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General schema theory for genetic programming with subtree-swapping crossover: part I.

Riccardo Poli1, Nicholas Freitag McPhee

  • 1Department Computer Science, University of Essex, Colchester, CO4 3SQ, UK. rpoli@essex.ac.uk

Evolutionary Computation
|June 14, 2003
PubMed
Summary

This study introduces a general schema theory for genetic programming (GP) using a novel Cartesian node reference system. This system models subtree-swapping crossover points, enabling calculations for improved GP algorithms.

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Evolutionary Computation

Background:

  • Genetic programming (GP) is a machine learning technique that evolves computer programs.
  • Subtree-swapping crossover is a common genetic operator in GP.
  • A robust theoretical framework is needed to analyze GP operators like crossover.

Purpose of the Study:

  • To introduce a general schema theory for genetic programming (GP) with subtree-swapping crossover.
  • To develop a mathematical framework for analyzing crossover point selection in GP.
  • To lay the groundwork for a comprehensive schema theory in Part II.

Main Methods:

  • Development of a Cartesian node reference system to represent programs.
  • Modeling crossover point selection as a probability distribution over N(4).

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  • Calculation of useful quantities based on the proposed schema theory.

    • Main Results:

    • A general schema theory for GP with subtree-swapping crossover is presented.
    • The Cartesian node reference system provides a formal basis for GP analysis.
    • The proposed models allow for the calculation of relevant theoretical quantities.

    Conclusions:

    • Part I establishes the foundational concepts and models for a general schema theory in GP.
    • The presented theory offers a novel approach to understanding subtree-swapping crossover.
    • This work paves the way for a more complete schema theory in Part II.