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Nonbinary transforms for genetic algorithm problems

  • Paul Field
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 865)

Abstract

GA theory tends to be biased towards binary representations of problems. To try to redress the balance somewhat, this paper takes two important, related ideas, Walsh and partition coefficients, and generalises them to the nonbinary case. These coefficients provide an efficient way of calculating the fitnesses of low order schemata and of writing the conditions that characterise deceptive functions. Functions can be analysed for deception or created with varying degrees of deception by transforming between string fitnesses and coefficients or vice versa. In this paper, the matrix forms of the transforms are presented, the relationship between them examined and an efficient algorithm for performing the transforms is presented. Finally, an example of the coefficients' use is given.

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References

  1. Belew, R.K. and Booker, L.B. (Eds) (1991), Proceedings of the Forth International Conference on Genetic Algorithms, Morgan KaufmannGoogle Scholar
  2. Field, P. (1994), Walsh and Partition Functions Made Easy, Presented at the AISB 1994 Workshop on Evolutionary Computing, University of Leeds, England.Google Scholar
  3. Goldberg, D.E. (1989a), Genetic Algorithms and Walsh Functions: Part I, A Gentle Introduction, Complex Systems 3, pp.129–152MathSciNetGoogle Scholar
  4. Goldberg, D.E. (1989b), Genetic Algorithms and Walsh Functions: Part II, Deception and Its Analysis, Complex Systems 3, pp.153–171MathSciNetGoogle Scholar
  5. Graham, A. (1981), Kronecker Products and Matrix Calculus with Applications, Ellis Horwood.Google Scholar
  6. Homaifar, A., Qi, X. and Fost, J. (1991), Analysis and Design of a General GA Deceptive Problem. In Belew, R.K. and Booker, L.B, (1991).Google Scholar
  7. Mason, A.J. (1991), Partition Coefficients, Static Deception and Deceptive Problems for Non-Binary Alphabets. In Belew, R.K. and Booker, L.B. (1991).Google Scholar
  8. Whitley, L.D. (1991), Fundamental Principles of Deception in Genetic Search. In Rawlins, G. (Ed.), Foundations of Genetic Algorithms, Morgan KaufmannGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Paul Field
    • 1
  1. 1.Department of Computer ScienceQueen Mary and Westfield CollegeLondon

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