Coarse Graining Selection and Mutation

posted 11/23/04

Jonathan E. Rowe
School of Computer Science
University of Birmingham
Birmingham B15 2TT
Great Britaink

Michael D. Vose
Dept. of Computer Science 
University of Tennessee
203 Claxton Complex
1122 Volunteer Blvd.
Knoxville, TN  37996-3450

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


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.