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General cardinality genetic algorithms

Koehler1, Bhattacharyya, Vose

  • 1Warrington College of Business Administration, University of Florida, Gainesville 32611, USA. koehler@ufl.edu

Evolutionary Computation
|January 1, 1997
PubMed
Summary
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This study generalizes the Vose genetic algorithm to higher cardinality cases, replacing Boolean operators with arithmetic operations. Results demonstrate a viable extension of this evolutionary computation model.

Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Evolutionary Computation

Background:

  • The Vose genetic algorithm is a foundational model in evolutionary computation, traditionally limited to binary representations.
  • Extending genetic algorithm models to higher cardinality alphabets is crucial for broader applicability in complex problem-solving.

Purpose of the Study:

  • To provide a comprehensive generalization of the Vose genetic algorithm from binary to higher cardinality settings.
  • To adapt core genetic algorithm operators for non-binary domains.

Main Methods:

  • Replaced binary Boolean AND and EXCLUSIVE-OR operators with multiplication and addition over rings of integers.
  • Generalized Walsh matrices using finite Fourier transforms to accommodate higher cardinality inputs.

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  • Empirically compared the performance and characteristics of the generalized model against the original binary Vose model.

    • Main Results:

    • Successfully adapted the Vose model for higher cardinality alphabets, demonstrating its theoretical and practical extension.
    • The use of arithmetic operations over integer rings proved effective in mimicking Boolean logic for genetic operations.
    • Finite Fourier transforms provided a robust method for generalizing Walsh matrices in this new context.

    Conclusions:

    • The generalized Vose genetic algorithm offers a powerful extension for evolutionary computation beyond binary constraints.
    • This work opens avenues for applying genetic algorithms to a wider range of combinatorial optimization and machine learning problems.