Comprehensive Learning Gene Expression Programming for Automatic Implicit Equation Discovery

  • Yongliang Chen
  • Jinghui ZhongEmail author
  • Mingkui Tan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10860)


Implicit equation is loose in form, which makes it more powerful than explicit equation for data regression. The mainstream method for automatic implicit equation discovery is based on calculating derivatives. However, this derivative-based mechanism requires high time consumption and it is difficult to solve problems with sparse data. To solve these deficiencies, this paper proposes a new mechanism named Comprehensive Learning Fitness Evaluation Mechanism (CL-FEM). The mechanism learns knowledge from disturbed information collected from several previously generated stochastic datasets, to check the validity of the equation model. Only the valid equations can be candidates of selection, which is a process to pick out the equation with the smallest output. We integrate the proposed mechanism with the simplified Self-Learning Gene Expression Programming (SL-GEP) and propose the Comprehensive Learning Gene Expression Programming (CL-GEP). The experiment results have demonstrated that CL-GEP can offer very promising performance.


Implicit equation Symbolic regression Gene expression programming (GEP) disturbed knowledge learning 



This work was supported in part by the National Natural Science Foundation of China (Grant No. 61602181), and by the Fundamental Research Funds for the Central Universities (Grant No. 2017ZD053).


  1. 1.
    Brameier, M.F., Banzhaf, W.: Linear Genetic Programming. Springer, Heidelberg (2007).
  2. 2.
    Ferreira, C.: Gene expression programming in problem solving. In: Roy, R., Köppen, M., Ovaska, S., Furuhashi, T., Hoffmann, F. (eds.) Soft Computing and Industry, pp. 635–653. Springer, Heidelberg (2002). Scholar
  3. 3.
    Koza, J.R.: Genetic Programming: on the Programming of Computers by Means of Natural Selection, vol. 1. MIT Press, Cambridge (1992)Google Scholar
  4. 4.
    Lee, Y.S., Tong, L.I.: Forecasting time series using a methodology based on autoregressive integrated moving average and genetic programming. Knowl.-Based Syst. 24(1), 66–72 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    McPhee, N.F., Poli, R., Langdon, W.B.: Field Guide to Genetic Programming. Lulu Enterprises, UK Ltd (2008)Google Scholar
  6. 6.
    Miller, J.F., Thomson, P.: Cartesian genetic programming. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 121–132. Springer, Heidelberg (2000). Scholar
  7. 7.
    O’Neil, M., Ryan, C.: Grammatical evolution. In: Grammatical Evolution, pp. 33–47. Springer, Heidelberg (2003). Scholar
  8. 8.
    Sabar, N.R., Ayob, M., Kendall, G., Qu, R.: Automatic design of a hyper-heuristic framework with gene expression programming for combinatorial optimization problems. IEEE Trans. Evol. Comput. 19(3), 309–325 (2015)CrossRefGoogle Scholar
  9. 9.
    Schmidt, M., Lipson, H.: Symbolic regression of implicit equations. In: Riolo, R., O’Reilly, U.M., McConaghy, T. (eds.) Genetic Programming Theory and Practice VII, pp. 73–85. Springer, Heidelberg (2010). Scholar
  10. 10.
    Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhong, J., Cai, W., Lees, M., Luo, L.: Automatic model construction for the behavior of human crowds. Appl. Soft Comput. 56, 368–378 (2017)CrossRefGoogle Scholar
  12. 12.
    Zhong, J., Feng, L., Ong, Y.S.: Gene expression programming: a survey. IEEE Comput. Intell. Mag. 12(3), 54–72 (2017)CrossRefGoogle Scholar
  13. 13.
    Zhong, J., Luo, L., Cai, W., Lees, M.: Automatic rule identification for agent-based crowd models through gene expression programming. In: Proceedings of the 2014 International Conference on Autonomous Agents and Multi-agent Systems, pp. 1125–1132. International Foundation for Autonomous Agents and Multiagent Systems (2014)Google Scholar
  14. 14.
    Zhong, J., Ong, Y.S., Cai, W.: Self-learning gene expression programming. IEEE Trans. Evol. Comput. 20(1), 65–80 (2016)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer Science and EngineeringSouth China University of TechnologyGuangzhouChina
  2. 2.School of Software EngineeringSouth China University of TechnologyGuangzhouChina

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