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. (C) 2006 Elsevier B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 111-129 |
| Number of pages | 19 |
| Journal | Theoretical Computer Science |
| Volume | 361 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 28 Aug 2006 |
Keywords
- differentiable
- form invariance
- mutation
- coarse graining
- selection