Hybrid Nature-Inspired Algorithm for Symbol Regression Problem

  • Boris K. Lebedev
  • Oleg B. LebedevEmail author
  • Elena M. Lebedeva
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 464)


The problem of symbolic regression is to find mathematical expressions in symbolic form, approximating the relationship between the finite set of values of the independent variables and the corresponding values of the dependent variables. The criterion of quality approach is a mean square error: the sum of the squares of the difference between the model and the values of the dependent variable for all values of the independent variable as an argument. The paper offers a hybrid algorithm for solving symbolic regression. The traditional idea of an algebraic formula in syntax tree form is used. Leaf nodes correspond to variables or numeric constants rather than leaf nodes contain the operation that is performed on the child nodes. A distinctive feature of the process tree representation as a linear recording is preclude loss plurality of terminal elements, but the model can be an arbitrary function of the superposition of a set.


Symbolic regression Syntax tree Terminal set Functional set Ant colony Genetic search Hybrid algorithm 



This research is supported by grant of the Russian Science Foundation (project # 14-11-00242) in the Southern Federal University.


  1. 1.
    Witten, I.H., Frank, E., Mark A.: Hall Data Mining: Practical Machine Learning Tools and Techniques, 3rd edn. Morgan Kaufmann (2011)Google Scholar
  2. 2.
    Sammut, C., Webb, G.I.: Symbolic Regression, Encyclopedia of Machine Learning. Springer, Berlin (2010)CrossRefzbMATHGoogle Scholar
  3. 3.
    Barsegyan, A.A., Kupriyanov, M.S., Stepanenko, V.V., Kholod, I.I.: Metody i modeli analiza dannykh: OLAP i Data Mining [Methods and Models of Data Analysis: OLAP and Data Mining]. BKhV-Peterburg, St. Peterburg, p. 336 (2004)Google Scholar
  4. 4.
    Radchenko, S.G.: Metodologiya regressionnogo analiza: Monografiya [Methodology Regression Analysis: Monograph], p. 376. K.: Korniychuk (2011)Google Scholar
  5. 5.
    Lebedev B.K., Lebedev V.B.: Evolyutsionnaya protsedura obucheniya pri raspoznavanii obrazov [Evolutionary procedure learning in pattern recognition]. Izvestiya TRTU [Izv. TSURe] 8(43), 83–88 (2004)Google Scholar
  6. 6.
    Rudoy, G.I., Strizhov, V.V.: Algoritmy induktivnogo porozhdeniya superpozitsiy dlya approksimatsii izmeryaemykh dannykh [Algorithms for inductive generation of superpositions for approximation of the measured data]. Informatika i ee primeneniya [Inf. Appl.] 7(1), 44–53 (2013)Google Scholar
  7. 7.
    Bukhtoyarov, V.V., Semenkin, E.S.: Razrabotka i issledovanie gibridnogo metoda geneticheskogo programmirovaniya [Research and development of hybrid method of genetic programming]. Programmnye produkty i sistemy [Softw. Prod. Syst.] 3, 34–38 (2010)Google Scholar
  8. 8.
    Kureichik, V.M., Lebedev, B.K., Lebedev, V.B.: VLSI floorplanning based on the integration of adaptive search models. Int. J. Comput. Syst. Sci. 52(1), 80–96 (2013). ISSN: 1064_2307Google Scholar
  9. 9.
    Koza, J.R.: Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Springer (2005)Google Scholar
  10. 10.
    Barmpalexis, P., Kachrimanis, K., Tsakonas, A., Georgarakis, E.: Symbolic regression via genetic programming in the optimization of a controlled release pharmaceutical formulation. Chemometr. Intell. Lab. Syst. 107(1), 75–82 (2011)CrossRefGoogle Scholar
  11. 11.
    Johnson, C.G.: Artificial immune systems programming for symbolic regression. In: 6th European Conference on Genetic Programming, pp. 345–353 (2003). ISBN: 3-540-00971-XGoogle Scholar
  12. 12.
    Lebedev, O.B.: Modeli adaptivnogo povedeniya murav’inoy kolonii v zadachakh proektirovaniya [Models of Adaptive Behavior, Ant Colony in the Task of Designing], p. 199. Izd-vo YuFU, Taganrog (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Boris K. Lebedev
    • 1
  • Oleg B. Lebedev
    • 1
    Email author
  • Elena M. Lebedeva
    • 1
  1. 1.Southern Federal UniversityRostov-on-DonRussia

Personalised recommendations