Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-06-12T03:57:50.178Z Has data issue: false hasContentIssue false
  • English
  • Français

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: totero@udc.es)
V. S. PEÑARANDA
Affiliation:
Departamento de Matemáticas, E.U.P. de Ferrol, Universidade da Coruña, Campus de Serantes, Ferrol, Spain (email: vesp@udc.es)
C. VIDAL
Affiliation:
Departamento de Computación, Faculdad de Informática, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain (email: eicovima@udc.es)
A. VERSCHOREN
Affiliation:
Department of Mathematics and Computer Sciences, University of Antwerp, Administratief Hoofdgebouw, UA-Middelheimcampus, Middelheimlaen 1, B2020 Antwerpen, Belgium (email: alain.verschoren@ua.ac.be)
*
✉For correspondence; e-mail: totero@udc.es
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Davidor, Y., ‘Epistasis and variance: A viewpoint on GA-hardness’, in: Foundations of genetic algorithms, Vol. 1 (ed. G. J. E. Rawlins) (Morgan Kaufmann, San Mateo, CA, 1991), pp. 23–25.Google Scholar
[2]Forrest, S. and Mitchell, M., ‘Relative building-block fitness and the building-block hypothesis’, in: Foundations of genetic algorithms, Vol. 2 (ed. L. D. Whitley) (Morgan Kaufmann, San Mateo, CA, 1993).Google Scholar
[3]Garey, M. R. and Johnson, D. S., Computers and intractability: A guide to the theory of NP-completeness (ed. W. H. Freeman, San Francisco, 1979).Google Scholar
[4]Goldberg, D., ‘Genetic algorithms and Walsh functions: Part I, A gentle introduction’, Complex Systems 3 (1989), 129–152.Google Scholar
[5]Iglesias, M. T., Peñaranda, V. S. and Verschoren, A., ‘Higher order functions and Walsh coefficients’, Bull. Belgi. Math. Soc. Simon Stevin 13 (2006), 633–643.Google Scholar
[6]Iglesias, M. T., Peñaranda, V. S., Vidal, C. and Verschoren, A., ‘‘The 2-epistasis of fitness functions’’, Bull. Austral. Math. Soc. 76 (2007), 397–419.CrossRefGoogle Scholar
[7]Iglesias, M. T., Verschoren, A. and Vidal, C., ‘A combinatorial approach to epistasis’, in: Foundations of generic optimization, Vol. 1 (Springer, Dordrecht, 2005).Google Scholar
[8]Naudts, B., Suys, D. and Verschoren, A., ‘Epistasis, deceptivity and Walsh transforms’, Proc. Int. ICSC Symp. on Engineering of Intelligent Systems (EIS’98), Genetic Algorithms/Theory, 1 (ICSC Academic Press, Millet, AC, 1998), pp. 210–216.Google Scholar
[9]Naudts, B., Suys, D. and Verschoren, A., ‘Generalized royal road functions and their epistasis’, Artificial Intelligence 19 (2000), 317–334.Google Scholar
[10]Peñaranda, V. S., ‘Epistasis superior’, PhD thesis, Universidade da Coruña, Spain, 2006.Google Scholar
[11]Rawlins, G. J. E., Foundations of genetic algorithms (Morgan Kaufmann, San Mateo, CA, 1991).Google Scholar
[12]Stickberger, M. M., Genetics (Collier-McMillan, London, 1968).Google Scholar
[13]Suys, D. and Verschoren, A., ‘Extreme epistasis’, in: Proc. Int. Conf. Intelligent Technologies in Human-Related Sciences (ITHURS’96), Vol. II (Universidad de León, 1996), pp. 251–258.Google Scholar
[14]Van Hove, H. and Verschoren, A., ‘On epistasis’, Comput. Artificial Intell. 14 (1994), 271–277.Google Scholar