Skip to main content

On the complexity of learning in classifier systems

  • Conference paper
  • First Online:
Parallel Problem Solving from Nature — PPSN III (PPSN 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 866))

Included in the following conference series:

Abstract

Genetic algorithms are employed in classifier systems in order to discover new classifiers. The paper formalises this rule discovery or learning problem for classifier systems and uses methods of computational complexity theory to analyse its inherent difficulty. It is proved that two distinct learning problems are NP-complete, i.e. not likely to be solvable efficiently. The practical relevance of these theoretical results is briefly discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.L. Balcàzar, J. Díaz, and J. Gabarró. Structural Complexity I. EATCS, Monographs on Theoretical Computer Science. Springer-Verlag, Berlin, 1st edition, 1988.

    Google Scholar 

  2. L.B. Booker, D.E. Goldberg, and J.H. Holland. Classifier Systems and Genetic Algorithms. Artificial Intelligence, 40:235–282, 1989.

    Article  Google Scholar 

  3. M.R. Garey and D.S. Johnson. Computers and Intractability. Freeman and Company, New York, 1979.

    Google Scholar 

  4. D.E. Goldberg. Genetic Algorithmis in Search, Optimizations & Machine Learning. Addison-Wesley Publishing Company, Reading, Massachusetts.

    Google Scholar 

  5. A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge University Press, Cambridge, UK, 1988.

    Google Scholar 

  6. W.E. Hart and R.K. Belew. Optimizing an Arbitrary Function is Hard for the Genetic Algorithm. In Proceedings of the fourth International Conference on Genetic Algorithms, R.K. Belew, L.B. Booker (eds.), Morgan Kaufmann Publishers, San Mateo, CA, pp. 318–323, 1991

    Google Scholar 

  7. U. Hartmann. Computational Complexity of Neural Networks and Classifier Systems. Diplomarbeit, University of Dortmund, Germany, July 1992.

    Google Scholar 

  8. U. Hartmann. Efficient Parallel Learning in Classifier Systems. In Proceedings of the International Conference on Neural Networks and Genetic Algortihms, Insbruck, R.F. Albrecht, C.R. Reeves, N.C. Steele (eds.), Springer-Verlag, Wien, pp. 515–521, 1993.

    Google Scholar 

  9. J.H. Holland. Adaptation. In R. Rosen and F.M. Snell, editors, Progress in Theoretical Biology IV, pages 263–293. Academic Press, New York, 1976.

    Google Scholar 

  10. S. Judd. Neural Network Design and the Complexity of Learning. Neural Network Modeling and Connectionism. The MIT Press, Cambridge, MA, 1990.

    Google Scholar 

  11. G.E. Liepins and L.A. Wang. Classifier System Learning Boolean Concepts. In Proceedings of the fourth International Conference on Genetic Algorithms, R.K. Belew, L.B. Booker (eds.), Morgan Kaufmann Publishers, San Mateo, CA, pp. 318–323, 1991

    Google Scholar 

  12. L. Pitt and L. Valiant. Computational Limitations on Learning from Examples. Journal of the Association of Computing Machinery, 35(4):965–984, October 1988.

    Google Scholar 

  13. H. Ros. Some Results on Boolean Concept Learning by Genetic Algorithms. In Proceedings of the third International Conference on Genetic Algorithms, J.D. Schaffer (ed.), Morgan Kaufmann Publishers, San Mateo, CA, pp. 28–33, 1989

    Google Scholar 

  14. L.G. Valiant. A Theory of the Learnable. Communications of the ACM, 27(11):1134–1142, November 1984.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Yuval Davidor Hans-Paul Schwefel Reinhard Männer

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hartmann, U. (1994). On the complexity of learning in classifier systems. In: Davidor, Y., Schwefel, HP., Männer, R. (eds) Parallel Problem Solving from Nature — PPSN III. PPSN 1994. Lecture Notes in Computer Science, vol 866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58484-6_272

Download citation

  • DOI: https://doi.org/10.1007/3-540-58484-6_272

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58484-1

  • Online ISBN: 978-3-540-49001-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics