Journal of Global Optimization

, Volume 67, Issue 1–2, pp 283–323 | Cite as

A diverse human learning optimization algorithm

  • Ling WangEmail author
  • Lu An
  • Jiaxing Pi
  • Minrui Fei
  • Panos M. Pardalos


Human Learning Optimization is a simple but efficient meta-heuristic algorithm in which three learning operators, i.e. the random learning operator, the individual learning operator, and the social learning operator, are developed to efficiently search the optimal solution by imitating the learning mechanisms of human beings. However, HLO assumes that all the individuals possess the same learning ability, which is not true in a real human population as the IQ scores of humans, one of the most important indices of the learning ability of humans, follow Gaussian distribution and increase with the development of society and technology. Inspired by this fact, this paper proposes a Diverse Human Learning Optimization algorithm (DHLO), into which the Gaussian distribution and dynamic adjusting strategy are introduced. By adopting a set of Gaussian distributed parameter values instead of a constant to diversify the learning abilities of DHLO, the robustness of the algorithm is strengthened. In addition, by cooperating with the dynamic updating operation, DHLO can adjust to better parameter values and consequently enhances the global search ability of the algorithm. Finally, DHLO is applied to tackle the CEC05 benchmark functions as well as knapsack problems, and its performance is compared with the standard HLO as well as the other eight meta-heuristics, i.e. the Binary Differential Evolution, Simplified Binary Artificial Fish Swarm Algorithm, Adaptive Binary Harmony Search, Binary Gravitational Search Algorithms, Binary Bat Algorithms, Binary Artificial Bee Colony, Bi-Velocity Discrete Particle Swarm Optimization, and Modified Binary Particle Swarm Optimization. The experimental results show that the presented DHLO outperforms the other algorithms in terms of search accuracy and scalability.


Human learning optimization Gaussian distribution Meta-heuristic Global optimization Computational experiments 



This work is supported by National Natural Science Foundation of China (Grant No. 61304031, 61374044 & 61304143), Innovation Program of Shanghai Municipal Education Commission (14YZ007), Key Project of Science and Technology Commission of Shanghai Municipality under Grant No. 14JC1402200 and 14DZ1206302, Key Project of Shanghai Municipal Commission of Economy and Informatization (ZB-ZBYZ-02-14-0825), AirForce and DTRA grants (P. Pardalos, J. Pi), and a Paul and Heidi Brown Preeminent Professorship in Industrial and Systems Engineering, University of Florida.


  1. 1.
    Kim, H., Liou, M.S.: New fitness sharing approach for multi-objective genetic algorithms. J. Global Optim. 55(3), 579–595 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)CrossRefGoogle Scholar
  3. 3.
    Kaucic, M.: A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization. J. Global Optim. 55(1), 165–188 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dorigo, M., Blum, C.: Ant colony optimization theory: a survey. Theor. Comput. Sci. 344(2), 243–278 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Wang, L., Ni, H.Q., Yang, R.X., Pappu, V., Fenn, M.B., Pardalos, P.M.: Feature selection based on meta-heuristics for biomedicine. Optim. Methods Softw. 29(4), 703–719 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Wang, L., Ni, H.Q., Zhou, W.F., Pardalos, P.M., Fang, J.T., Fei, M.R.: MBPOA-based LQR controller and its application to the double-parallel inverted pendulum system. Eng. Appl. Artif. Intell. 36, 262–268 (2014)CrossRefGoogle Scholar
  7. 7.
    Wang, L., Ye, W., Mao, Y.F., Georgiev, P.G., Wang, H.K., Fei, M.R.: The node placement of large-scale industrial wireless sensor networks based on binary differential evolution harmony search algorithm. Int. J. Innov. Comput. Inf. Control. 9(3), 955–970 (2013)Google Scholar
  8. 8.
    Rocha, A.M.A., Costa, M.F.P., Fernandes, E.M.: A filter-based artificial fish swarm algorithm for constrained global optimization: theoretical and practical issues. J. Global Optim. 60(2), 239–263 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Akay, B.: Synchronous and asynchronous Pareto-based multi-objective Artificial Bee Colony algorithms. J. Global Optim. 57(2), 415–445 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Yang, X.S.: A New Metaheuristic Bat-Inspired Algorithm. Nature Inspired Cooperative Strategies for Optimization. Springer, Berlin (2010)Google Scholar
  11. 11.
    Oftadeh, R., Mahjoob, M.J., Shariatpanahi, M.: A novel meta-heuristic optimization algorithm inspired by group hunting of animals: hunting search. Comput. Math. Appl. 60(7), 2087–2098 (2010)CrossRefzbMATHGoogle Scholar
  12. 12.
    Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)CrossRefGoogle Scholar
  13. 13.
    Pan, W.T.: A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl. Based Syst. 26, 69–74 (2012)CrossRefGoogle Scholar
  14. 14.
    Fister, I., Yang, X.S., Brest, J.: A comprehensive review of firefly algorithms. Swarm Evol. Comput. 13, 34–46 (2013)CrossRefGoogle Scholar
  15. 15.
    Elbeltagi, E., Hegazy, T., Grierson, D.: A modified shuffed frog-leaping optimization algorithm: applications to project management. Struct. Infrastruct. Eng. 3(1), 53–60 (2007)CrossRefGoogle Scholar
  16. 16.
    Yang, X.S.: Cuckoo Search and Firefly Algorithm. Springer, Berlin (2014)CrossRefzbMATHGoogle Scholar
  17. 17.
    Wang, L., Ni, H.Q., Yang, R.X., Fei, M.R., Ye, W.: A simple human learning optimization algorithm. Commun. Comput. Inf. Sci. 462, 56–65 (2014)Google Scholar
  18. 18.
    Herrnstein, R.J., Murry, C.: The bell curve: intelligence and class structure in American life. The Free Press, New York (1994)Google Scholar
  19. 19.
    Flynn, J.R.: Are We Getting Smarter? Rising IQ in the Twenty-first Century. Cambridge University Press, New York (2012)CrossRefGoogle Scholar
  20. 20.
    Flynn, J.R.: The mean IQ of Americans: massive gains 1932 to1978. Psychol. Bull. 95(1), 29 (1984)CrossRefGoogle Scholar
  21. 21.
    Cziko, G.: Without Miracles: Universal Selection Theory and the Second Darwinian Revolution. MIT Press, Cambridge (1997)Google Scholar
  22. 22.
    Forcheri, P., Molfino, M.T., Quarati, A.: ICT driven individual learning: new opportunities and perspectives. Educ. Technol. Soc. 3, 51–61 (2000)Google Scholar
  23. 23.
    Andrews, K.M., Delahaye, B.L.: Influences on knowledge processes in organizational learning: the psychosocial filter. J. Manag. Stud. 37(6), 797–810 (2002)CrossRefGoogle Scholar
  24. 24.
    Zhong, J.G.: A review of studies on the individual difference of intelligence in the IQ-normal group. Psychol. Sci. 30(2), 394–399 (2007). (in Chinese)Google Scholar
  25. 25.
    Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y., Auger, A., Tiwari, S.: Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization, KanGAL Report 2005005 (2005)Google Scholar
  26. 26.
    Chen, Y., Xie, W., Zou, X.: A binary differential evolution algorithm learning from explored solutions. Neurocomputing 149, 1038–1047 (2015)CrossRefGoogle Scholar
  27. 27.
    Azad, M.A.K., Rocha, A.M.A.C., Fernandes, E.M.G.P.: A simplified binary artificial fish swarm algorithm for 0.1 quadratic knapsack problems. J. Comput. Appl. Math. 259, 897–904 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Wang, L., Yang, R.X., Xu, Y., Niu, Q., Pardalos, P.M., Fei, M.R.: An improved adaptive binary Harmony Search algorithm. Inf. Sci. 232, 58–87 (2013)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Yuan, X., Ji, B., Zhang, S., Tian, H., Hou, Y.: A new approach for unit commitment problem via binary gravitational search algorithm. Appl. Soft Comput. 22, 249–260 (2014)CrossRefGoogle Scholar
  30. 30.
    Mirjalili, S., Mirjalili, S.M., Yang, X.S.: Binary bat algorithm. Neural Comput. Appl. 25(3–4), 1–19 (2014)Google Scholar
  31. 31.
    Chandrasekaran, K., Hemamalini, S., Simon, S.P., Padhy, N.P.: Thermal unit commitment using binary/real coded artificial bee colony algorithm. Electric Power Syst. Res. 84, 109–119 (2012)CrossRefGoogle Scholar
  32. 32.
    Shen, M., Zhan, Z.H., Chen, W.N., Gong, Y.J., Zhang, J., Li, Y.: Bi-velocity discrete particle swarm optimization and its application to multicast routing problem in communication networks. IEEE Trans. Ind. Electron. 61(12), 7141–7151 (2014)CrossRefGoogle Scholar
  33. 33.
    Bansal, J.C., Deep, K.: A modified binary particle swarm optimization for knapsack problems. Appl. Math. Comput. 218(22), 11042–11060 (2012)MathSciNetzbMATHGoogle Scholar
  34. 34.
    Liao, T., Molina, D., Stutzle, T.: Performance evaluation of automatically tuned continuous optimizers on different benchmark sets. Appl. Soft Comput. 27, 490–503 (2015)CrossRefGoogle Scholar
  35. 35.
    Zou, D., Gao, L., Li, S., Wu, J.: Solving 0–1 knapsack problem by a novel global harmony search algorithm. Appl. Soft Comput. 11(2), 1556–1564 (2011)CrossRefGoogle Scholar
  36. 36.
    Wang, L., Ni, H.Q., Yang, R.X., Pardalos, P.M., Du, X., Fei, M.R.: An adaptive simplified human learning optimization algorithm. Inf. Sci. 320, 126–139 (2015)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Gottlieb, J.: On the feasibility problem of penalty-based evolutionary algorithms for knapsack problems. Lecture Notes in Computer Science, pp. 50–59 (2001)Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Ling Wang
    • 1
    Email author
  • Lu An
    • 1
  • Jiaxing Pi
    • 2
  • Minrui Fei
    • 1
  • Panos M. Pardalos
    • 2
  1. 1.Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronics Engineering and AutomationShanghai UniversityShanghaiChina
  2. 2.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

Personalised recommendations