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HIGHER EPISTASIS IN GENETIC ALGORITHMS

Part of: Discrete mathematics in relation to computer science

Published online by Cambridge University Press:  01 April 2008

M. T. IGLESIAS ,
V. S. PEÑARANDA ,
C. VIDAL  and
A. VERSCHOREN
M. T. IGLESIAS*
Affiliation:
Departamento de Matemáticas, Facultad de Informática, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain (email: [email protected])
V. S. PEÑARANDA
Affiliation:
Departamento de Matemáticas, E.U.P. de Ferrol, Universidade da Coruña, Campus de Serantes, Ferrol, Spain (email: [email protected])
C. VIDAL
Affiliation:
Departamento de Computación, Faculdad de Informática, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain (email: [email protected])
A. VERSCHOREN
Affiliation:
Department of Mathematics and Computer Sciences, University of Antwerp, Administratief Hoofdgebouw, UA-Middelheimcampus, Middelheimlaen 1, B2020 Antwerpen, Belgium (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We study the k-epistasis of a fitness function over a search space. This concept is a natural generalization of that of epistasis, previously considered by Davidor, Suys and Verschoren and Van Hove and Verschoren [Y. Davidor, in: Foundations of genetic algorithms, Vol. 1, (1991), pp. 23–25; D. Suys and A. Verschoren, ‘Proc Int. Conf. on Intelligent Technologies in Human-Related Sciences (ITHURS’96), Vol. II (1996), pp. 251–258; H. Van Hove and A. Verschoren, Comput. Artificial Intell.14 (1994), 271–277], for example. We completely characterize fitness functions whose k-epistasis is minimal: these are exactly the functions of order k. We also obtain an upper bound for the k-epistasis of nonnegative fitness functions.

Keywords

genetic algorithmGA-hardnessepistasisorderWalsh coefficients

MSC classification

Secondary: 68R99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 2 , April 2008 , pp. 225 - 243
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

This research was partially supported by a research grant of Dirección Xeral de Investigación e Desenvolvemento da Consellería de Innovación, Industria e Comercio da Xunta de Galicia, PGIDIT03PXIA10502PR and by the project REGACA 2006/38.

References

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