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Related Experiment Videos

Group properties of crossover and mutation.

Jonathan E Rowe1, Michael D Vose, Alden H Wright

  • 1School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK. J.E.Rowe@cs.bham.ac.uk

Evolutionary Computation
|August 16, 2002
PubMed
Summary

This study explores symmetries in genetic algorithms, showing how crossover and mutation operators can be represented using matrices. This leads to a generalized understanding of schemas and potential group structures within search spaces.

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Area of Science:

  • Evolutionary Computation
  • Group Theory
  • Combinatorial Optimization

Background:

  • Genetic algorithms operate on finite search spaces.
  • Symmetries within these search spaces can be mathematically described using permutation groups.
  • Standard genetic operators like crossover and mutation may preserve these symmetries.

Purpose of the Study:

  • To mathematically model genetic algorithm operators respecting search space symmetries.
  • To generalize the concept of schemas under symmetry-preserving operators.
  • To explore induced group structures on search spaces.

Main Methods:

  • Representing search space symmetries using permutation groups.
  • Describing crossover and mutation operators via mixing and permutation matrices.

Related Experiment Videos

  • Investigating invariant subsets of the search space under crossover.
  • Analyzing conditions for induced group structures.

    • Main Results:

    • Symmetry-respecting crossover and mutation can be precisely defined using matrix representations.
    • A generalized definition of schemas is derived based on symmetry invariance.
    • The possibility of inducing group structures on the search space itself is demonstrated.

    Conclusions:

    • Understanding symmetries enhances the theoretical framework of genetic algorithms.
    • The generalized schema concept offers new analytical tools.
    • The study reveals deeper algebraic structures within evolutionary computation.