Coarse Graining Selection and Mutation

posted 11/23/04

Jonathan E. Rowe
School of Computer Science
University of Birmingham
Birmingham B15 2TT
Great Britaink
J.E.Rowe@cs.bham.ac.uk

Michael D. Vose
Dept. of Computer Science 
University of Tennessee
203 Claxton Complex
1122 Volunteer Blvd.
Knoxville, TN  37996-3450
USA
vose@cs.utk.edu

Alden H. Wright
Computer Science Dept.
Univ. of Montana
Missoula, MT 59812
wright@cs.umt.edu
(406) 243-4790



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.