Skip to main content

Advertisement

Log in

Wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems

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

Abstract

Nowadays, the design of optimization algorithms is very popular to solve problems in various scientific fields. The optimization algorithms usually inspired by the natural behaviour of an agent, which can be humans, animals, plants, or a physical or chemical agent. Most of the algorithms proposed in the last decade inspired by animal behaviour. In this article, we present a new optimizer algorithm called the wild horse optimizer (WHO), which is inspired by the social life behaviour of wild horses. Horses usually live in groups that include a stallion and several mares and foals. Horses exhibit many behaviours, such as grazing, chasing, dominating, leading, and mating. A fascinating behaviour that distinguishes horses from other animals is the decency of horses. Horse decency behaviour is such that the foals of the horse leave the group before reaching puberty and join other groups. This departure is to prevent the father from mating with the daughter or siblings. The main inspiration for the proposed algorithm is the decency behaviour of the horse. The proposed algorithm was tested on several sets of test functions such as CEC2017 and CEC2019 and compared with popular and new optimization methods. The results showed that the proposed algorithm presented very competitive results compared to other algorithms. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/90787-wild-horse-optimizer.

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

Access this article

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

Similar content being viewed by others

References

  1. Chong EKP, Żak SH (2008) An introduction to optimization. Wiley, Hoboken

    Book  MATH  Google Scholar 

  2. Dréo J (2006) Metaheuristics for hard optimization. Springer-Verlag, Berlin/Heidelberg

    MATH  Google Scholar 

  3. Mafarja M, Aljarah I, Heidari AA et al (2018) Evolutionary population dynamics and grasshopper optimization approaches for feature selection problems. Knowl-Based Syst 145:25–45. https://doi.org/10.1016/j.knosys.2017.12.037

    Article  Google Scholar 

  4. Aljarah I, Mafarja M, Heidari AA et al (2018) Asynchronous accelerating multi-leader salp chains for feature selection. Appl Soft Comput 71:964–979. https://doi.org/10.1016/j.asoc.2018.07.040

    Article  Google Scholar 

  5. Holland JH (1967) Genetic algorithms understand genetic algorithms. Surprise 96(1):12–15. https://doi.org/10.2307/24939139

    Article  Google Scholar 

  6. Eberhart R, Kennedy J (2002) A new optimizer using particle swarm theory. In: MHS’95. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, pp 39–43

  7. Yang X-S (2010) Firefly algorithm, Lévy flights and global optimization. Research and development in intelligent systems XXVI. Springer, London, pp 209–218

    Chapter  Google Scholar 

  8. 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 

  9. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci (NY) 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  MATH  Google Scholar 

  10. Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98. https://doi.org/10.1016/j.advengsoft.2015.01.010

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27:495–513. https://doi.org/10.1007/s00521-015-1870-7

    Article  Google Scholar 

  13. Mirjalili S, Gandomi AH, Mirjalili SZ et al (2017) Salp Swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002

    Article  Google Scholar 

  14. Samareh Moosavi SH, Bardsiri VK (2019) Poor and rich optimization algorithm: a new human-based and multi populations algorithm. Eng Appl Artif Intell 86:165–181. https://doi.org/10.1016/j.engappai.2019.08.025

    Article  Google Scholar 

  15. Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872. https://doi.org/10.1016/j.future.2019.02.028

    Article  Google Scholar 

  16. Abdullah JM, Ahmed T (2019) Fitness dependent optimizer: inspired by the bee swarming reproductive process. IEEE Access 7:43473–43486. https://doi.org/10.1109/ACCESS.2019.2907012

    Article  Google Scholar 

  17. Anita YA, Kumar N (2020) Artificial electric field algorithm for engineering optimization problems. Expert Syst Appl 149:113308. https://doi.org/10.1016/j.eswa.2020.113308

    Article  Google Scholar 

  18. Houssein EH, Saad MR, Hashim FA et al (2020) Lévy flight distribution: a new metaheuristic algorithm for solving engineering optimization problems. Eng Appl Artif Intell 94:103731. https://doi.org/10.1016/j.engappai.2020.103731

    Article  Google Scholar 

  19. Kaur S, Awasthi LK, Sangal AL, Dhiman G (2020) Tunicate Swarm Algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intell 90:103541. https://doi.org/10.1016/j.engappai.2020.103541

    Article  Google Scholar 

  20. Awad NH, MZ. Ali JJ, Liang BY, Qu PS (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. Tech Rep

  21. Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249. https://doi.org/10.1016/j.knosys.2015.07.006

    Article  Google Scholar 

  22. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  23. Carson K, Wood-Gush DGM (1983) Equine behaviour: I. A review of the literature on social and dam—Foal behaviour. Appl Anim Ethol 10:165–178. https://doi.org/10.1016/0304-3762(83)90138-4

    Article  Google Scholar 

  24. Carson K, Wood-Gush DGM (1983) Equine behaviour: II. A review of the literature on feeding, eliminative and resting behaviour. Appl Anim Ethol 10:179–190. https://doi.org/10.1016/0304-3762(83)90139-6

    Article  Google Scholar 

  25. Feist JD, McCullough DR (1975) Reproduction in feral horses. J Reprod Fertil Suppl (23):13–18. PMID:1060766

  26. Klingel H (1975) Social organization and reproduction in equids. J Reprod Fertil Suppl 7–11

  27. Wells SM, Goldschmidt-Rothschild B (2010) Social behaviour and relationships in a herd of camargue horses. Z Tierpsychol 49:363–380. https://doi.org/10.1111/j.1439-0310.1979.tb00299.x

    Article  Google Scholar 

  28. Miller R, Dennisto RH (2010) Interband dominance in feral horses. Z Tierpsychol 51:41–47. https://doi.org/10.1111/j.1439-0310.1979.tb00670.x

    Article  Google Scholar 

  29. Squires VR, Daws GT (1975) Leadership and dominance relationships in Merino and Border Leicester sheep. Appl Anim Ethol 1:263–274. https://doi.org/10.1016/0304-3762(75)90019-X

    Article  Google Scholar 

  30. Welsh DA, University D (1975) Population, behavioural and grazing ecology of the horses of Sable Island, Nova Scotia. PhD thesis, Dalhousie University

  31. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1016/j.advengsoft.2017.01.004

    Article  Google Scholar 

  32. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  33. Awad NH, Ali MZ, Suganthan PN, Liang JJ, Qu BY (2017) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. In: 2017 IEEE Congress on Evolutionary Computation (CEC)

  34. Price KV, Awad NH, Ali MZ, PNS (2018) The 100-digit challenge: problem definitions and evaluation criteria for the 100-digit challenge special session and competition on single objective numerical optimization. Sch Elect Electron Eng, Nanyang Technol Univ, Singapore, Tech Rep

    Google Scholar 

  35. Kumar A, Wu G, Ali MZ et al (2020) A test-suite of non-convex constrained optimization problems from the real-world and some baseline results. Swarm Evol Comput 56:100693. https://doi.org/10.1016/j.swevo.2020.100693

    Article  Google Scholar 

  36. Floudas CA, Ciric AR, Grossmann IE (1986) Automatic synthesis of optimum heat exchanger network configurations. AIChE J 32:276–290. https://doi.org/10.1002/aic.690320215

    Article  Google Scholar 

  37. Kocis GR, Grossmann IE (1988) Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis. Ind Eng Chem Res 27:1407–1421. https://doi.org/10.1021/ie00080a013

    Article  Google Scholar 

  38. Kocis GR, Grossmann IE (1989) A modelling and decomposition strategy for the minlp optimization of process flowsheets. Comput Chem Eng 13:797–819. https://doi.org/10.1016/0098-1354(89)85053-7

    Article  Google Scholar 

  39. Belegundu AD, Arora JS (1985) A study of mathematical programming methods for structural optimization. Part I: theory. Int J Numer Methods Eng 21:1583–1599. https://doi.org/10.1002/nme.1620210904

    Article  MATH  Google Scholar 

  40. Nowacki H (1973) Optimization in pre-contract ship design. In: International Conference on Computer Applications in the Automation of Shipyard Operation and ShipDesign, pp 1–12

  41. Rao SS (1996) Engineering optimization: theory and practice. New Age International Publishers

    Google Scholar 

  42. Gupta S, Tiwari R, Nair SB (2007) Multi-objective design optimisation of rolling bearings using genetic algorithms. Mech Mach Theory 42:1418–1443. https://doi.org/10.1016/j.mechmachtheory.2006.10.002

    Article  MATH  Google Scholar 

  43. Beightler CSPD (1976) Applied geometric programming. Wiley

    MATH  Google Scholar 

  44. Mautner DH (1972) Applied nonlinear programming. McGraw-Hill Co

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Farshid Keynia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Naruei, I., Keynia, F. Wild horse optimizer: a new meta-heuristic algorithm for solving engineering optimization problems. Engineering with Computers 38 (Suppl 4), 3025–3056 (2022). https://doi.org/10.1007/s00366-021-01438-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-021-01438-z

Keywords

Navigation