An EDA based on local markov property and gibbs sampling

Abstract

The key ideas behind most of the recently proposed Markov networks based EDAs were to factorise the joint probability distribution in terms of the cliques in the undirected graph. As such, they made use of the global Markov property of the Markov network. Here we presents a Markov Network based EDA that exploits Gibbs sampling to sample from the Local Markov property, the Markovianity, and does not directly model the joint distribution. We call it Markovianity based Optimisation Algorithm. Some initial results on the performance of the proposed algorithm shows that it compares well with other Bayesian network based EDAs.

An introduction and survey of estimation of distribution algorithms

“…In other words, some of the difficulty moves from learning to sampling the probabilistic model compared to EDAs based on Bayesian networks. Shakya and Santana (2008) uses Gibbs sampling to generate new solutions from its model in the Markovianity based optimisation algorithm (MOA). MOA was shown to have comparable performance to some Bayesian network based EDAs on deceptive test problems.…”

Mateda-2.0: AMATLABPackage for the Implementation and Analysis of Estimation of Distribution Algorithms

“…Mateda-2.0 includes an algorithm based on a thresholding of the mutual information (Shakya and Santana 2008) to learn the structure of Markov networks in EDAs. This algorithm constructs an approximation of the neighborhood of each variable by computing the variables whose mutual information is above a given threshold.…”

“…In addition, a temperature parameter is included as part of the sampling algorithms. Thanks to this parameter, linear and Boltzman schedules can be applied to sample the model using simulated annealing (Kirkpatrick et al 1983) as done in (Shakya and Santana 2008).…”

A fully multivariate DEUM algorithm

“…Some research on the use of undirected graphical models (Markov networks) [2] [15] [21] in EDAs has also been done [27] [32][33] [28] [30][29] [31]. Some of the well known instances of Markov network based EDA includes Distribution Estimation Using Markov Networks (DEUM) algorithm [30], Markov Network EDA (MN-EDA) [28], Markov Network Factorised Distribution Algorithm (MN-FDA) [27] and a recently proposed Markovianity based Optimisation Algorithm (MOA) [36], [35]. MN F. Fournier is with ODS-Petrodata, Aberdeen, UK (phone: +44 (0)1224 597846; email: ffournier@ods-petrodata.com).…”