Skip to main content
Log in

Improved GWO algorithm for optimal design of truss structures

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

In this article, an improved grey wolf optimizer (IGWO) algorithm is developed for optimal design of truss structures. Grey wolf optimizer (GWO) is a recently proposed algorithm for optimization, which is herein improved to handle structural optimization in an efficient manner. In this work, performance of the GWO in structural optimization is also investigated. A few tunable parameters are defined to provide proper adaptability for the algorithm and to optimize the structures using fewer structural analyses, while obtaining finer solutions. Hence, in addition to reduce the computational efforts, better solutions are obtained as it is shown by several benchmark examples, where both GWO and IGWO are employed for the optimization. Mathematical functions as well as various design examples from small to large truss structures with different search spaces are examined to demonstrate the ability and efficiency of the present improved version in comparison to its standard version.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Publishing Company, Boston

    MATH  Google Scholar 

  2. Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Micro machine and human science, 1995. MHS’95. In: Proceedings of the sixth international symposium on, IEEE, pp 39–43

  3. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68. https://doi.org/10.1177/003754970107600201

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Yang X-S, Deb S (2009) Cuckoo search via Lévy flights. Nature and biologically inspired computing, 2009. NaBIC 2009. World Congress on, IEEE, pp 210–214

  6. Kaveh A, Farhoudi N (2013) A new optimization method: dolphin echolocation. Adv Eng Softw 59:53–70. https://doi.org/10.1016/j.advengsof.2013.03.004

    Article  Google Scholar 

  7. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  8. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95(Supplement C):51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  9. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw. https://doi.org/10.1016/j.advengsoft.2017.07.002

    Google Scholar 

  10. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680

    Article  MathSciNet  MATH  Google Scholar 

  11. Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213(3):267–289. https://doi.org/10.1007/s00707-009-0270-4

    Article  MATH  Google Scholar 

  12. Kaveh A, Mahdavi VR (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27. https://doi.org/10.1016/j.compstruc.2014.04.005

    Article  Google Scholar 

  13. Kaveh A, Khayatazad M (2012) A new meta-heuristic method: ray optimization. Comput Struct 112:283–294. https://doi.org/10.1016/j.compstruc.2012.09.003

    Article  Google Scholar 

  14. Kaveh A, Bakhshpoori T (2016) A new metaheuristic for continuous structural optimization: water evaporation optimization. Struct Multidiscip Optim 54(1):23–43. https://doi.org/10.1007/s00158-015-1396-8

    Article  Google Scholar 

  15. Saka MP, Hasançebi O, Geem ZW (2016) Metaheuristics in structural optimization and discussions on harmony search algorithm. Swarm Evol Comput 28:88–97. https://doi.org/10.1016/j.swevo.2016.01.005

    Article  Google Scholar 

  16. Kaveh A (2016) Advances in metaheuristic algorithms for optimal design of structures. Springer, Berlin

    MATH  Google Scholar 

  17. Kaveh A, Ilchi Ghazaan M (2015) A comparative study of CBO and ECBO for optimal design of skeletal structures. Comput Struct 153:137–147. https://doi.org/10.1016/j.compstruc.2015.02.028

    Article  Google Scholar 

  18. Degertekin SO, Hayalioglu MS (2013) Sizing truss structures using teaching-learning-based optimization. Comput Struct 119:177–188. https://doi.org/10.1016/j.compstruc.2012.12.011

    Article  Google Scholar 

  19. Charles VC, Barron JB (2004) Design of space trusses using ant colony optimization. J Struct Eng 130(5):741–751. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:5(741)

    Article  Google Scholar 

  20. Shobeiri V (2016) The optimal design of structures using ACO and EFG. Eng Comput 32(4):645–653. https://doi.org/10.1007/s00366-016-0443-4

    Article  Google Scholar 

  21. Kaveh A, Zakian P (2013) Optimal design of steel frames under seismic loading using two meta-heuristic algorithms. J Constr Steel Res 82:111–130. https://doi.org/10.1016/j.jcsr.2012.12.003

    Article  Google Scholar 

  22. Gholizadeh S, Fattahi F (2014) Design optimization of tall steel buildings by a modified particle swarm algorithm. Struct Des Tall Spec Build 23(4):285–301. https://doi.org/10.1002/tal.1042

    Article  Google Scholar 

  23. Hasançebi O, Bahçecioğlu T, Kurç Ö, Saka MP (2011) Optimum design of high-rise steel buildings using an evolution strategy integrated parallel algorithm. Comput Struct 89(21):2037–2051. https://doi.org/10.1016/j.compstruc.2011.05.019

    Article  Google Scholar 

  24. Gholizadeh S, Baghchevan A (2017) Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm. Eng Comput. https://doi.org/10.1007/s00366-017-0515-0

    Google Scholar 

  25. Kaveh A, Zakian P (2014) Enhanced bat algorithm for optimal design of skeletal structures. Asian J Civ Eng (BHRC) 15(2):179–212

    Google Scholar 

  26. Kaveh A, Ilchi Ghazaan M (2014) Enhanced colliding bodies optimization for design problems with continuous and discrete variables. Adv Eng Softw 77(0):66–75. https://doi.org/10.1016/j.advengsoft.2014.08.003

    Article  Google Scholar 

  27. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579. https://doi.org/10.1016/j.amc.2006.11.033

    MathSciNet  MATH  Google Scholar 

  28. Kaveh A, Talatahari S (2009) Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures. Comput Struct 87(5):267–283. https://doi.org/10.1016/j.compstruc.2009.01.003

    Article  Google Scholar 

  29. Li LJ, Huang ZB, Liu F, Wu QH (2007) A heuristic particle swarm optimizer for optimization of pin connected structures. Comput Struct 85(7):340–349. https://doi.org/10.1016/j.compstruc.2006.11.020

    Article  Google Scholar 

  30. Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172(Supplement C):371–381. https://doi.org/10.1016/j.neucom.2015.06.083

    Article  Google Scholar 

  31. Mirjalili S, Saremi S, Mirjalili SM, Coelho LdS (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst Appl 47(Supplement C):106–119. https://doi.org/10.1016/j.eswa.2015.10.039

    Article  Google Scholar 

  32. Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with Lévy flight for optimization tasks. Appl Soft Comput 60:115–134. https://doi.org/10.1016/j.asoc.2017.06.044

    Article  Google Scholar 

  33. Lu C, Gao L, Li X, Xiao S (2017) A hybrid multi-objective grey wolf optimizer for dynamic scheduling in a real-world welding industry. Eng Appl Artif Intell 57(Supplement C):61–79. https://doi.org/10.1016/j.engappai.2016.10.013

    Article  Google Scholar 

  34. Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82(9):781–798. https://doi.org/10.1016/j.compstruc.2004.01.002

    Article  Google Scholar 

  35. Charles VC (2007) Design of space trusses using big Bang–Big Crunch optimization. J Struct Eng 133(7):999–1008. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:7(999)

    Article  Google Scholar 

  36. Kaveh A, Talatahari S (2009) Size optimization of space trusses using Big Bang–Big Crunch algorithm. Comput Struct 87(17):1129–1140. https://doi.org/10.1016/j.compstruc.2009.04.011

    Article  Google Scholar 

  37. Erbatur F, Hasançebi O, Tütüncü İ, Kılıç H (2000) Optimal design of planar and space structures with genetic algorithms. Comput Struct 75(2):209–224. https://doi.org/10.1016/S0045-7949(99)00084-X

    Article  Google Scholar 

  38. Kaveh A, Khayatazad M (2013) Ray optimization for size and shape optimization of truss structures. Comput Struct 117:82–94. https://doi.org/10.1016/j.compstruc.2012.12.010

    Article  Google Scholar 

  39. Degertekin SO (2012) Improved harmony search algorithms for sizing optimization of truss structures. Comput Struct 92:229–241. https://doi.org/10.1016/j.compstruc.2011.10.022

    Article  Google Scholar 

  40. Lamberti L (2008) An efficient simulated annealing algorithm for design optimization of truss structures. Comput Struct 86 (19):1936–1953. https://doi.org/10.1016/j.compstruc.2008.02.004

    Article  Google Scholar 

  41. Talatahari S, Gandomi AH, Yun GJ (2014) Optimum design of tower structures using Firefly algorithm. Struct Des Tall Spec Build 23(5):350–361. https://doi.org/10.1002/tal.1043

    Article  Google Scholar 

  42. Rahami H, Kaveh A, Aslani M, Najian Asl R (2011) A hybrid modified genetic-nelder mead simplex algorithm for large-scale truss optimization. Int J Optim Civil Eng 1(1):29–46

    Google Scholar 

  43. Hasançebi O, Erbatur F (2002) On efficient use of simulated annealing in complex structural optimization problems. Acta Mech 157(1):27–50. https://doi.org/10.1007/BF01182153

    Article  MATH  Google Scholar 

  44. Hasançebi O (2008) Adaptive evolution strategies in structural optimization: enhancing their computational performance with applications to large-scale structures. Comput Struct 86 (1):119–132. https://doi.org/10.1016/j.compstruc.2007.05.012

    Article  Google Scholar 

  45. Gandomi AH, Talatahari S, Yang X-S, Deb S (2013) Design optimization of truss structures using cuckoo search algorithm. Struct Des Tall Spec Build 22(17):1330–1349. https://doi.org/10.1002/tal.1033

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Kaveh.

Ethics declarations

Conflict of interest

No potential conflict of interest was reported by the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaveh, A., Zakian, P. Improved GWO algorithm for optimal design of truss structures. Engineering with Computers 34, 685–707 (2018). https://doi.org/10.1007/s00366-017-0567-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-017-0567-1

Keywords