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Adaptive grey wolf optimizer

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Abstract

Swarm-based metaheuristic optimization algorithms have demonstrated outstanding performance on a wide range of optimization problems in both science and industry. Despite their merits, a major limitation of such techniques originates from non-automated parameter tuning and lack of systematic stopping criteria that typically leads to inefficient use of computational resources. In this work, we propose an improved version of grey wolf optimizer (GWO) named adaptive GWO which addresses these issues by adaptive tuning of the exploration/exploitation parameters based on the fitness history of the candidate solutions during the optimization. By controlling the stopping criteria based on the significance of fitness improvement in the optimization, AGWO can automatically converge to a sufficiently good optimum in the shortest time. Moreover, we propose an extended adaptive GWO (\(\hbox {AGWO}^\varDelta\)) that adjusts the convergence parameters based on a three-point fitness history. In a thorough comparative study, we show that AGWO is a more efficient optimization algorithm than GWO by decreasing the number of iterations required for reaching statistically the same solutions as GWO and outperforming a number of existing GWO variants.

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References

  1. Soerensen JS, Johannesen L, Grove U, Lundhus K, Couderc JP, Graff C (2010) A comparison of IIR and wavelet filtering for noise reduction of the ECG. In: 2010 computing in cardiology (IEEE, 2010), pp. 489–492

  2. Abdel-Basset M, Abdel-Fatah L, Sangaiah AK (2018) Chapter 10 - metaheuristic algorithms: a comprehensive review. In: Sangaiah AK, Sheng M, Zhang Z (eds) Computational intelligence for multimedia big data on the cloud with engineering applications. Intelligent data-centric systems. Academic Press, London, pp 185–231

    Google Scholar 

  3. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press, London

    Book  Google Scholar 

  4. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: proceedings of ICNN’95-international conference on neural networks, vol. 4 (IEEE, 1995), vol. 4, pp. 1942–1948

  5. Storn R, Price K (1997) Differential evolution - a simple and efficient Heuristic for global optimization over continuous spaces. J Global Optim 11(4):341. https://doi.org/10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  6. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67

    Article  Google Scholar 

  7. Glover F (1989) Tabu search-part I. ORSA J Comput 1(3):190. https://doi.org/10.1287/ijoc.1.3.190

    Article  MATH  Google Scholar 

  8. Glover F, Kochenberger G (2002) Iterated local search. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. Kluwer, Netherlands

    MATH  Google Scholar 

  9. Bäck T (1996) Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, Oxford, UK

    Book  Google Scholar 

  10. Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702. https://doi.org/10.1109/TEVC.2008.919004

    Article  Google Scholar 

  11. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232

    Article  Google Scholar 

  12. Erol OK, Eksin I (2006) A new optimization method: big bang-big crunch. Adv Eng Softw 37(2):106. https://doi.org/10.1016/j.advengsoft.2005.04.005

    Article  Google Scholar 

  13. Dorigo M, Birattari M, Stützle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28

    Article  Google Scholar 

  14. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459

    Article  MathSciNet  Google Scholar 

  15. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: proceedings of the sixth international symposium on micro machine and human science, pp. 39–43

  16. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 world congress on nature & biologically inspired computing, NaBIC 2009. (IEEE, 2009), pp. 210–214

  17. Passino K (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 22(3):52. https://doi.org/10.1109/MCS.2002.1004010

    Article  Google Scholar 

  18. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46

    Article  Google Scholar 

  19. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51

    Article  Google Scholar 

  20. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228

    Article  Google Scholar 

  21. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053. https://doi.org/10.1007/s00521-015-1920-1

    Article  MathSciNet  Google Scholar 

  22. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30. https://doi.org/10.1016/j.advengsoft.2017.01.004

    Article  Google Scholar 

  23. Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw. https://doi.org/10.1016/j.advengsoft.2015.01.010

    Article  Google Scholar 

  24. Tu Q, Chen X, Liu X (2019) Hierarchy strengthened grey wolf optimizer for numerical optimization and feature selection. IEEE Access 7:78012. https://doi.org/10.1109/ACCESS.2019.2921793

    Article  Google Scholar 

  25. Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with Lévy flight for optimization tasks. Appl Soft Comput 60:115. https://doi.org/10.1016/j.asoc.2017.06.044

    Article  Google Scholar 

  26. Lu C, Gao L, Yi J (2018) Grey wolf optimizer with cellular topological structure. Exp Syst Appl 107:89. https://doi.org/10.1016/j.eswa.2018.04.012

    Article  Google Scholar 

  27. Negi G, Kumar A, Pant S, Ram M (2021) GWO: a review and applications. Int J Syst Assur Eng Manag 12(1):1. https://doi.org/10.1007/s13198-020-00995-8

    Article  Google Scholar 

  28. Faris H, Aljarah I, Al-Betar MA, Mirjalili S (2018) Grey wolf optimizer: a review of recent variants and applications. Neural Comput Appl 30(2):413. https://doi.org/10.1007/s00521-017-3272-5

    Article  Google Scholar 

  29. Malik MRS, Mohideen ER, Ali L (2015) Weighted distance grey wolf optimizer for global optimization problems. In: 2015 IEEE international conference on computational intelligence and computing research (ICCIC)

  30. Mittal N, Singh U, Sohi BS (2016) Modified grey wolf optimizer for global engineering optimization. Appl Comp Intell Soft Comput. https://doi.org/10.1155/2016/7950348

    Article  Google Scholar 

  31. Long W, Liang X, Cai S, Jiao J, Zhang W (2017) A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems. Neural Comput Appl 28(1):421. https://doi.org/10.1007/s00521-016-2357-x

    Article  Google Scholar 

  32. Rodríguez L, Castillo O, Soria J (2016) Grey wolf optimizer with dynamic adaptation of parameters using fuzzy logic. In: 2016 IEEE congress on evolutionary computation (CEC), pp. 3116–3123. https://doi.org/10.1109/CEC.2016.7744183

  33. RodrÍguez L, Castillo O, Soria J, Melin P, Valdez F, Gonzalez CI, Martinez GE, Soto J (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315. https://doi.org/10.1016/j.asoc.2017.03.048

    Article  Google Scholar 

  34. Dudani K, Chudasama A (2016) Partial discharge detection in transformer using adaptive grey wolf optimizer based acoustic emission technique. Cogent Eng 3(1):1256083. https://doi.org/10.1080/23311916.2016.1256083

    Article  Google Scholar 

  35. Long W, Jiao J, Liang X, Tang M (2018) An exploration-enhanced grey wolf optimizer to solve high-dimensional numerical optimization. Eng Appl Artif Intell 68:63. https://doi.org/10.1016/j.engappai.2017.10.024

    Article  Google Scholar 

  36. Long W, Jiao J, Liang X, Cai S, Xu M (2019) A random opposition-based learning grey wolf optimizer. IEEE Access 7:113810. https://doi.org/10.1109/ACCESS.2019.2934994

    Article  Google Scholar 

  37. Sharma S, Salgotra R, Singh U (2017) An enhanced grey wolf optimizer for numerical optimization. In: 2017 international conference on innovations in information, embedded and communication systems (ICIIECS)

  38. Nadimi-Shahraki MH, Taghian S, Mirjalili S (2021) An improved grey wolf optimizer for solving engineering problems. Exp Syst Appl 166:113907. https://doi.org/10.1016/j.eswa.2020.113917

    Article  Google Scholar 

  39. Zhang S, Zhou Y (2015) Grey wolf optimizer based on powell local optimization method for clustering analysis. Discrete Dyn Nat Soc. https://doi.org/10.1155/2015/481360

    Article  Google Scholar 

  40. Mahdad B, Srairi K (2015) Blackout risk prevention in a smart grid based flexible optimal strategy using Grey Wolf-pattern search algorithms. Energy Convers Manag 98:411. https://doi.org/10.1016/j.enconman.2015.04.005

    Article  Google Scholar 

  41. Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26(5):1257. https://doi.org/10.1007/s00521-014-1806-7

    Article  Google Scholar 

  42. Jayabarathi T, Raghunathan T, Adarsh B, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630. https://doi.org/10.1016/j.energy.2016.05.105

    Article  Google Scholar 

  43. Wang JS, Li SX (2019) An improved grey wolf optimizer based on differential evolution and elimination mechanism. Sci Rep 9(1):7181. https://doi.org/10.1038/s41598-019-43546-3

    Article  Google Scholar 

  44. Guha D, Roy PK, Banerjee S (2016) Load frequency control of large scale power system using quasi-oppositional grey wolf optimization algorithm. Eng Sci Technol Int J 19(4):1693. https://doi.org/10.1016/j.jestch.2016.07.004

    Article  Google Scholar 

  45. Gaidhane PJ, Nigam MJ (2018) A hybrid grey wolf optimizer and artificial bee colony algorithm for enhancing the performance of complex systems. J Comput Sci 27:284. https://doi.org/10.1016/j.jocs.2018.06.008

    Article  Google Scholar 

  46. Alomoush AA, Alsewari AA, Alamri HS, Aloufi K, Zamli KZ (2019) Hybrid harmony search algorithm with grey wolf optimizer and modified opposition-based learning. IEEE Access 7:68764. https://doi.org/10.1109/ACCESS.2019.2917803

    Article  Google Scholar 

  47. Aleti A, Moser I (2016) A systematic literature review of adaptive parameter control methods for evolutionary algorithms. ACM Comput Surv. https://doi.org/10.1145/2996355

    Article  Google Scholar 

  48. Zhan ZH, Zhang J, Li Y, Chung HSH (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybern Part B (Cybernetics) 39(6):1362. https://doi.org/10.1109/TSMCB.2009.2015956

    Article  Google Scholar 

  49. Naik MK, Panda R (2016) A novel adaptive cuckoo search algorithm for intrinsic discriminant analysis based face recognition. Appl Soft Comput 38:661. https://doi.org/10.1016/j.asoc.2015.10.039

    Article  Google Scholar 

  50. You K, Long M, Wang J, Jordan MI (2019) How does learning rate decay help modern neural networks?

  51. Yan F, Xu J, Yun K (2019) Dynamically dimensioned search grey wolf optimizer based on positional interaction information. Complexity. https://doi.org/10.1155/2019/7189653

    Article  Google Scholar 

  52. Duchi J, Hazan E, Singer Y (2011) Adaptive subgradient methods for online learning and stochastic optimization. J Mach Learn Res 12:2121–2159

    MathSciNet  MATH  Google Scholar 

  53. Kingma DP, Ba J (2017) Adam: a method for stochastic optimization

  54. Sutskever I, Martens J, Dahl G, Hinton G (2013) On the importance of initialization and momentum in deep learning. In: proceedings of the 30th international conference on international conference on machine learning - Vol 28 (JMLR.org, 2013), ICML’13, p. III-1139-III-1147

  55. Digalakis J, Margaritis K (2001) On benchmarking functions for genetic algorithms. Int J Comput Math 77(4):481. https://doi.org/10.1080/00207160108805080

    Article  MathSciNet  MATH  Google Scholar 

  56. Qais MH, Hasanien HM, Alghuwainem S (2018) Augmented grey wolf optimizer for grid-connected PMSG-based wind energy conversion systems. Appl Soft Comput 69:504. https://doi.org/10.1016/j.asoc.2018.05.006

    Article  Google Scholar 

  57. Zielinski K, Peters D, Laur R (2005) Stopping criteria for single-objective optimization

  58. Zielinski K, Laur R (2007) Stopping criteria for a constrained single-objective particle swarm optimization algorithm. Informatica (Slovenia) 31:51

    MATH  Google Scholar 

  59. Fernández-Vargas JA, Bonilla-Petriciolet A, Rangaiah GP, Fateen SEK (2016) Performance analysis of stopping criteria of population-based metaheuristics for global optimization in phase equilibrium calculations and modeling. Fluid Phase Equilibria 427:104. https://doi.org/10.1016/j.fluid.2016.06.037

    Article  Google Scholar 

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Funding

This work is supported by the start-up fund provided by CMU Mechanical Engineering, USA, and funding from National Science Foundation (CBET–1953222), United States.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    Kazem Meidani, AmirPouya Hemmasian & Amir Barati Farimani

  2. Centre for Artificial Intelligence Research and Optimization, Torrens University Australia, Adelaide, Australia

    Seyedali Mirjalili

  3. Yonsei Frontier Lab, Yonsei University, Seoul, Republic of Korea

    Seyedali Mirjalili

  4. Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA

    Amir Barati Farimani

  5. Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    Amir Barati Farimani

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  1. Kazem Meidani
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  2. AmirPouya Hemmasian
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Correspondence to Amir Barati Farimani.

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The code of the algorithm can be accessed from: https://github.com/BaratiLab/Adaptive-Grey-Wolf-Optimization-Algorithm-AGWO.

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Meidani, K., Hemmasian, A., Mirjalili, S. et al. Adaptive grey wolf optimizer. Neural Comput & Applic 34, 7711–7731 (2022). https://doi.org/10.1007/s00521-021-06885-9

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