Differentiable coarse graining

Authors:
Jonathan E. Rowe;Michael D. Vose;Alden H. Wright
Affiliations:
School of Computer Science, University of Birmingham, England;Computer Science Department, University of Tennessee;Department of Computer Science, University of Montana
Venue:
Theoretical Computer Science - Foundations of genetic algorithms
Year:
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.