya, B. "Reactive power planning by opposition-based grey wolf optimization method", International Transactions on Electrical Energy Systems, 28(6) (2018). https://doi.org/10.1002/etep.2551.
18. Singh, N. and Singh, S.B. "One half global best position particle swarm optimization algorithm", International Journal of Scientific & Engineering Research, 2(8), pp. 1-10 (2011).
19. Singh, N., Singh, S., and Singh, S.B. "Half mean particle swarm optimization algorithm", International Journal of Scientific & Engineering Research, 3(8), pp. 1-9 (2012).
20. Singh, N. and Singh, S.B. "Personal best position particle swarm optimization", Journal of Applied Computer Science & Mathematics, 12(6), pp. 69-76 (2012).
21. Singh, N., Singh, S., and Singh, S.B. "HPSO: A new version of particle swarm optimization algorithm", Journal of Artificial Intelligence, 3(3), pp. 123-134 (2012).
22. Singh, N., Singh, S., and Singh, S.B. "A new hybrid MGBPSO-GSA variant for improving function optimization solution in search space", Evolutionary Bioinformatics, 13(1), pp. 1-13 (2017).
23. Singh, N., and Singh, S.B. "A modified mean grey wolf optimization approach for benchmark and biomedical problems", Evolutionary Bioinformatics, 13(1), pp. 1- 28 (2017).
24. Singh, N., and Singh, S.B. "Hybrid algorithm of particle swarm optimization and grey wolf optimizer for improving convergence performance", Journal of Applied Mathematics, Article ID 2030489, 2017, pp. 1-15 (2017). https://doi.org/10.1155/2017/2030489.
25. Singh, N. and Singh, S.B. "A novel hybrid GWOSCA approach for optimization problems", Engineering Science and Technology, an International Journal, Elsevier, 20(6) (2017). https://doi.org/10.1016/j.jestch.2017.11.001.
26. Singh, N. and Hachimi, H. "A new hybrid whale optimizer algorithm with mean strategy of grey wolf optimizer for global optimization", Mathematical and Computational Applications, 23(14), pp. 1-32 (2018).
27. Simon, D. "Biogeography-based optimization", Evolutionary Computation, IEEE Transactions on, 12(6),pp. 702-713 (2008).
28. Yang, X.S. "A new metaheuristic bat-inspired algorithm", Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), 284, pp. 65-74 (2010).
29. Yang, X.S. "Flower pollination algorithm for global optimization", Unconventional Computation and Natural Computation, 7445, pp. 240-249 (2012).
30. Mirjalili, S. "How effective is the grey wolf optimizer in training multi-layer perceptrons", Applied Intelligence, Springer, 43(1), pp. 150-161 (2015).
31. Singh, N. and Singh, S.B. "A modified mean grey wolf optimization approach for benchmark and biomedical problems", Evolutionary Bioinformatics, 13(1), pp.1- 28 (2017).
32. Mittal, N., Singh, U., and Sohi, B.S. "Modified grey wolf optimizer for global engineering optimization", Applied Computational Intelligence and Soft Computing, Article id 7950348, 2016, pp. 1-16 (2016). https://doi.org/10.1155/2016/7950348.
33. Emary, E., Zawbaa, H.M., Grosan, C., and Hassenian, A.E. "Feature subset selection approach by gray-wolf optimization", In Afro-European Conference for Industrial Advancement of Advances in Intelligent Systems and Computing, Springer, 334 (2015).
34. Kamboj, V.K., Bath, S.K., and Dhillon, J.S. "Solution of non-convex economic load dispatch problem using grey wolf optimizer", Neural Computing and Applications, 27(5), pp. 1301-1316 (2015).
35. Komaki, G.M. and Kayvanfar, V. "Grey wolf optimizer algorithm for the two-stage assembly  flow shop scheduling problem with release time", Journal of Computational Science, 8(2), pp. 109-120 (2015).
36. Gholizadeh, S. "Optimal design of double layer grids considering nonlinear behaviour by sequential grey wolf algorithm", Journal of Optimization in Civil Engineering, 5(4), pp. 511-523 (2015).
37. Yusof, Y. and Mustaffa, Z. "Time series forecasting of energy commodity using grey wolf optimizer", In Proceedings of the International Multi Conference of Engineers and Computer Scientists (IMECS '15), 1(1), Hong Kong (2015).
38. Shankar, K. and Eswaran, P. "A secure visual secret share (VSS) creation scheme in visual cryptography using elliptic curve cryptography with optimization technique", Australian Journal of Basic & Applied Science, 9(36), pp. 150-163 (2015).
39. El-Fergany, A.A. and Hasanien, H.M. "Single and multi-objective optimal power  flow using grey wolf optimizer and differential evolution algorithms", Electric Power Components and Systems, 43(13), pp. 1548- 1559 (2015).
40. Kamboj, V.K. "A novel hybrid PSOGWO approach for unit commitment problem", Neural Computing and Applications (2015).
41. Emary, E., Zawbaa, H.M., and Hassanien, A.E. "Binary grey wolf optimization approaches for feature selection", Neurocomputing, 172(2), pp. 371-381 (2016).
42. Pan, T.S., Dao, T.K., Nguyen, T.T., and Chu, S.C. "A communication strategy for paralleling grey wolf optimizer", Advances in Intelligent Systems and Computing, 388, pp. 253-262 (2015).
43. Jayapriya, J. and Arock, M. "A parallel GWO technique for aligning multiple molecular sequences", In Proceedings of the International Conference on Advances in Computing, Communications and Informatics (ICACCI '15), IEEE, Kochi, India, pp. 210-215 (2015).
44. Zhu, A., Xu, C., Li, Z., Wu, J., and Liu, Z. "Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC", Journal of Systems Engineering and Electronics, 26(2), pp. 317-328 (2015).
45. Li, L., Sun, L., Guo, J., Qi, J., Xu, B., and Li, S. "Modified discrete grey wolf optimizer algorithm for multilevel image thresholding", Computational Intelligence and Neuroscience, Article id 3295769, 2017, pp. 1-16 (2017). https://doi.org/10.1155/2017/3295769.
46. Liu, H., Hua, G., Yin, H., and Xu, Y. "An intelligent grey wolf optimizer algorithm for distributed compressed sensing", Computational Intelligence Neuroscience, Article id 1723191, 2018, pp. 1-10 (2018). https://doi.org/10.1155/2018/1723191.
47. Mirjalili, S., Gandomi, A.H., Mirjalili, S.Z., Saremi, S., Faris, H., and Mirjalili, S.M. "Salp swarm algorithm: A bio-inspired optimizer for engineering design problems", Advances in Engineering Software, 114, pp. 163-191 (2017).
48. Raj, S. and Bhattacharyya, B. "Optimal placement of TCSC and SVC for reactive power planning using whale optimization algorithm", Swarm and Evolutionary Computation, 40, pp. 131-143 (2017).
49. Saremi, S., Mirjalili, S.Z., and Mirjalili, S.M. "Evolutionary population dynamics and grey wolf optimizer", Neural Computing and Applications, 26(5), pp. 1257- 1263 (2015).
50. Mahdad, B. and Srairi, K. "Blackout risk prevention in a smart grid based  flexible optimal strategy using grey wolf-pattern search algorithms", Energy Conversion and Management, 98, pp. 411-429 (2015).
51. Lu, Y., Zhou, Y., and Wu, X. "A hybrid lightning search algorithm-simplex method for global optimization", Discrete Dynamics in Nature and Society, Article id 8342694, pp. 1-23 (2017).
52. Chickermane, H. and Gea, H.C. "Structural optimization using a new local approximation method", International Journal for Numerical Methods in Engineering, 39(5), pp. 829-846 (1996).
53. Cheng, M.Y. and Prayogo, D. "Symbiotic organisms search: a new metaheuristic optimization algorithm", Computers & Structures, 139, pp. 98|112 (2014).
Volume 27, Issue 3
Transactions on Computer Science & Engineering and Electrical Engineering (D)
June 2020
Pages 1450-1466
  • Receive Date: 27 December 2017
  • Revise Date: 05 April 2018
  • Accept Date: 02 July 2018