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Theoretical Computer Science
Volume 361, Issue 1, 28 August 2006, Pages 111-129
Foundations of Genetic Algorithms
 
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doi:10.1016/j.tcs.2006.04.007    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2006 Elsevier B.V. All rights reserved.

Differentiable coarse graining

Jonathan E. Rowea, Michael D. Voseb, Corresponding Author Contact Information, E-mail The Corresponding Author and Alden H. Wrightc

aSchool of Computer Science, University of Birmingham, England bComputer Science Department, University of Tennessee, USA cDepartment of Computer Science, University of Montana, USA

Available online 22 May 2006.

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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, ranking selection, and mutation. A nonlinear coarse graining for ranking selection is also presented. A number of results concerning “form invariance” are given. Within the context of GAs, the primary contribution made is the illustration of a technique by which coarse grainings may be analyzed. It is applied to obtain a number of new coarse graining results.

Keywords: Differentiable; Coarse graining; Selection; Mutation; Form invariance


Theoretical Computer Science
Volume 361, Issue 1, 28 August 2006, Pages 111-129
Foundations of Genetic Algorithms
 
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