Differentiable coarse graining

Jonathan Rowe, MD Vose, AH Wright

Research output: Contribution to journalArticle

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)111-129
Number of pages19
JournalTheoretical Computer Science
Issue number1
Publication statusPublished - 28 Aug 2006


  • differentiable
  • form invariance
  • mutation
  • coarse graining
  • selection


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