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Improved grey wolf optimization based on the two-stage search of hybrid CMA-ES

  • Yun-tao ZhaoEmail author
  • Wei-gang Li
  • Ao Liu
Methodologies and Application
  • 31 Downloads

Abstract

Hybrid algorithms with different features are an important trend in algorithm improvement. In this paper, an improved grey wolf optimization based on the two-stage search of hybrid covariance matrix adaptation-evolution strategy (CMA-ES) is proposed to overcome the shortcomings of the original grey wolf optimization that easily falls into the local minima when solving complex optimization problems. First, the improved algorithm divides the whole search process into two stages. In the first stage, the improved algorithm makes full use of the global search ability of grey wolf optimization on a large scale and thoroughly explores the location of the optimal solution. In the second stage, due to CMA-ES having a strong local search capability, the three CMA-ES instances use the α wolf, β wolf and δ wolf as the starting points. In addition, these instances have different step size for parallel local exploitations. Second, in order to make full use of the global search ability of the grey wolf algorithm, the Beta distribution is used to generate as much of an initial population as possible in the non-edge region of the solution space. Third, the new algorithm improves the hunting formula of the grey wolf algorithm, which increases the diversity of the population through the interference of other individuals and reduces the use of the head wolf’s guidance to the population. Finally, the new algorithm is quantitatively evaluated by fifteen standard benchmark functions, five test functions of CEC 2014 suite and two engineering design cases. The results show that the improved algorithm significantly improves the convergence, robustness and efficiency for solving complex optimization problems compared with other six well-known optimization algorithms.

Keywords

Grey wolf optimization CMA-ES Function optimization Hybrid algorithm Two-stage search 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve this paper. This work is supported by the National Natural Science Foundation of China [Grant Number 51774219] and the Science and Technology Research Program of Hubei Ministry of Education [Grant Number MADT201706].

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Ethical approval

This article does not contain any studies with animals performed by any of the authors.

References

  1. Anand A, Suganthi L (2018) Hybrid GA-PSO optimization of artificial neural network for forecasting electricity demand. Energies 11(4):1–15Google Scholar
  2. Aydilek İB (2018) A hybrid firefly and particle swarm optimization algorithm for computationally expensive numerical problems. Appl Soft Comput 66:232–249Google Scholar
  3. Chakri A, Khelif R, Benouaret M, Yang XS (2017) New directional bat algorithm for continuous optimization problems. Expert Syst Appl 69:159–175Google Scholar
  4. Chen Y, Li L, Xiao J, Yang Y, Liang J, Li T (2018) Particle swarm optimizer with crossover operation. Eng Appl Artif Intell 70:159–169Google Scholar
  5. Chi R, Su Y, Zhang D, Chi X, Zhang H (2017) A hybridization of cuckoo search and particle swarm optimization for solving optimization problems. Neural Comput Appl 4:1–18Google Scholar
  6. Daniel E, Anitha J, Gnanaraj J (2017) Optimum laplacian wavelet mask based medical image using hybrid cuckoo search—grey wolf optimization algorithm. Knowl Based Syst 131:58–69Google Scholar
  7. Eberhart R, Kennedy J (2002) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the 6th international symposium on micro machine and human science, pp 39–43Google Scholar
  8. Emary E, Zawbaa HM, Hassanien AE (2015) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172(8):371–381Google Scholar
  9. Gupta S, Deep K (2018a) Cauchy grey wolf optimiser for continuous optimisation problems. J Exp Theor Artif Intell 30(6):1051–1075Google Scholar
  10. Gupta S, Deep K (2018b) Random walk grey wolf optimizer for constrained engineering optimization problems. Comput Intell 34(4):1025–1045MathSciNetGoogle Scholar
  11. Gupta S, Deep K (2018c) An opposition-based chaotic grey wolf optimizer for global optimisation tasks. J Exp Theor Artif Intell 30:1–29Google Scholar
  12. Gupta S, Deep K (2019) A novel random walk grey wolf optimizer. Swarm Evol Comput 44:101–112Google Scholar
  13. Hansen N (2006) The CMA evolution strategy: a comparing review. Stud Fuzziness Soft Comput 192:75–102Google Scholar
  14. Kamboj VK, Bath SK, Dhillon JS (2016) Solution of non-convex economic load dispatch problem using grey wolf optimizer. Neural Comput Appl 27(5):1301–1316Google Scholar
  15. Klein CE, Segundo EHV, Mariani VC, Coelho LDS (2016) Modified social-spider optimization algorithm applied to electromagnetic optimization. IEEE Trans Magn 52(3):1–4Google Scholar
  16. Liang JJ, Qu BY, Suganthan PN (2013) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Technical report, Zhengzhou University and Nanyang Technological UniversityGoogle Scholar
  17. Lin JT, Chiu C-C (2018) A hybrid particle swarm optimization with local search for stochastic resource allocation problem. J Intell Manuf 29(3):481–495Google Scholar
  18. Medjahed SA, Saadi TA, Benyettou A, Ouali M (2016) Gray wolf optimizer for hyperspectral band selection. Appl Soft Comput 40:178–186Google Scholar
  19. Melo VVD, Iacca G (2014) A modified covariance matrix adaptation evolution strategy with adaptive penalty function and restart for constrained optimization. Expert Syst Appl 41(16):7077–7094Google Scholar
  20. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67Google Scholar
  21. Mirjalili SA, Hashim SZM, Sardroudi HM (2012) Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm. Appl Math Comput 218(22):11125–11137MathSciNetzbMATHGoogle Scholar
  22. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69(3):46–61Google Scholar
  23. Mirjalili S, Mirjalili SM, Hatamlou A (2015) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27(2):495–513Google Scholar
  24. Nagano MS, Moccellin JV (2002) A high quality solution constructive heuristic for flow shop sequencing. J Oper Res Soc 53(12):1374–1379zbMATHGoogle Scholar
  25. Olorunda O, Engelbrecht AP (2008) Measuring exploration/exploitation in particle swarms using swarm diversity. In: Proceedings of the IEEE congress on evolutionary computation, Hong Kong, IEEE Congress on, pp 1128–1134Google Scholar
  26. Pan WT (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl Based Syst 26(2):69–74Google Scholar
  27. Peng H, Li L, Kurths J, Li S, Yang Y (2013) Topology identification of complex network via chaotic ant swarm algorithm. Math Probl Eng 3:1–5MathSciNetzbMATHGoogle Scholar
  28. Pradhan M, Roy PK, Pal T (2016) Grey wolf optimization applied to economic load dispatch problems. Int J Electr Power Energy Syst 83:325–334Google Scholar
  29. Preuss M (2010) Niching the CMA-ES via nearest-better clustering. In: Conference companion on genetic & evolutionary computation, vol 78. ACM, pp 1711–1718Google Scholar
  30. Qiu J, Xie J, Cheng F, Zhang X (2017) A hybrid social spider optimization algorithm with differential evolution for global optimization. J Univers Comput Sci 23(7):619–635MathSciNetGoogle Scholar
  31. Raidl GR (2006) A unified view on hybrid metaheuristics. In: Proceedings of the 3rd international workshop on hybrid metaheuristics, Gran Canaria, Spain, pp 1–12Google Scholar
  32. Saxena A, Kumar R, Das S (2018) β-Chaotic map enabled grey wolf optimizer. Appl Soft Comput 75:84–105Google Scholar
  33. Singh N, Singh SB (2017) Hybrid algorithm of particle swarm optimization and grey wolf optimizer for improving convergence performance. J Appl Math 2017:1–15MathSciNetGoogle Scholar
  34. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetzbMATHGoogle Scholar
  35. Sujitha J, Baskaran K (2017) Genetic grey wolf optimizer based channel estimation in wireless communication system. Wirel Pers Commun 99(2):965–984Google Scholar
  36. Venkatakrishnan GR, Rengaraj R, Salivahanan S (2018) Grey wolf optimizer to real power dispatch with non-linear constraints. CMES Computer Model Eng Sci 115(1):25–45Google Scholar
  37. Wang X, Haynes RD, Feng Q (2016) A multilevel coordinate search algorithm for well placement, control and joint optimization. Comput Chem Eng 95:75–96Google Scholar
  38. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82Google Scholar
  39. Xu Z, Iizuka H, Yamamoto M (2017) Attraction basin sphere estimation approach for niching cma-es. Soft Comput 21(5):1327–1345Google Scholar
  40. Yamany W, Emary E, Hassanien AE (2016) New rough set attribute reduction algorithm based on grey wolf optimization. In: The 1st international conference on advanced intelligent system and informatics, Beni Suef, pp 241–251Google Scholar
  41. Zhu A, Xu C, Li Z, Wu J, Liu Z (2015) Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC. J Syst Eng Electron 26(2):317–328Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Information Science and EngineeringWuhan University of Science and TechnologyWuhanChina
  2. 2.Engineering Research Center for Metallurgical Automation and Measurement Technology of Ministry of EducationWuhanChina
  3. 3.School of ManagementWuhan University of Science and TechnologyWuhanChina

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