The theory of virtual alphabets

  • David E. Goldberg
Genetic Algorithms Genetic Algorithm Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 496)

Abstract

This paper presents a theory of convergence for real-coded genetic algorithms—GAs that use floating-point or other high-cardinality codings in their chromosomes. The theory is consistent with the theory of schemata and postulates that selection dominates early GA performance and restricts subsequent search to intervals with above-average function value dimension by dimension. These intervals may be further subdivided on the basis of their attraction under genetic hillclimbing. Each of these subintervals is called a virtual character, and the collection of characters along a given dimension is called a virtual alphabet. It is the virtual alphabet that is searched during the recombinative phase of the genetic algorithm, and in many problems this is sufficient to ensure that good solutions are found. Although the theory helps explain why many problems have been solved using real-coded GAs, it also suggests that real-coded GAs can be blocked from further progress in those situations when local optima separate the virtual characters from the global optimum.

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References

  1. Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley.Google Scholar
  2. Goldberg, D. E. (1990). Real-coded genetic algorithms, virtual alphabets, and blocking (IlliGAL Report No. 90001). Urbana: University of Illinois at Urbana-Champaign, The Illinois Genetic Algorithms Laboratory.Google Scholar
  3. Goldberg, D. E., & Deb, K. (1990). A comparative analysis of selection schemes used in genetic algorithms (TCGA Report No. 90007). Tuscaloosa: University of Alabama, The Clearinghouse for Genetic Algorithms.Google Scholar
  4. Holland, J. H. (1975). Adaptation in natural and artificial systems. Ann Arbor: The University of Michigan Press.Google Scholar
  5. Wright, A. H. (1990). Genetic algorithms for real parameter optimization. Unpublished manuscript, University of Montana, Computer Science Department, Missoula.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • David E. Goldberg
    • 1
  1. 1.University of Illinois at Urbana-ChampaignUrbana

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