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Related Experiment Videos

General schema theory for genetic programming with subtree-swapping crossover: Part II.

Riccardo Poli1, Nicholas Freitag McPhee

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

Evolutionary Computation
|July 24, 2003
PubMed
Summary

This study presents a general schema theory for genetic programming (GP) using subtree-swapping crossover. It provides exact formulations for schema propagation, enhancing understanding of GP evolution.

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Evolutionary Computation

Background:

  • Genetic Programming (GP) schema theory traditionally provides lower bounds on schema propagation.
  • Existing theories often lack exact formulations for the expected number of schema instances.

Purpose of the Study:

  • To introduce a general schema theory for genetic programming (GP) with subtree-swapping crossover.
  • To provide an exact formulation for the expected number of schema instances in the next generation.

Main Methods:

  • Development of a Cartesian node reference system.
  • Introduction of a variable-arity hyperschema concept.
  • Formulation of microscopic and macroscopic schema theorems.

Main Results:

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  • An exact formulation for schema propagation in GP with subtree-swapping crossover.
  • The microscopic theorem applies to various crossover operators, including Koza's.
  • The macroscopic theorem addresses crossover operators dependent on parent size and shape.

Conclusions:

  • The developed theory offers precise insights into GP schema evolution.
  • It enables specialization for specific crossover operators and derivation of general results.
  • The theory yields an exact definition of effective fitness and a size-evolution equation.