Skip to main content
Log in

A modified whale optimization algorithm with multi-strategy mechanism for global optimization problems

  • S.I.: Hybrid Approaches to Nature-inspired Optimization Algorithms and Their Applications
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Whale Optimization Algorithm (WOA) is an outstanding nature-inspired algorithm widely used to solve many complex engineering optimization problems. However, WOA has a poor balance in exploration and exploitation, which converges to local optimum easily. This article proposes a Modified Whale Optimization Algorithm (MWOA) with multi-strategy mechanism, which introduces the elite reverse learning strategy, nonlinear convergence factor, DE/rand/1 mutation strategy and Lévy flight disturbance strategy. MWOA can improve the convergent ability and maintain the balance of exploitation and exploration to avoid local optimum. Compared with WOA, PSO, MFO, SOA, SCA and other four WOA variants on the CEC2017 benchmark suite, MWOA has strong competitiveness and can better improve the efficiency of WOA according to the experimental results and analysis.

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

Similar content being viewed by others

Data availability

The data that support the findings of this study are not openly available the university’s data sharing guidelines but are available from the corresponding author upon reasonable request.

References

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

    Article  Google Scholar 

  2. Yang B et al (2020) Comprehensive overview of meta-heuristic algorithm applications on PV cell parameter identification. Energy Convers Manage 208:112595

    Article  Google Scholar 

  3. Wu Y (2021) A survey on population-based meta-heuristic algorithms for motion planning of aircraft. Swarm Evol Comput 62:100844

    Article  Google Scholar 

  4. Lu P et al (2021) Review of meta-heuristic algorithms for wind power prediction: methodologies, applications and challenges. Appl Energy 301:117446

    Article  Google Scholar 

  5. Hu G et al (2022) An enhanced manta ray foraging optimization algorithm for shape optimization of complex CCG-Ball curves. Knowl-Based Syst 240:108071

    Article  Google Scholar 

  6. Mirjalili S (2019) Genetic algorithm. In: Evolutionary algorithms and neural networks. Springer, pp 43–55

  7. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN'95-international conference on neural networks. IEEE

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

    Article  Google Scholar 

  9. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B (Cybernetics) 26(1): 29–41

  10. Hu G et al (2022) An enhanced chimp optimization algorithm for optimal degree reduction of Said-Ball curves. Math Comput Simul 197:207–252

    Article  MATH  Google Scholar 

  11. Basturk B (2006) An artificial bee colony (ABC) algorithm for numeric function optimization. In: IEEE swarm intelligence symposium, Indianapolis, IN, USA

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

    Article  Google Scholar 

  13. Gharehchopogh FS, Gholizadeh H (2019) A comprehensive survey: whale optimization algorithm and its applications. Swarm Evol Comput 48:1–24

    Article  Google Scholar 

  14. Nasiri J, Khiyabani FM (2018) A whale optimization algorithm (WOA) approach for clustering. Cogent Math Stat 5(1):1483565

    Article  MATH  Google Scholar 

  15. Cui D (2017) Application of whale optimization algorithm in reservoir optimal operation. Adv Sci Technol Water Resour 37(3):72–79

    Google Scholar 

  16. Pham Q-V et al (2020) Whale optimization algorithm with applications to resource allocation in wireless networks. IEEE Trans Veh Technol 69(4):4285–4297

    Article  Google Scholar 

  17. Srivastava V, Srivastava S (2019) Whale optimization algorithm (WOA) based control of nonlinear systems. In: 2019 2nd International conference on power energy, environment and intelligent control (PEEIC). IEEE

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

    Google Scholar 

  19. Zhong M, Long W (2017) Whale optimization algorithm with nonlinear control parameter. In: MATEC web of conferences. 2017. EDP Sciences

  20. Li S, Luo X, Wu L (2021) An improved whale optimization algorithm for locating critical slip surface of slopes. Adv Eng Softw 157:103009

    Article  Google Scholar 

  21. Kushwah R, Kaushik M, Chugh K (2021) A modified whale optimization algorithm to overcome delayed convergence in artificial neural networks. Soft Comput 25(15):10275–10286

    Article  Google Scholar 

  22. Abd Elaziz M, Oliva D (2018) Parameter estimation of solar cells diode models by an improved opposition-based whale optimization algorithm. Energy conversion and management, 171: 1843–1859

  23. Zhang J, Wang J-S (2020) Improved whale optimization algorithm based on nonlinear adaptive weight and golden sine operator. IEEE Access 8:77013–77048

    Article  Google Scholar 

  24. Chen H et al (2020) An efficient double adaptive random spare reinforced whale optimization algorithm. Expert Syst Appl 154:113018

    Article  Google Scholar 

  25. Liu J, et al (2022) A novel enhanced global exploration whale optimization algorithm based on Lévy flights and judgment mechanism for global continuous optimization problems. Eng Comput, 1–29

  26. Chakraborty S, et al. (2022) A novel improved whale optimization algorithm to solve numerical optimization and real-world applications. Artif Intell Rev, 1–112

  27. Nadimi-Shahraki MH, Zamani H, Mirjalili S (2022) Enhanced whale optimization algorithm for medical feature selection: a COVID-19 case study. Comput Biol Med 148:105858

    Article  Google Scholar 

  28. Trivedi IN, et al (2018) A novel hybrid PSO–WOA algorithm for global numerical functions optimization. In: Advances in computer and computational sciences. Springer, p 53–60

  29. Mohammed H, Rashid T (2020) A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design. Neural Comput Appl 32(18):14701–14718

    Article  Google Scholar 

  30. Kaveh A, Rastegar Moghaddam M (2018) A hybrid WOA-CBO algorithm for construction site layout planning problem. Sci Iranica 25(3): 1094–1104

  31. Mostafa Bozorgi S, Yazdani S (2019) IWOA: an improved whale optimization algorithm for optimization problems. J Comput Des Eng 6(3): 243–259

  32. Bentouati B, Chaib L, Chettih S (2016) A hybrid whale algorithm and pattern search technique for optimal power flow problem. In: 2016 8th international conference on modelling, identification and control (ICMIC). IEEE

  33. Tang C et al (2022) A hybrid whale optimization algorithm with artificial bee colony. Soft Comput 26(5):2075–2097

    Article  Google Scholar 

  34. Dey B, Bhattacharyya B (2022) Comparison of various electricity market pricing strategies to reduce generation cost of a microgrid system using hybrid WOA-SCA. Evol Intel 15(3):1587–1604

    Article  Google Scholar 

  35. Chakraborty S et al (2021) A novel enhanced whale optimization algorithm for global optimization. Comput Ind Eng 153:107086

    Article  Google Scholar 

  36. Jin Q, Xu Z, Cai W (2021) An improved whale optimization algorithm with random evolution and special reinforcement dual-operation strategy collaboration. Symmetry 13(2):238

    Article  Google Scholar 

  37. Yuan X et al (2020) Multi-strategy ensemble whale optimization algorithm and its application to analog circuits intelligent fault diagnosis. Appl Sci 10(11):3667

    Article  Google Scholar 

  38. Sun G et al (2022) An improved whale optimization algorithm based on nonlinear parameters and feedback mechanism. Int J Comput Intell Syst 15(1):1–17

    Article  Google Scholar 

  39. Li X, et al (2022) A multi-strategy hybrid adaptive whale optimization algorithm. J Comput Des Eng

  40. Xiao Z-Y, Liu S (2019) Study on elite opposition-based golden-sine whale optimization algorithm and its application of project optimization. Acta Electon Sin 47(10): 2177

  41. Tang C, et al (2019) A hybrid improved whale optimization algorithm. In: 2019 IEEE 15th international conference on control and automation (ICCA). IEEE

  42. Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359

    Article  MATH  Google Scholar 

  43. Xue Y, Tong Y, Neri F (2022) An ensemble of differential evolution and Adam for training feed-forward neural networks. Inf Sci 608:453–471

    Article  Google Scholar 

  44. Chakraborty S, et al (2021) A hybrid whale optimization algorithm for global optimization. J Ambient Intell Human Comput, 1–37

  45. Hu G et al (2022) An enhanced black widow optimization algorithm for feature selection. Knowl-Based Syst 235:107638

    Article  Google Scholar 

  46. Yang X-S, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 World congress on nature and biologically inspired computing (NaBIC). IEEE

  47. Houssein EH et al (2020) Lévy flight distribution: a new metaheuristic algorithm for solving engineering optimization problems. Eng Appl Artif Intell 94:103731

    Article  Google Scholar 

  48. Liu M, Yao X, Li Y (2020) Hybrid whale optimization algorithm enhanced with Lévy flight and differential evolution for job shop scheduling problems. Appl Soft Comput 87:105954

    Article  Google Scholar 

  49. Mohseni S et al (2021) Lévy-flight moth-flame optimisation algorithm-based micro-grid equipment sizing: an integrated investment and operational planning approach. Energy AI 3:100047

    Article  Google Scholar 

  50. Mohiz MJ et al (2021) Application mapping using cuckoo search optimization with Lévy flight for NoC-based system. IEEE Access 9:141778–141789

    Article  Google Scholar 

  51. Mzanh A, et al (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization

  52. Dhiman G, Kumar V (2019) Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl-Based Syst 165:169–196

    Article  Google Scholar 

  53. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133

    Article  Google Scholar 

  54. Yang W et al (2022) A multi-strategy Whale optimization algorithm and its application. Eng Appl Artif Intell 108:104558

    Article  Google Scholar 

  55. Li Y et al (2019) An adaptive whale optimization algorithm using Gaussian distribution strategies and its application in heterogeneous UCAVs task allocation. IEEE Access 7:110138–110158

    Article  Google Scholar 

Download references

Acknowledgements

This research was funded by the National Natural Science Foundation of China (Nos. 72274099, 71974100), Humanities and Social Sciences Fund of the Ministry of Education, China (No. 22YJC630144), Major Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu province (2019SJZDA039), and Project of Meteorological Industry Research Center (sk20220204).

Author information

Authors and Affiliations

Authors

Contributions

Mingyuan Li: Conceptualization, Methodology, Writing- Original draft preparation. Xiaobing Yu: Reviewing and Editing. Bingbing Fu: Data curation, Investigation. Xuming Wang: Editing. Xianrui Yu: Editing.

Corresponding author

Correspondence to Xiaobing Yu.

Ethics declarations

Conflict of interest

The authors declare that there is 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

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, M., Yu, X., Fu, B. et al. A modified whale optimization algorithm with multi-strategy mechanism for global optimization problems. Neural Comput & Applic (2023). https://doi.org/10.1007/s00521-023-08287-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00521-023-08287-5

Keywords

Navigation