Estimation of distribution algorithm: Difference between revisions

Revision as of 01:15, 22 July 2023

Revision as of 13:21, 24 August 2023

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===Bivariate marginal distribution algorithm (BMDA)===

The BMDA<ref>{{cite book|last1=Pelikan|first1=Martin|last2=Muehlenbein|first2=Heinz|title=Advances in Soft Computing |chapter=The Bivariate Marginal Distribution Algorithm|journal=Advances in Soft Computing|date=1 January 1999|pages=521–535|doi=10.1007/978-1-4471-0819-1_39|isbn=978-1-85233-062-0|citeseerx=10.1.1.55.1151}}</ref> factorizes the joint probability distribution in bivariate distributions. First, a randomly chosen variable is added as a node in a graph, the most dependent variable to one of those in the graph is chosen among those not yet in the graph, this procedure is repeated until no remaining variable depends on any variable in the graph (verified according to a threshold value).

The resulting model is a forest with multiple trees rooted at nodes <math>\Upsilon_t</math>. Considering <math>I_t</math> the non-root variables, BMDA estimates a factorized distribution in which the root variables can be sampled independently, whereas all the others must be conditioned to the parent variable <math>\pi_i</math>.

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===Linkage-tree Genetic Algorithm (LTGA)===

The LTGA<ref>{{cite book|last1=Thierens|first1=Dirk|chapter=The Linkage Tree Genetic Algorithm|journaltitle=Parallel Problem Solving from Nature, PPSN XI |chapter=The Linkage Tree Genetic Algorithm|date=11 September 2010|pages=264–273|doi=10.1007/978-3-642-15844-5_27|isbn=978-3-642-15843-8}}</ref> differs from most EDA in the sense it does not explicitly model a probability distribution but only a linkage model, called linkage-tree. A linkage <math>T</math> is a set of linkage sets with no probability distribution associated, therefore, there is no way to sample new solutions directly from <math>T</math>. The linkage model is a linkage-tree produced stored as a [[Family of sets]] (FOS).

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