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

  • Authors:

  • Mori Naoki;Bob Mckay;Nguyen Xuan;Essam Daryl;Saori Takeuchi

  • Affiliations:

  • Osaka Prefecture University, Osaka, Japan;Structural Complexity Laboratory, Seoul National University, Seoul, Korea;Structural Complexity Laboratory, Seoul National University, Seoul, Korea;School of Information Technology and Elec. Eng., University of New South Wales ADFA, Canberra, Australia;Mitsubishi Electric Corporation, Tokyo, Japan

  • Venue:
  • IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part II: Distributed Computing, Artificial Intelligence, Bioinformatics, Soft Computing, and Ambient Assisted Living
  • Year:
  • 2009

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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.