Coarse-Graining in Genetic Algorithms: Some Issues and Examples

Contreras, Andrés Aguilar; Rowe, Jonathan E.; Stephens, Christopher R.

doi:10.1007/3-540-45105-6_100

Cited by 4 publications

(6 citation statements)

References 9 publications

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“…Whereas the phrase "coarse graining" has previously been used by other researchers in connection with GAs (most notably by Chris Stephens [1]) that use typically ascribes a different meaning to the phrase than considered here.…”

Section: Resultsmentioning

confidence: 97%

Differentiable coarse graining

Rowe

Vose

Wright

2006

Theoretical Computer Science

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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.

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Section: Resultsmentioning

confidence: 97%

Differentiable coarse graining

Rowe

Vose

Wright

2006

Theoretical Computer Science

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“…temperature). Coarse-graining has been applied in the same spirit to genetic algorithms in [11,10,13,8,2]. In these works the statistical property sought (but only obtained for a very specific fitness function -unitation -in [2]) is a transition matrix specifying the exact or approximate evolutionary dynamics in the coarse-grained space.…”

Section: Introductionmentioning

confidence: 99%

“…Coarse-graining has been applied in the same spirit to genetic algorithms in [11,10,13,8,2]. In these works the statistical property sought (but only obtained for a very specific fitness function -unitation -in [2]) is a transition matrix specifying the exact or approximate evolutionary dynamics in the coarse-grained space. In this paper we will be using coarse-graining in a different spirit; our aim is not so much to "solve" for some statistical property of an evolutionary system, as to understand how, for each evolutionary operation, the composition of some post-operative population is constrained by the composition of the pre-operative population.…”

Section: Introductionmentioning

confidence: 99%

A general coarse-graining framework for studying simultaneous inter-population constraints induced by evolutionary operations

Burjorjee

Pollack

2006

Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation

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The use of genotypic populations is necessary for adaptation in Evolutionary Algorithms. We use a technique called form-invariant commutation to study the immediate effect of evolutionary operations on populations of genotypes. This technique allows us to understand compositional changes induced by evolutionary operations in terms of constraints between populations. Deep insight into the population-level effect of some evolutionary operation is possible when multiple constraints can be derived for all pairs of pre and post operative populations; for each such pair of populations the constraints between them are then said to hold simultaneously. When selection is fitness proportional we show that any coarse-graining of the genotype set can be used to systematically derive single constraints between between all pairs of pre and post selection populations. Matters are not so simple in the case of variation. We develop an abstract condition called ambivalence and show that when a coarse-graining and a variation operation satisfy this condition then a systematic derivation of single constraints between all pairs of pre and post variation populations is possible. Finally we show that it is possible to use schema partitions to systematically derive simultaneous constraints for any combination of variation operations that are commonly used in GAs.

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“…Elsewhere the phrase coarse-graining has been defined as "a collection of subsets of the search space that covers the search space" [6], and more egregiously as "just a function from a genotype set to some other set" [5].…”

Section: Inconsistent Use Of the Phrase 'Coarse-graining'mentioning

confidence: 99%

“…Therefore a numerical iteration of the the new system is only computationally tractable when the length of the genomes is relatively short. Elsewhere the term coarse-graining has been defined as "a collection of subsets of the search space that covers the search space" [5], and as "just a function from a genotype set to some other set" [4].…”

Section: The Promise Of Coarse-grainingmentioning

confidence: 99%

Sufficient Conditions for Coarse-Graining Evolutionary Dynamics

Burjorjee

Foundations of Genetic Algorithms

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Previous theoretical results in the Evolutionary Computation literature only permit analyses of evolutionary dynamics in the immediate term -i.e. over a single generation -or in the asymptote of time. There are currently no theoretical results that permit a principled analysis of any non-trivial aspect of evolutionary dynamics in the short term, i.e. over a small number of generations. In the absence of such analyses we believe that accurate theories of evolutionary adaptation will continue to evade discovery. We describe a technique called coarsegraining which has been widely used in other scientific disciplines to study the emergent phenomena of complex systems. This technique is a promising approach towards the formulation of more principled theories of evolutionary adaptation because, if successfully applied, it permits a principled analysis of evolutionary dynamics across multiple generations. We develop a simple yet powerful abstract framework for studying the dynamics of an infinite population evolutionary algorithm (IPEA). Using this framework we show that the short term dynamics of an IPEA can be coarse-grained if it satisfies certain abstract conditions. We then use this result to argue that the dynamics of an infinite population genetic algorithm with uniform crossover and fitness proportional selection can be coarse-grained for at least a small number of generations, provided that the initial population belongs to a particular class of distributions (which includes the uniform distribution), and the fitness function satisfies a relatively weak constraint.

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Coarse-Graining in Genetic Algorithms: Some Issues and Examples

Cited by 4 publications

References 9 publications

Differentiable coarse graining

Differentiable coarse graining

A general coarse-graining framework for studying simultaneous inter-population constraints induced by evolutionary operations

Sufficient Conditions for Coarse-Graining Evolutionary Dynamics

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