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Schemata Theory for the real coding and arithmetical operators

Published: 14 March 2004 Publication History

Abstract

The Schemata Theory analyzes the effect of the selection process, mutation and crossover over the number of individuals that belong to a given schema, within generations. This analysis considers, in its original form, the binary coding and operators. In this article, we present an analogous study, focusing on the real number coding and arthmetical operators. Unfortunately, the conventional schema definition is tightly dependent on discrete alphabets. Therefore, following a generalization of the concept of schema, we present a particular definition that suits better the continuous domain. Using this new definition, we reach an expression similar to the Fundamental Theorem of Genetic Algorithms [6] valid for the real coding of chromosomes.

References

[1]
Jim Antonisse. A new interpretation of schema notation that overturns the binary encoding constraint. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms. Morgan Kaufmann Publishers, 1989.
[2]
Lawrence Davis, editor. Handbook of Genetic Algorithms. Van Nostrand Reinhold, 1991.
[3]
Kenneth A. De Jong, William M. Spears, and Diana F. Gordon. Using markov chains to analyze GAFOs. In L. Darrell Whitely and Michael D. Vose, editors, Foundations of Genetic Algorithms 3, pages 115--137. Morgan Kaufmann, San Francisco, CA, 1995.
[4]
David Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Adison-Wesley, 1989.
[5]
William A. Greene. A non-linear schema theorem for genetic algorithms. In Proceedings of the Genetic and Evolutionary Computation Conference, pages 189--194. Morgan Kaufmann, July 2000.
[6]
John Holland. Adaptation in Natural and Artificial Systems. University of Michigan Press, 1975.
[7]
Zbigniew Michalewicz, editor. Genetic Algorithms + Data Structures = Evolution Programs. Springer, 1996.

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  • (2015)Incorporating Hybrid Operators on an Immune Based Framework for Multiobjective Optimization2015 IEEE International Conference on Systems, Man, and Cybernetics10.1109/SMC.2015.490(2809-2816)Online publication date: Oct-2015

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cover image ACM Conferences
SAC '04: Proceedings of the 2004 ACM symposium on Applied computing
March 2004
1733 pages
ISBN:1581138121
DOI:10.1145/967900
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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 March 2004

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Author Tags

  1. genetic algorithms
  2. real coding
  3. schemata theory

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SAC04
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SAC04: The 2004 ACM Symposium on Applied Computing
March 14 - 17, 2004
Nicosia, Cyprus

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Overall Acceptance Rate 1,650 of 6,669 submissions, 25%

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  • (2015)Incorporating Hybrid Operators on an Immune Based Framework for Multiobjective Optimization2015 IEEE International Conference on Systems, Man, and Cybernetics10.1109/SMC.2015.490(2809-2816)Online publication date: Oct-2015

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