An enhanced associative learning-based exploratory whale optimizer for global optimization

Abstract

Whale optimization algorithm (WOA) is a recent nature-inspired metaheuristic that mimics the cooperative life of humpback whales and their spiral-shaped hunting mechanism. In this research, it is first argued that the exploitation tendency of WOA is limited and can be considered as one of the main drawbacks of this algorithm. In order to mitigate the problems of immature convergence and stagnation problems, the exploitative and exploratory capabilities of modified WOA in conjunction with a learning mechanism are improved. In this regard, the proposed WOA with associative learning approaches is combined with a recent variant of hill climbing local search to further enhance the exploitation process. The improved algorithm is then employed to tackle a wide range of numerical optimization problems. The results are compared with different well-known and novel techniques on multi-dimensional classic problems and new CEC 2017 test suite. The extensive experiments and statistical tests show the superiority of the proposed BMWOA compared to WOA and several well-established algorithms.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  1. 1.

    Abbassi R, Abbassi A, Heidari AA, Mirjalili S (2019) An efficient salp swarm-inspired algorithm for parameters identification of photovoltaic cell models. Energy Convers Manag 179:362–372

    Google Scholar 

  2. 2.

    Abdel-Basset M, Abdle-Fatah L, Sangaiah AK (2018) An improved lévy based whale optimization algorithm for bandwidth-efficient virtual machine placement in cloud computing environment. Cluster Comput. https://doi.org/10.1007/s10586-018-1769-z

    Article  Google Scholar 

  3. 3.

    Abdel-Basset M, El-Shahat D, El-Henawy I, Sangaiah AK (2018) A modified flower pollination algorithm for the multidimensional knapsack problem: human-centric decision making. Soft Comput 22(13):4221–4239

    Google Scholar 

  4. 4.

    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. Mobile Netw Appl 23(4):1–11

    Google Scholar 

  5. 5.

    Abdel-Basset M, Hessin AN, Abdel-Fatah L (2018) A comprehensive study of cuckoo-inspired algorithms. Neural Comput Appl 29(2):345–361

    Google Scholar 

  6. 6.

    Abdel-Basset M, Manogaran G, Abdel-Fatah L, Mirjalili S (2018) An improved nature inspired meta-heuristic algorithm for 1-d bin packing problems. Pers Ubiquitous Comput 22(5):1–16

    Google Scholar 

  7. 7.

    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. Future Gener Comput Syst 85:129–145

    Google Scholar 

  8. 8.

    Abdel-Basset M, Manogaran G, El-Shahat D, Mirjalili S (2018) Integrating the whale algorithm with tabu search for quadratic assignment problem: a new approach for locating hospital departments. Appl Soft Comput 73:530–546

    Google Scholar 

  9. 9.

    Al-Betar MA (2016) Beta-hill climbing: an exploratory local search. Neural Comput Appl 28(1):1–16

    Google Scholar 

  10. 10.

    Aljarah I, Faris H, Mirjalili S (2016) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22(1):1–15

    Google Scholar 

  11. 11.

    Aljarah I, Mafarja M, Heidari AA, Faris H, Zhang Y, Mirjalili S (2018) Asynchronous accelerating multi-leader salp chains for feature selection. Appl Soft Comput 71:964–979

    Google Scholar 

  12. 12.

    Awad NH, Ali MZ, Suganthan PN, Reynolds RG (2017) Cade: a hybridization of cultural algorithm and differential evolution for numerical optimization. Inf Sci 378:215–241

    Google Scholar 

  13. 13.

    Chen J, Xin B, Peng Z, Dou L, Zhang J (2009) Optimal contraction theorem for exploration-exploitation tradeoff in search and optimization. IEEE Trans Syst Man Cybern Part A Syst Hum 39(3):680–691

    Google Scholar 

  14. 14.

    Chen J, Zheng J, Wu P, Zhang L, Wu Q (2017) Dynamic particle swarm optimizer with escaping prey for solving constrained non-convex and piecewise optimization problems. Expert Syst Appl 86:208–223

    Google Scholar 

  15. 15.

    Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1(1):3–18

    Google Scholar 

  16. 16.

    El-Abd M, Kamel M (2005) A taxonomy of cooperative search algorithms. Hybrid Metaheuristics 3636:32–41

    Google Scholar 

  17. 17.

    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 

  18. 18.

    Eriksen N, Miller LA, Tougaard J, Helweg DA (2005) Cultural change in the songs of humpback whales (megaptera novaeangliae) from tonga. Behaviour 142(3):305–328

    Google Scholar 

  19. 19.

    Faris H, Al-Zoubi AM, Heidari AA, Aljarah I, Mafarja M, Hassonah MA, Fujita H (2019) An intelligent system for spam detection and identification of the most relevant features based on evolutionary random weight networks. Inf Fusion 48:67–83. https://doi.org/10.1016/j.inffus.2018.08.002

    Article  Google Scholar 

  20. 20.

    Faris H, Mafarja MM, Heidari AA, Aljarah I, Ala’M AZ, Mirjalili S, Fujita H (2018) An efficient binary salp swarm algorithm with crossover scheme for feature selection problems. Knowl Based Syst 154:43–67

    Google Scholar 

  21. 21.

    Gandomi AH, Yang XS, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23):2325–2336

    Google Scholar 

  22. 22.

    Gao Y, Du W, Yan G (2015) Selectively-informed particle swarm optimization. Sci Rep 5:9295

    Google Scholar 

  23. 23.

    Greiner R (1996) Palo: a probabilistic hill-climbing algorithm. Artif Intell 84(1–2):177–208

    MathSciNet  Google Scholar 

  24. 24.

    Heidari AA, Abbaspour RA, Jordehi AR (2017) An efficient chaotic water cycle algorithm for optimization tasks. Neural Comput Appl 28(1):57–85

    Google Scholar 

  25. 25.

    Heidari AA, Abbaspour RA, Jordehi AR (2017) Gaussian bare-bones water cycle algorithm for optimal reactive power dispatch in electrical power systems. Appl Soft Comput 57:657–671

    Google Scholar 

  26. 26.

    Heidari AA, Faris H, Aljarah I, Mirjalili S (2018) An efficient hybrid multilayer perceptron neural network with grasshopper optimization. Soft Comput. https://doi.org/10.1007/s00500-018-3424-2

  27. 27.

    Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with lévy flight for optimization tasks. Appl Soft Comput 60:115–134

    Google Scholar 

  28. 28.

    Jordehi AR (2015) Enhanced leader PSO (ELPSO): a new PSO variant for solving global optimisation problems. Appl Soft Comput 26:401–417

    Google Scholar 

  29. 29.

    Jordehi AR (2015) A review on constraint handling strategies in particle swarm optimisation. Neural Comput Appl 26(6):1265–1275

    Google Scholar 

  30. 30.

    Jordehi AR (2016) Time varying acceleration coefficients particle swarm optimisation (TVACPSO): a new optimisation algorithm for estimating parameters of PV cells and modules. Energy Convers Manag 129:262–274

    Google Scholar 

  31. 31.

    Jordehi AR (2018) Enhanced leader particle swarm optimisation (ELPSO): an efficient algorithm for parameter estimation of photovoltaic (PV) cells and modules. Solar Energy 159:78–87

    Google Scholar 

  32. 32.

    LaTorre A, Peña JM (2017) A comparison of three large-scale global optimizers on the CEC 2017 single objective real parameter numerical optimization benchmark. In: 2017 IEEE congress on evolutionary computation (CEC). IEEE, pp 1063–1070

  33. 33.

    Li R, Hu S, Wang Y, Yin M (2017) A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem. Neural Comput Appl 28(7):1775–1785

    Google Scholar 

  34. 34.

    Lin SW, Lee ZJ, Ying KC, Lee CY (2009) Applying hybrid meta-heuristics for capacitated vehicle routing problem. Expert Syst Appl 36(2):1505–1512

    Google Scholar 

  35. 35.

    Mafarja M, Aljarah I, Heidari AA, Faris H, Fournier-Viger P, Li X, Mirjalili S (2018) Binary dragonfly optimization for feature selection using time-varying transfer functions. Knowl Based Syst 161:185–204. https://doi.org/10.1016/j.knosys.2018.08.003

    Article  Google Scholar 

  36. 36.

    Mafarja M, Aljarah I, Heidari AA, Hammouri AI, Faris H, Ala’M AZ, Mirjalili S (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 

  37. 37.

    Mafarja MM, Mirjalili S (2017) Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing 260:302–312

    Google Scholar 

  38. 38.

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

    Google Scholar 

  39. 39.

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

    Google Scholar 

  40. 40.

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

    Google Scholar 

  41. 41.

    Mohamed AAA, Mohamed YS, El-Gaafary AA, Hemeida AM (2017) Optimal power flow using moth swarm algorithm. Electr Power Syst Res 142:190–206

    Google Scholar 

  42. 42.

    Oliva D, El Aziz MA, Hassanien AE (2017) Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm. Appl Energy 200:141–154

    Google Scholar 

  43. 43.

    Parks SE, Cusano DA, Stimpert AK, Weinrich MT, Friedlaender AS, Wiley DN (2014) Evidence for acoustic communication among bottom foraging humpback whales. Sci Rep 4:7508

    Google Scholar 

  44. 44.

    Ramp C, Hagen W, Palsbøll P, Bérubé M, Sears R (2010) Age-related multi-year associations in female humpback whales (megaptera novaeangliae). Behav Ecol Sociobiol 64(10):1563–1576

    Google Scholar 

  45. 45.

    Reddy VV, Manohar TG et al (2017) Optimal renewable resources placement in distribution networks by combined power loss index and whale optimization algorithms. J Electr Syst Inf Technol 28:669–678

    Google Scholar 

  46. 46.

    Rendell L, Whitehead H (2001) Culture in whales and dolphins. Behav Brain Sci 24(2):309–324

    Google Scholar 

  47. 47.

    Simon D (2008) Biogeography-based optimization. IEEE Trans Evolut Comput 12(6):702–713

    Google Scholar 

  48. 48.

    Tharwat A, Moemen YS, Hassanien AE (2017) Classification of toxicity effects of biotransformed hepatic drugs using whale optimized support vector machines. J Biomed Inform 68:132–149

    Google Scholar 

  49. 49.

    Tsamardinos I, Brown LE, Aliferis CF (2006) The max–min hill-climbing bayesian network structure learning algorithm. Mach Learn 65(1):31–78

    Google Scholar 

  50. 50.

    Wang L, Zeng Y, Chen T (2015) Back propagation neural network with adaptive differential evolution algorithm for time series forecasting. Expert Syst Appl 42(2):855–863

    Google Scholar 

  51. 51.

    Yang XS, Hossein Gandomi A (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483

    Google Scholar 

  52. 52.

    Yang XS, Karamanoglu M, He X (2014) Flower pollination algorithm: a novel approach for multiobjective optimization. Eng Optim 46(9):1222–1237

    MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ali Asghar Heidari.

Ethics declarations

Ethical standard

This article does not contain any studies with human participants or animals performed by any of the authors.

Conflict of interest

There is no conflict of interest to declare.

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

Verify currency and authenticity via CrossMark

Cite this article

Heidari, A.A., Aljarah, I., Faris, H. et al. An enhanced associative learning-based exploratory whale optimizer for global optimization. Neural Comput & Applic 32, 5185–5211 (2020). https://doi.org/10.1007/s00521-019-04015-0

Download citation

Keywords

  • Nature-inspired computing
  • Metaheuristic
  • Optimization
  • Swarm intelligence