Skip to main content

An adaptive human learning optimization with enhanced exploration–exploitation balance


Human Learning Optimization (HLO) is a simple yet efficient binary meta-heuristic, in which three learning operators, i.e. the random learning operator (RLO), individual learning operator (ILO) and social learning operator (SLO), are developed to mimic human learning mechanisms to solve optimization problems. Among these three operators, RLO directly influences the exploration and exploitation abilities of HLO, and therefore its control parameter pr is of great importance since it controls the balance between exploration and exploitation. In this paper, an adaptive human learning optimization with enhanced exploration-exploitation balance (AHLOee) is proposed to improve the performance of HLO, in which a new adaptive pr strategy is carefully designed to meet the different requirements of HLO at different stages of iterations. A comprehensive parameter study is performed to evaluate the influences of the proposed adaptive strategy on exploration and exploitation, and then the deep insights on the role of RLO and the reason why the proposed adaptive strategy can achieve a practically ideal trade-off between exploration and exploitation are provided. The experimental results on the CEC05 and CEC15 benchmarks demonstrate that the proposed AHLOee has advantages over previous HLO variants and outperforms recent state-of-art binary meta-heuristics.

This is a preview of subscription content, access via your institution.


  1. Kar, A.K.: Bio inspired computing – A review of algorithms and scope of applications. Expert Sys. Appl. 59, 20–32 (2016)

    Article  Google Scholar 

  2. Zhang, Q., Guan, X., Pardalos, P.M.: Maximum shortest path interdiction problem by upgrading edges on trees under weighted l1 norm. J. Global Opti. 79(2), 1–29 (2020)

    Google Scholar 

  3. Zhang, Y., Jin, Z.: Group teaching optimization algorithm: a novel metaheuristic method for solving global optimization problems. Expert Syst. Appl. 148, 113246 (2020)

    Article  Google Scholar 

  4. Hu, J., Gui, W., Heidari, A.A., Cai, Z., Liang, G., Chen, H., Pan, Z.: Dispersed foraging slime mould algorithm: continuous and binary variants for global optimization and wrapper-based feature selection. Knowl.-Based Syst. 237, 107761 (2022)

    Article  Google Scholar 

  5. Chen, D., Wang, P., Renquan, L., Zou, F.: Learning backtracking search optimisation algorithm and its application. Inf. Sci. Intern. J. 376, 71–94 (2017)

    Google Scholar 

  6. Maier, H.R., Razavi, S., Kapelan, Z., Matott, L.S., Kasprzyk, J., Tolson, B.A.: Introductory overview: Optimization using evolutionary algorithms and other metaheuristics. Environ. Modell. Softw. 114(APR), 195–213 (2019)

    Article  Google Scholar 

  7. Peng, J., Li, Y., Kang, H., Shen, Y., Sun, X., Chen, Q.: Impact of population topology on particle swarm optimization and its variants: An information propagation perspective. Swarm. Evolution. Comput. 69, 100990 (2022)

    Article  Google Scholar 

  8. Stodola, P., Otřísal, P., Hasilová, K.: Adaptive ant Colony optimization with node clustering applied to the travelling salesman problem. Swarm. Evolution. Comput. 70, 101056 (2022)

    Article  Google Scholar 

  9. Tang, C., Song, S., Ji, J., Tang, Y., Tang, Z., Todo, Y.: A cuckoo search algorithm with scale-free population topology. Expert Syst. Appl. 188, 116049 (2022)

    Article  Google Scholar 

  10. Chen, M.-R., Huang, Y.-Y., Zeng, G.-Q., Lu, K.-D., Yang, L.-Q.: An improved bat algorithm hybridized with extremal optimization and Boltzmann selection. Expert Syst. Appl. 175, 114812 (2021)

    Article  Google Scholar 

  11. Durgut, R., Aydin, M.E.: Adaptive binary artificial bee colony algorithm. Appl. Soft Comput. 101, 107054 (2021)

    Article  Google Scholar 

  12. Zhu, Q., Tang, X., Li, Y., Yeboah, M.O.: An improved differential-based harmony search algorithm with linear dynamic domain. Knowl. Based Sys. 187(Jan.), 104809. 14 (2020)

    Google Scholar 

  13. Xue, Y., Zhang, Q., Zhao, Y.: An improved brain storm optimization algorithm with new solution generation strategies for classification. Eng. Appl. Artif. Intell. 110, 104677 (2022)

    Article  Google Scholar 

  14. Sathya, P.D., Kalyani, R., Sakthivel, V.P.: Color image segmentation using Kapur, Otsu and minimum cross entropy functions based on exchange market algorithm. Expert Syst. Appl. 172, 114636 (2021)

    Article  Google Scholar 

  15. H. Kashan, and Ali, “League Championship Algorithm (LCA): An algorithm for global optimization inspired by sport championships,” Appl. Soft Comput., vol. 16, pp. 171–200, 2014

  16. Wang, L., Ni, H., Yang, R., Fei, M., Ye, W.: A simple human learning optimization algorithm. In Computational Intelligence, Networked Systems and Their Applications Springer, Berlin, Heidelberg. pp. 56–65 (2014)

  17. Wang, L., Ni, H., Yang, R., Pardalos, P.M., Du, X., Fei, M.: An adaptive simplified human learning optimization algorithm. Inf. Sci. 320, 126–139 (2015)

    MathSciNet  Article  Google Scholar 

  18. Sadeghian, Z., Akbari, E., Nematzadeh, H.: A hybrid feature selection method based on information theory and binary butterfly optimization algorithm. Eng. Appl. Artif. Intell. 97, 104079 (2021)

    Article  Google Scholar 

  19. Xiang, W.L., Li, Y.Z., He, R.C., An, M.Q.: Artificial bee colony algorithm with a pure crossover operation for binary optimization. Comput. Ind. Eng. 152, 107011 (2020)

    Article  Google Scholar 

  20. Wang, L., An, L., Ni, H.Q., Wei, Y., Fei, M.R.: Pareto-based multi-objective node placement of industrial wireless sensor networks using binary differential evolution harmony search. Adv. Manufact. 4(1), 66–78 (2016)

    Article  Google Scholar 

  21. Gupta, D., Arora, J., Agrawal, U., Khanna, A., de Albuquerque, V.H.C.: Optimized binary bat algorithm for classification of white blood cells. Measurement. 143, 180–190 (2019)

    Article  Google Scholar 

  22. Ba, E., Lker, E.: A binary social spider algorithm for continuous optimization task. Soft. Comput. 24(17), 12953–12979 (2020)

    Article  Google Scholar 

  23. Yang, R., Xu, M., He, J., Ranshous, S., Samatova, N. F.: “An intelligent weighted fuzzy time series model based on a sine-cosine adaptive human learning optimization algorithm and its application to financial markets forecasting,” Int. Conf. Adv. Data Min. Appl. 595–607 (2017)

  24. Wang, L., An, L., Pi, J., Fei, M., Pardalos, P.M.: A diverse human learning optimization algorithm. J. Glob. Optim. 67(1–2), 1–41 (2017)

    MathSciNet  MATH  Google Scholar 

  25. Wang, L., Pei, J., Menhas, M.I., Pi, J., Fei, M., Pardalos, P.M.: A hybrid-coded human learning optimization for mixed-variable optimization problems. Knowl.-Based Syst. 127, 114–125 (2017)

    Article  Google Scholar 

  26. Li, X., Yao, J., Wang, L., Menhas, M. I.: “Application of human learning optimization algorithm for production scheduling optimization.” In Advanced Computational Methods in Life System Modeling and Simulation. Springer, Singapore. pp. 242–252 (2017)

  27. Alguliyev, R., Aliguliyev, R., Isazade, N.: A sentence selection model and HLO algorithm for extractive text summarization. In 2016 IEEE 10th International Conference on Application of Information and Communication Technologies (AICT) IEEE. pp. 1–4 (2017)

  28. Cao, J., Yan, Z., He, G.: Application of multi-objective human learning optimization method to solve AC/DC multi-objective optimal power flow problem. Int. J. Emerg. Electric Power Sys. 17(3), 327–337 (2016)

  29. Cao, J., Yan, Z., Xu, X., He, G., Huang, S.: Optimal power flow calculation in AC/DC hybrid power system based on adaptive simplified human learning optimization algorithm. J. Modern Power Sys. Clean Energy. 4(4), 690–701 (2016)

    Article  Google Scholar 

  30. Wang, L., Yang, R., Ni, H., Ye, W., Fei, M., Pardalos, P. M.: A human learning optimization algorithm and its application to multi-dimensional knapsack problems. Appl. Soft Comput. 34, 736–743 (2015)

  31. Iacca, G., Caraffini, F., Neri, F.: MULTI-STRATEGY COEVOLVING AGING PARTICLE OPTIMIZATION. Int. J. Neural Syst. 24(01), 709–110 (2014)

    Article  Google Scholar 

  32. Molleman, L., Van den Berg, P., Weissing, F.J.: Consistent individual differences in human social learning strategies. Nat. Commun. 5(1), 1–9 (2014)

    Article  Google Scholar 

  33. Kendal, R.L., Boogert, N.J., Rendell, L., Laland, K.N., Webster, M., Jones, P.L.: Social learning strategies: bridge-building between fields. Trends Cogn. Sci. 22(7), 651–665 (2018)

    Article  Google Scholar 

  34. Zendehrouh, S., Ahmadabadi, M.N.: Individually irrational pruning is essential for ecological rationality in a social context. Cogn. Psychol. 118, 101272 (2020)

    Article  Google Scholar 

  35. Lewis, H.M., Laland, K.N.: Transmission fidelity is the key to the build-up of cumulative culture. Philos. Trans. R. Soc., B. 367(1599), 2171–2180 (2012)

    Article  Google Scholar 

  36. Mesoudi, A.: An experimental comparison of human social learning strategies: payoff-biased social learning is adaptive but underused. Evol. Hum. Behav. 32(5), 334–342 (2011)

    Article  Google Scholar 

  37. Ling, W., Ji, P., Wen, Y., Pi, J., Fei, M., Pardalos, P.M.: An Improved Adaptive Human Learning Algorithm for Engineering Optimization. Appl. Soft Comput. 71, S1568494618304393 (2018)

    Google Scholar 

  38. Karna, S.K., Sahai, R.: An overview on Taguchi method. Int. J. Math. Eng. Manage. Sci. 1, 1–7 (2012)

    Google Scholar 

  39. Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Tiwari, S.: Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization. Nat. Comput. 341, 357 (2005)

    Google Scholar 

  40. Kennedy, J., Eberhart, R. C.: A discrete binary version of the particle swarm algorithm. In 1997 IEEE International conference on systems, man, and cybernetics. Computational Cybern. Simulation. IEEE. 5, 4104–4108 (1997)

  41. Jordehi, A.R.: Binary particle swarm optimisation with quadratic transfer function: A new binary optimisation algorithm for optimal scheduling of appliances in smart homes. Appl. Soft Comput. 78, 465–480 (2019)

  42. Reddy K.S., Panwar, L., Panigrahi, B.K., Kumar, R.: Binary whale optimization algorithm: a new metaheuristic approach for profit-based unit commitment problems in competitive electricity markets. Eng. Optim. 51(3), 369–389 (2019)

  43. Ji, B., Lu, X., Sun, G., Zhang, W., Xiao, Y.: Bio-inspired feature selection: an improved binary particle swarm optimization approach. IEEE Access. PP(99), 1–1 (2020)

    Google Scholar 

  44. Ali, I.M., Essam, D., Kasmarik, K.: Novel binary differential evolution algorithm for knapsack problems. Inf. Sci. 542, 177–194 (2021)

    MathSciNet  Article  Google Scholar 

  45. Chen, Q., Liu, B., Zhang, Q., Liang, J., Suganthan, P., Qu, B.: Problem definitions and evaluation criteria for CEC 2015 special session on bound constrained single-objective computationally expensive numerical optimization. Technical Report, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Technical Report, Nanyang Technological University. (2014)

Download references


This work is supported by National Key Research and Development Program of China (No. 2019YFB1405500), National Natural Science Foundation of China (Grant No. 92067105 & 61833011), Key Project of Science and Technology Commission of Shanghai Municipality under Grant No. 19510750300 & 19500712300, and 111 Project under Grant No. D18003. The work of P.M. Pardalos was conducted within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Ling Wang.

Ethics declarations

Competing interests

The authors declare that they have no know competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher’s Note

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

Supplementary Information


(DOCX 91 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Du, J., Wen, Y., Wang, L. et al. An adaptive human learning optimization with enhanced exploration–exploitation balance. Ann Math Artif Intell (2022).

Download citation

  • Published:

  • DOI:


  • Human learning optimization
  • Adaptive HLO
  • Random learning
  • Social learning
  • Meta-heuristic