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Enhancement of GWO for solving numerical functions and engineering problems

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Abstract

Due to using nature-inspired metaheuristic algorithms to solve real-world applications in different fields, this area has become very popular among researchers because of the flexibility of using optimization algorithms. Therefore, these algorithms can be measured based on their operator, diversity of populations, and balancing between the exploration and exploitation phases. The Grey Wolf Optimization algorithm is one of the competitive metaheuristic algorithms that was proposed in 2014. It mimics the hunting mechanism of wolves. It uses three types of wolves: alpha, beta, and delta for searching in the search space. Despite having competitive performance, GWO has problems regarding local optima and has low exploration. Therefore, enhancement GWO (EGWO) is proposed in this paper in order to solve these problems. EGWO used different methods to improve the performance of GWO: using gamma, z-position, and golden ratio. MGWO is evaluated using CEC2019 ten benchmark functions. Statistical results proved that EGWO outperforms well in six functions out of ten compared to GWO, fitness-dependent optimizer (FDO), cat swarm optimizer, and FOX optimizer. It is also used to solve two real-world applications such as pressure vessel design and 10-bar truss design problems. Results showed that EGWO is very competitive against GWO, FDO, and FOX.

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Data availability

All data generated or analysed during this study are included in this published article. The code of the algorithm will be available on https://github.com/Hardi-Mohammed/ after publication.

References

  1. Liang JJ et al (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Article  Google Scholar 

  2. Yang XS, He X (2016) Nature-inspired optimization algorithms in engineering: overview and applications. Nature-inspired computation in engineering, 1–20

  3. Derrac J et al (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 1(1):3–18

    Article  Google Scholar 

  4. Cui Z, Gao X (2012) Theory and applications of swarm intelligence. Springer, Berlin, pp 205–206

    Google Scholar 

  5. Hussain K et al (2019) Metaheuristic research: a comprehensive survey. Artif Intell Rev 52:2191–2233

    Article  Google Scholar 

  6. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  7. Beni G, Wang J (1993) Swarm intelligence in cellular robotic systems. In: Robots and biological systems: towards a new bionics?. Springer

  8. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39

    Article  Google Scholar 

  9. Faris H et al (2018) Grey wolf optimizer: a review of recent variants and applications. Neural Comput Appl 30:413–435

    Article  Google Scholar 

  10. Tchomté SK, Gourgand M (2009) Particle swarm optimization: a study of particle displacement for solving continuous and combinatorial optimization problems. Int J Prod Econ 121(1):57–67

    Article  Google Scholar 

  11. Parpinelli RS, Lopes HS (2011) New inspirations in swarm intelligence: a survey. Int J Bio-Inspired Comput 3(1):1–16

    Article  Google Scholar 

  12. Leboucher C et al (2012) A swarm intelligence method combined to evolutionary game theory applied to the resources allocation problem. Int J Swarm Intell Res (IJSIR) 3(2):20–38

    Article  Google Scholar 

  13. Zhang Z et al (2013) On swarm intelligence inspired self-organized networking: its bionic mechanisms, designing principles and optimization approaches. IEEE Commun Surv Tutor 16(1):513–537

    Article  MathSciNet  Google Scholar 

  14. Long W et al (2018) Inspired grey wolf optimizer for solving large-scale function optimization problems. Appl Math Model 60:112–126

    Article  MathSciNet  Google Scholar 

  15. Komaki G, Kayvanfar V (2015) Grey Wolf Optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time. J Comput Sci 8:109–120

    Article  Google Scholar 

  16. Wang J-S, Li S-X (2019) An improved grey wolf optimizer based on differential evolution and elimination mechanism. Sci Rep 9(1):1–21

    ADS  MathSciNet  Google Scholar 

  17. Tawhid MA, Ibrahim AM (2020) A hybridization of grey wolf optimizer and differential evolution for solving nonlinear systems. Evol Syst 11:65–87

    Article  CAS  Google Scholar 

  18. Luo J et al (2019) Multi-strategy boosted mutative whale-inspired optimization approaches. Appl Math Model 73:109–123

    Article  ADS  MathSciNet  Google Scholar 

  19. Singh N (2020) A modified variant of grey wolf optimizer. Scientia Iranica. Trans D Comput Sci Eng Electr 27(3):1450–1466

    Google Scholar 

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

    Article  Google Scholar 

  21. Gao ZM, Zhao J (2019) An improved grey wolf optimization algorithm with variable weights. Comput Intell Neurosci 2019

  22. Hu P et al (2018) Improved alpha-guided grey wolf optimizer. IEEE Access 7:5421–5437

    Article  Google Scholar 

  23. Yang Y et al (2019) An improved grey wolf optimizer algorithm for energy-aware service composition in cloud manufacturing. Int J Adv Manuf Technol 105:3079–3091

    Article  Google Scholar 

  24. Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381

    Article  Google Scholar 

  25. Mirjalili S et al (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst Appl 47:106–119

    Article  Google Scholar 

  26. Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26:1257–1263

    Article  Google Scholar 

  27. Kumar V (2016) Modified grey wolf algorithm for optimization problems. In: 2016 international conference on inventive computation technologies (ICICT). 2016. IEEE

  28. Ozsoydan FB (2019) Effects of dominant wolves in grey wolf optimization algorithm. Appl Soft Comput 83:105658

    Article  Google Scholar 

  29. Panda M, Das B (2019) Grey wolf optimizer and its applications: a survey. In: proceedings of the third international conference on microelectronics, computing and communication systems: MCCS 2018. 2019. Springer

  30. Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization

  31. Cagnina LC, Esquivel SC, Coello CAC (2008) Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32(3):319–326

    Google Scholar 

  32. Walker M, Tabakov P (2013) Design optimization of anisotropic pressure vessels with manufacturing uncertainties accounted for. Int J Press Vessels Pip 104:96–104

    Article  Google Scholar 

  33. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249

    Article  Google Scholar 

  34. Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203

    Article  Google Scholar 

  35. Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127

    Article  Google Scholar 

  36. Dasgupta D, Michalewicz Z (2013) Evolutionary algorithms in engineering applications. Springer Science & Business Media, UK

    Google Scholar 

  37. Mezura-Montes E, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473

    Article  MathSciNet  Google Scholar 

  38. Huang F-Z, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356

    MathSciNet  Google Scholar 

  39. He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99

    Article  Google Scholar 

  40. Kaveh A, Talatahari S (2010) An improved ant colony optimization for constrained engineering design problems. Eng Comput 27(1):155–182

    Article  Google Scholar 

  41. Sulaiman M et al (2014) A plant propagation algorithm for constrained engineering optimisation problems. Math Probl Eng 2014:1–10

    Article  Google Scholar 

  42. Petrovic N, Kostic N, Marjanovic N (2017) Comparison of approaches to 10 bar truss structural optimization with included buckling constraints. Appl Eng Lett 2(3):98–103

    Google Scholar 

  43. Gan BS et al (2017) Evolutionary ACO algorithms for truss optimization problems. Procedia Eng 171:1100–1107

    Article  Google Scholar 

  44. Cazacu R, Grama L (2014) Steel truss optimization using genetic algorithms and FEA. Procedia Technol 12:339–346

    Article  Google Scholar 

  45. Asl RN, Aslani M, Panahi MS (2013) Sizing optimization of truss structures using a hybridized genetic algorithm. arXiv preprint arXiv:1306.1454

  46. Farshi B, Alinia-Ziazi A (2010) Sizing optimization of truss structures by method of centers and force formulation. Int J Solids Struct 47(18–19):2508–2524

    Article  Google Scholar 

  47. Cheng M-Y et al (2016) A hybrid harmony search algorithm for discrete sizing optimization of truss structure. Autom Constr 69:21–33

    Article  Google Scholar 

  48. Degertekin S, Hayalioglu M (2013) Sizing truss structures using teaching-learning-based optimization. Comput Struct 119:177–188

    Article  Google Scholar 

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Acknowledgements

All authors would like to thank Charmo University.

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Authors and Affiliations

  1. Computer Science Department, College of Science, Charmo University, 46023, Chamchamal/Sulaimani, Kurdistan region, Iraq

    Hardi Mohammed & Zrar Abdul

  2. Information Technology Department, Dukan Technical Institute, Sulaimani Polytechnic University, Kurdistan Region, Iraq

    Zana Hamad

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  1. Hardi Mohammed
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  2. Zrar Abdul
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  3. Zana Hamad
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Correspondence to Hardi Mohammed.

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Mohammed, H., Abdul, Z. & Hamad, Z. Enhancement of GWO for solving numerical functions and engineering problems. Neural Comput & Applic 36, 3405–3413 (2024). https://doi.org/10.1007/s00521-023-09292-4

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