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A New Method for Simplifying Algebraic Expressions in Genetic Programming Called Equivalent Decision Simplification

  • Mori Naoki
  • Bob McKay
  • Nguyen Xuan
  • Essam Daryl
  • Saori Takeuchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5518)

Abstract

Symbolic Regression is one of the most important applications of Genetic Programming, but these applications suffer from one of the key issues in Genetic Programming, namely bloat – the uncontrolled growth of ineffective code segments, which do not contribute to the value of the function evolved, but complicate the evolutionary proces, and at minimum greatly increase the cost of evaluation. For a variety of reasons, reliable techniques to remove bloat are highly desirable – to simplify the solutions generated at the end of runs, so that there is some chance of understanding them, to permit systematic study of the evolution of the effective core of the genotype, or even to perform simplification of expressions during the course of a run.

This paper introduces an alternative approach, Equivalent Decision Simplification, in which subtrees are evaluated over the set of regression points; if the subtrees evaluate to the same values as known simple subtrees, they are replaced. The effectiveness of the proposed method is confirmed by computer simulation taking simple Symbolic Regression problems as examples.

Keywords

Genetic Program Algebraic Expression Symbolic Regression Neutral Part Redundant Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.D.: Genetic Programming – An Introduction; On the Automatic Evolution of Computer Programs and its Applications. Morgan Kaufmann, San Francisco (1998)zbMATHGoogle Scholar
  2. 2.
    Hoai, N.X.: Solving trignometric identities with tree adjunct grammar guided genetic programming. In: Abraham, A., Koppen, M. (eds.) 2001 International Workshop on Hybrid Intelligent Systems, Adelaide, Australia, December 11-12. LNCS, pp. 339–352. Springer, Heidelberg (2001)Google Scholar
  3. 3.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  4. 4.
    Koza, J.R., Keane, M.A., Streeter, M.J., Mydlowec, W., Yu, J., Lanza, G.: Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Kluwer Academic Publishers, Dordrecht (2003)zbMATHGoogle Scholar
  5. 5.
    Solomonoff, R.: A theory of inductive inference. Information and Control 7, 1–22, 224–254 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Soule, T.: Code Growth in Genetic Programming. PhD thesis, University of Idaho, Moscow, Idaho, USA, May 15 (1998)Google Scholar
  7. 7.
    Soule, T., Foster, J.A.: Support for multiple causes of code growth in GP. Position paper at the Workshop on Evolutionary Computation with Variable Size Representation at ICGA 1997, July 20 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mori Naoki
    • 1
  • Bob McKay
    • 2
  • Nguyen Xuan
    • 2
  • Essam Daryl
    • 3
  • Saori Takeuchi
    • 4
  1. 1.Osaka Prefecture UniversityOsakaJapan
  2. 2.Structural Complexity LaboratorySeoul National UniversitySeoulKorea
  3. 3.School of Information Technology and Elec. Eng.University of New South Wales ADFACanberraAustralia
  4. 4.Mitsubishi Electric CorporationTokyoJapan

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