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Structural search spaces and genetic operators.

Jonathan E Rowe1, Michael D Vose, Alden H Wright

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

Evolutionary Computation
|March 17, 2005
PubMed
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This study generalizes genetic algorithms for search spaces with group actions, introducing structural crossover operators and a generalized schema theorem. It explores group structures and their impact on genetic operators and transforms.

Area of Science:

  • Computational intelligence
  • Theoretical computer science
  • Group theory

Background:

  • Previous work generalized genetic algorithm theory to search spaces with arbitrary group actions, defining generalized schemata.
  • This study builds upon that foundation by examining more detailed group structures within search spaces.

Purpose of the Study:

  • To define structural crossover operators that respect schemata within detailed group structures.
  • To generalize the schema theorem for these structural operators.
  • To extend Fourier transform results to these group actions and investigate the implications for genetic algorithms.

Main Methods:

  • Analysis of group actions on search spaces.
  • Definition and examination of structural crossover operators.

Related Experiment Videos

  • Generalization of the schema theorem.
  • Application and extension of Fourier (Walsh) transform techniques to matrix groups representing search spaces.

    • Main Results:

    • A class of structural crossover operators respecting schemata in detailed group structures is defined.
    • A generalized schema theorem is derived.
    • Fourier transform results are generalized, showing simultaneous diagonalizability of the matrix group representing omega if and only if omega is Abelian.
    • Specific results for structural crossover and mutation in the Abelian case are presented.

    Conclusions:

    • The study provides a deeper theoretical understanding of genetic algorithms operating on structured search spaces.
    • The generalized schema theorem offers insights into the behavior of genetic operators in these complex environments.
    • The connection to Fourier transforms and group theory reveals fundamental properties of the search space relevant to algorithm design.