Coarse Graining Selection and Mutation
Jonathan E. Rowe
School of Computer Science
University of Birmingham
Birmingham B15 2TT
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
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.