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Walsh transforms, balanced sum theorems and partition coefficients over multary alphabets

Published: 25 June 2005 Publication History

Abstract

In this note, we indicate how the basic machinery of Walsh transforms can be generalized from the binary case ([3, 4]) to multary alphabets. Our main results show how Walsh coefficients are related to partition coefficients and how they may be used to calculate schema averages.

References

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P. Field, A Multary Theory for Genetic Algorithms: Unifying Binary and Nonbinary Problem Representations, Ph.D. Thesis, University of London, London, UK, 1996.
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D. E. Goldberg, Genetic Algorithms and Walsh Functions: Part I, A Gentle Introduction, Complex Systems 3 129--152, 1989.
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D. E. Goldberg. Genetic Algorithms and Walsh Functions: Part II: Deception and its Analysis. Complex Systems 3:153--171, 1989.
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M. T. Iglesias, C. Vidal, D. Suys and A. Verschoren, Generalized Walsh Transforms and Epistasis, to appear in Bulletin of Belgian Mathematical Society-Simon Stevin (accepted).
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A. J. Mason, Partition Coefficients, Static Deception and Deceptive Problems for Non-binary Alphabets, in: Proceedings of the 4th International Conference on Genetic Algorithms, eds. R. K. Belew and L. B. Booker, 210-214, Morgan Kaufmann Publishers, 210--214, 1991.
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Cited By

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  • (2008)Detecting the epistatic structure of generalized embedded landscapeGenetic Programming and Evolvable Machines10.1007/s10710-007-9045-79:2(125-155)Online publication date: 1-Jun-2008
  • (2007)Extended probe method for linkage discovery over high-cardinality alphabetsProceedings of the 9th annual conference on Genetic and evolutionary computation10.1145/1276958.1277228(1484-1491)Online publication date: 7-Jul-2007
  • (2007)Properties of Symmetric Fitness FunctionsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2007.89276411:6(743-757)Online publication date: 1-Dec-2007

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cover image ACM Conferences
GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computation
June 2005
2272 pages
ISBN:1595930108
DOI:10.1145/1068009
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 25 June 2005

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Author Tags

  1. genetic algorithm
  2. multary alphabet
  3. partition coefficient
  4. schema average
  5. schema theory
  6. walsh coefficient
  7. walsh function

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Cited By

View all
  • (2008)Detecting the epistatic structure of generalized embedded landscapeGenetic Programming and Evolvable Machines10.1007/s10710-007-9045-79:2(125-155)Online publication date: 1-Jun-2008
  • (2007)Extended probe method for linkage discovery over high-cardinality alphabetsProceedings of the 9th annual conference on Genetic and evolutionary computation10.1145/1276958.1277228(1484-1491)Online publication date: 7-Jul-2007
  • (2007)Properties of Symmetric Fitness FunctionsIEEE Transactions on Evolutionary Computation10.1109/TEVC.2007.89276411:6(743-757)Online publication date: 1-Dec-2007

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