SpringerLink
Log in

A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

A recent metaheuristic algorithm, such as Whale optimization algorithm (WOA), was proposed. The idea of proposing this algorithm belongs to the hunting behavior of the humpback whale. However, WOA suffers from poor performance in the exploitation phase and stagnates in the local best solution. Grey wolf optimization (GWO) is a very competitive algorithm comparing to other common metaheuristic algorithms as it has a super performance in the exploitation phase, while it is tested on unimodal benchmark functions. Therefore, the aim of this paper is to hybridize GWO with WOA to overcome the problems. GWO can perform well in exploiting optimal solutions. In this paper, a hybridized WOA with GWO which is called WOAGWO is presented. The proposed hybridized model consists of two steps. Firstly, the hunting mechanism of GWO is embedded into the WOA exploitation phase with a new condition which is related to GWO. Secondly, a new technique is added to the exploration phase to improve the solution after each iteration. Experimentations are tested on three different standard test functions which are called benchmark functions: 23 common functions, 25 CEC2005 functions, and 10 CEC2019 functions. The proposed WOAGWO is also evaluated against original WOA, GWO, and three other commonly used algorithms. Results show that WOAGWO outperforms other algorithms depending on the Wilcoxon rank-sum test. Finally, WOAGWO is likewise applied to solve an engineering problem such as pressure vessel design. Then the results prove that WOAGWO achieves optimum solution which is better than WOA and fitness-dependent optimizer (FDO).

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /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 includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295

    Google Scholar 

  2. Yang X-S, He X (2016) Nature-inspired optimization algorithms in engineering: overview and applications. In: Yang X-S (ed) Nature-Inspired Computation in Engineering. Studies in computational intelligence, vol 637. Springer, Cham

    Google Scholar 

  3. Michalewicz Z, Fogel DB (2004) How to solve it: modern heuristics. Springer, New York

    MATH  Google Scholar 

  4. Algorithms for hard problems (2004) Introduction to combinatorial optimization, randomization, approximation, heuristics, 2nd edn. Springer, New York

    Google Scholar 

  5. Wang G, Guo L (2013) A novel hybrid bat algorithm with harmony search for global numerical optimization. J Appl Math 2013:21

    MathSciNet  MATH  Google Scholar 

  6. De Giovanni L, Pezzella F (2010) An improved genetic algorithm for the distributed and flexible job-shop scheduling problem. Eur J Oper Res 200(2):395–408

    MATH  Google Scholar 

  7. Salman A, Ahmad I, Al-Madani S (2002) Particle swarm optimization for task assignment problem. Microprocess Microsyst 26(8):363–371

    Google Scholar 

  8. Tate DM, Smith AE (1995) A genetic approach to the quadratic assignment problem. Comput Oper Res 22(1):73–83

    MATH  Google Scholar 

  9. Yalcin GD, Erginel N (2015) Fuzzy multi-objective programming algorithm for vehicle routing problems with backhauls. Expert Syst Appl 42(13):5632–5644

    Google Scholar 

  10. Lozano J, Gonzalez-Gurrola L-C, Rodriguez-Tello E, Lacomme P (2016) A statistical comparison of objective functions for the vehicle routing problem with route balancing. In: 2016 Fifteenth Mexican international conference on artificial intelligence (MICAI)

  11. Quintana D, Cervantes A, Saez Y, Isasi P (2017) Clustering technique for large-scale home care crew scheduling problems. Appl Intell 47(2):443–455

    Google Scholar 

  12. Luna F et al (2011) Optimization algorithms for large-scale real-world instances of the frequency assignment problem. Soft Comput 15(5):975–990

    Google Scholar 

  13. Srinivas M, Patnaik LM (1994) Genetic algorithms: a survey. Computer (Long. Beach. Calif) 27(6):17–26

    Google Scholar 

  14. Eberhart R, Kennedy J (2002) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science

  15. Teodorović D (2009) Bee colony optimization (BCO). Stud Comput Intell 248:39–60

    Google Scholar 

  16. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Google Scholar 

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

    Google Scholar 

  18. Mohammed HM, Umar SU, Rashid TA (2019) A systematic and meta-analysis survey of whale optimization algorithm. Comput Intell Neurosci 2019:8718571

    Google Scholar 

  19. Trivedi IN, Pradeep J, Narottam J, Arvind K, Dilip L (2016) A novel adaptive whale optimization algorithm for global optimization. Indian J Sci Technol 9(38):1–6

    Google Scholar 

  20. Saidala RK, Devarakonda N (2018) Improved whale optimization algorithm case study: clinical data of anaemic pregnant woman. In: Satapathy S, Bhateja V, Raju K (eds) Advances in intelligent systems and computing, vol 542. Springer, Singapore, pp 271–281

    Google Scholar 

  21. Abdel-Basset M, El-Shahat D, El-henawy I, Sangaiah AK, Ahmed SH (2018) A novel whale optimization algorithm for cryptanalysis in Merkle–Hellman cryptosystem. Mob Netw Appl 23(4):723–733

    Google Scholar 

  22. Xu Z, Yu Y, Yachi H, Ji J, Todo Y, Gao S (2018) A novel memetic whale optimization algorithm for optimization. In: Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics)

  23. Soto R et al (2018) Adaptive black hole algorithm for solving the set covering problem. Math Probl Eng 2018:2183214

    Google Scholar 

  24. Abdel-Basset M, Manogaran G, El-Shahat D, Mirjalili S (2018) A hybrid whale optimization algorithm based on local search strategy for the permutation flow shop scheduling problem. Futur Gener Comput Syst 85:129–145

    Google Scholar 

  25. Kaveh A, Rastegar Moghaddam M (2017) A hybrid WOA-CBO algorithm for construction site layout planning problem. Sci Iran 25(3):1094–1104

    Google Scholar 

  26. Thanga Revathi S, Ramaraj N, Chithra S (2018) Brain storm-based whale optimization algorithm for privacy-protected data publishing in cloud computing. Cluster Comput 5:1–10

    Google Scholar 

  27. Trivedi IN, Jangir P, Kumar A, Jangir N, Totlani R (2018) A novel hybrid PSO–WOA algorithm for global numerical functions optimization. Adv Intell Syst Comput 554:53–60

    Google Scholar 

  28. Mohammed HM, Umar SU, Rashid TA (2019) A systematic and meta-analysis survey of whale optimization algorithm. Comput Intell Neurosci 2019:1–25

    Google Scholar 

  29. Mittal N, Singh U, Sohi BS (2016) Modified grey wolf optimizer for global engineering optimization. Appl Comput Intell Soft Comput 2016:7950348

    Google Scholar 

  30. Tawhid MA, Ibrahim AM (2019) A hybridization of grey wolf optimizer and differential evolution for solving nonlinear systems. Evol Syst. https://doi.org/10.1007/s12530-019-09291-8

    Article  Google Scholar 

  31. Li L, Sun L, Guo J, Qi J, Xu B, Li S (2017) Modified discrete grey wolf optimizer algorithm for multilevel image thresholding. Comput Intell Neurosci 2017:16

    Google Scholar 

  32. Liu H, Hua G, Yin H, Xu Y (2018) An intelligent grey wolf optimizer algorithm for distributed compressed sensing. Comput Intell Neurosci 2018:10

    Google Scholar 

  33. Mafarja MM, Mirjalili S (2017) Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing 206:302–312

    Google Scholar 

  34. Aljarah I, Faris H, Mirjalili S (2018) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22(1):1–15

    Google Scholar 

  35. Kaur G, Arora S (2018) Chaotic whale optimization algorithm. J Comput Des Eng 5(3):275–284

    Google Scholar 

  36. Abdel-Basset M, Abdle-Fatah L, Sangaiah AK (2019) An improved Lévy based whale optimization algorithm for bandwidth-efficient virtual machine placement in cloud computing environment. Clust Comput 22(S4):8319–8334

    Google Scholar 

  37. Zhong M, Long W (2017) Whale optimization algorithm with nonlinear control parameter. In: MATEC web of conferences. p 5

  38. El-Shafeiy E, El-Desouky A, El-Ghamrawy S (2018) An optimized artificial neural network approach based on sperm whale optimization algorithm for predicting fertility quality. Stud Inform Control 27(3):349–358

    Google Scholar 

  39. Thanga Revathi S, Ramaraj N, Chithra S (2019) Brain storm-based whale optimization algorithm for privacy-protected data publishing in cloud computing. Clust Comput 22(S2):3521–3530

    Google Scholar 

  40. El Aziz MA, Ewees AA, Hassanien AE (2017) Whale optimization algorithm and moth-flame optimization for multilevel thresholding image segmentation. Expert Syst Appl 83:242–256

    Google Scholar 

  41. Panda M, Das B (2019) Grey wolf optimizer and its applications: a survey. Lecture notes in electrical engineering. Springer, Singapore, pp 179–194

    Google Scholar 

  42. Rashid TA, Abbas DK, Turel YK (2019) A multi hidden recurrent neural network with a modified grey wolf optimizer PLoS One 14(3):e0213237

    Google Scholar 

  43. Kohli M, Arora S (2018) Chaotic grey wolf optimization algorithm for constrained optimization problems. J Comput Des Eng 5(4):458–472

    Google Scholar 

  44. Panwar LK, Reddy S, Verma A, Panigrahi BK, Kumar R (2018) Binary Grey Wolf Optimizer for large scale unit commitment problem. Swarm Evol Comput 38:251–266

    Google Scholar 

  45. Saxena A, Soni BP, Kumar R, Gupta V (2018) Intelligent grey wolf optimizer—development and application for strategic bidding in uniform price spot energy market. Appl Soft Comput J 69:1–13

    Google Scholar 

  46. Sánchez D, Melin P, Castillo O (2017) A grey Wolf optimizer for modular granular neural networks for human recognition. Comput Intell Neurosci 2017:26

    Google Scholar 

  47. Zhang S, Zhou Y (2015) Grey wolf optimizer based on powell local optimization method for clustering analysis. Discrete Dyn Nat Soc 2015:17

    Google Scholar 

  48. Shilaja C, Arunprasath T (2019) Internet of medical things-load optimization of power flow based on hybrid enhanced grey wolf optimization and dragonfly algorithm. Futur Gener Comput Syst 98:319–330

    Google Scholar 

  49. Rashid TA, Fattah P, Awla DK (2018) Using accuracy measure for improving the training of LSTM with metaheuristic algorithms. Procedia Comput Sci 140:324–333

    Google Scholar 

  50. Barraza J, Rodríguez L, Castillo O, Melin P, Valdez F (2018) A new hybridization approach between the fireworks algorithm and grey wolf optimizer algorithm. J Optim 2018:18

    MathSciNet  MATH  Google Scholar 

  51. Pan JS, Dao TK, Chu SC, Nguyen TT (2018) A novel hybrid GWO-FPA algorithm for optimization applications. In: Smart innovation, systems and technologies. pp 274–281

  52. Singh N, Singh SB (2017) A novel hybrid GWO-SCA approach for optimization problems. Eng Sci Technol Int J 20(6):1586–1601

    Google Scholar 

  53. Jayabarathi T, Raghunathan T, Adarsh BR, Suganthan PN (2016) Economic dispatch using hybrid grey wolf optimizer. Energy 111:630–641

    Google Scholar 

  54. Abdullah JM, Ahmed T (2019) Fitness dependent optimizer: inspired by the bee swarming reproductive process. IEEE Access 7:43473–43486

    Google Scholar 

Download references

Acknowledgements

The authors wish to thank the Sulaimani Polytechnic University and the University of Kurdistan Hewler (UKH).

Author information

Authors and Affiliations

  1. Applied Computer Department, College of Medicals and Applied Sciences, Charmo University, Sulaimani, Chamchamal, KRG, Iraq

    Hardi Mohammed

  2. Technical College of Informatics, Sulaimani Polytechnic University, Sulaimani, KRG, Iraq

    Hardi Mohammed

  3. Computer Science and Engineering, School of Computing and Engineering, University of Kurdistan Hewler (UKH), Hewler, KRG, Iraq

    Tarik Rashid

Authors
  1. Hardi Mohammed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tarik Rashid
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hardi Mohammed.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohammed, H., Rashid, T. A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design. Neural Comput & Applic 32, 14701–14718 (2020). https://doi.org/10.1007/s00521-020-04823-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-020-04823-9

Keywords

Search

Navigation