Abstract
Coarse graining is defined in terms of a commutative diagram. Necessary and sufficient conditions are given in the continuously differentiable case. The theory is applied to linear coarse grainings arising from partitioning the population space of a simple Genetic Algorithm (GA). Cases considered include proportional selection, binary tournament selection, and mutation. A nonlinear coarse graining for ranking selection is also presented. Within the context of GAs, the primary contribution made is the introduction and illustration of a technique by which the possibility for coarse grainings may be analyzed. A secondary contribution is that a number of new coarse graining results are obtained.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Muhlenbein, H., Voigt, H.M.: Gene pool recombination in genetic algorithms. In: Osman, I.H., Kelly, J.P. (eds.) Proceedings of the Metaheuristics Inter. Conf., Norwell, Kluwer Academic Publishers, Dordrecht (c1995)
Rabinovich, Y., Wigderson, A.: An analysis of a simple generic algorithm. In: Belew, R.K., Booker, L.B. (eds.) Proceedings of the 4th International Conference on Genetic Algorithms, pp. 215–221. Morgan Kaufmann Publishers, San Francisco (c1991)
Rowe, J.E., Vose, M.D., Wright, A.H.: State aggregation and population dynamics in linear systems, Artificial Life (in press), http://www.cs.umt.edu/u/wright/pubs.htm
Stephens, C.R., Waelbroeck, H.: Schemata Evolution and Building Blocks. Evolutionary Computation 7(2), 109–124 (1999)
Vose, M.D.: Coarse Graining. Dagstuhl Seminar No 04081, 15.02.-20.02.04, http://www.dagstuhl.de/04081/Materials/
Vose, M.D.: The Simple Genetic Algorithm: Foundations and Theory. MIT Press, Cambridge (c1999) ISBN: 026222058X
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rowe, J.E., Vose, M.D., Wright, A.H. (2005). Coarse Graining Selection and Mutation. In: Wright, A.H., Vose, M.D., De Jong, K.A., Schmitt, L.M. (eds) Foundations of Genetic Algorithms. FOGA 2005. Lecture Notes in Computer Science, vol 3469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11513575_10
Download citation
DOI: https://doi.org/10.1007/11513575_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27237-3
Online ISBN: 978-3-540-32035-7
eBook Packages: Computer ScienceComputer Science (R0)