2D Discontinuous Function Approximation with Real-Valued Grammar-Based Classifier System

  • Lukasz Cielecki
  • Olgierd Unold
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)


Learning classifier systems (LCSs) are rule-based, evolutionary learning systems. Recently, there is a growing interest among the researchers in exploring LCSs implemented in a real-valued environment, due to its practical applications. This paper describes the use of a real-valued Grammar-based Classifier System (rGCS) in a task of 2D function approximation. rGCS is based on Grammar-based Classifier System (GCS), which was originally used to process context free grammar sentences. In this paper, we propose an extension to rGCS, called Simple Accept Radius (SAR) mechanism, that filters invalid and unexpected input real values. Performance evaluations show that the additional Simple Accept Radius mechanism enables rGCS to accurately approximate 2D discontinuous function. Performance comparisons with another real-valued LCS show that rGCS yields competitive performance.


Learning classifier systems Grammatical inference Context-free grammar GCS 2D function estimation 


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  1. 1.
    Butz, M.: Kernel-based, Ellipsoidal Conditions in the Real-valued XCS Classifier System. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 1835–1842. ACM (2005)Google Scholar
  2. 2.
    Cielecki, L., Unold, O.: Real-valued GCS Classifier System. International Journal of Applied Mathematics and Computer Science 17(4), 539–547 (2007)CrossRefGoogle Scholar
  3. 3.
    Cielecki, L., Unold, O.: Modified Himmelblau Function Classification with RGCS System. In: Proc. of 8th International Conference on Hybrid Intelligent Systems, HIS 2008, pp. 879–884. IEEE (2008)Google Scholar
  4. 4.
    Gold, E.: Language Identification in the Limit. Information and Control 10(5), 447–474 (1967)zbMATHCrossRefGoogle Scholar
  5. 5.
    Holland, J.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. U. Michigan Press (1975)Google Scholar
  6. 6.
    Holland, J.: Adaptation. In: Rosen, R., Snell, F. (eds.) Progress in Theoretical Biology. Academic Press (1976)Google Scholar
  7. 7.
    Unold, O.: Context-free Grammar Induction with Grammar-based Classifier System. Archives of Control Science 15(4), 681–690 (2005)zbMATHGoogle Scholar
  8. 8.
    Unold, O., Cielecki, L.: Grammar-based Classifier System. In: Issues in Intelligent Systems: Paradigms, pp. 273–286 (2005)Google Scholar
  9. 9.
    Unold, O., Cielecki, L.: How to use Crowding Selection in Grammar-based Classifier System. In: Proceedings of 5th International Conference on Intelligent Systems Design and Applications, ISDA 2005, pp. 124–129. IEEE (2005)Google Scholar
  10. 10.
    Unold, O.: Playing a Toy-Grammar with GCS. In: Mira, J., Álvarez, J.R. (eds.) IWINAC 2005, Part II. LNCS, vol. 3562, pp. 300–309. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Wilson, S.W.: Get Real! XCS with Continuous-Valued Inputs. In: Lanzi, P.L., Stolzmann, W., Wilson, S.W. (eds.) IWLCS 1999. LNCS (LNAI), vol. 1813, pp. 209–219. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Younger, D.: Recognition and Parsing of Context-free Languages in Time n3. Information and Control 10(2), 189–208 (1967)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lukasz Cielecki
    • 1
  • Olgierd Unold
    • 1
  1. 1.Institute of Computer Engineering, Control and RoboticsWroclaw University of TechnologyWroclawPoland

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