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Markov Random Field (MRF) modelling techniques have been recently proposed as a novel approach to probabilistic modelling for Estimation of Distribution Algorithms (EDAs). An EDA using this technique was called Distribution Estimation using Markov Random Fields (DEUM). DEUM was later extended to DEUM d . DEUM and DEUM d use a univariate model of probability distribution, and have been shown to perform better than other univariate EDAs for a range of optimization problems. This paper extends DEUM to use a bivariate model and applies it to the Ising spin glass problems. We propose two variants of DEUM that use different sampling techniques. Our experimental result show a noticeable gain in performance.

This paper presents a methodology for using heuristic search methods to optimise cancer chemotherapy. Specifically, two evolutionary algorithms -Population Based Incremental Learning (PBIL), which is an Estimation of Distribution Algorithm (EDA), and Genetic Algorithms (GAs) have been applied to the problem of finding effective chemotherapeutic treatments. To our knowledge, EDAs have been applied to fewer real world problems compared to GAs, and the aim of the present paper is to expand the application domain of this technique.We compare and analyse the performance of both algorithms and draw a conclusion as to which approach to cancer chemotherapy optimisation is more efficient and helpful in the decision-making activity led by the oncologists.

This paper presents a Markov random field (MRF) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM). DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are: 1) use of MRF models, 2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model.

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Several Estimation of Distribution Algorithms (EDAs) based on Markov networks have been recently proposed. The key idea behind these EDAs was to factorise the joint probability distribution of solution variables in terms of cliques in the undirected graph. As such, they made use of the global Markov property of the Markov network in one form or another. This paper presents a Markov Network based EDA that is based on the use of the local Markov property, the Markovianity, and does not directly model the joint distribution. We call it Markovianity based Optimisation Algorithm. The algorithm combines a novel method for extracting the neighbourhood structure from the mutual information between the variables, with a Gibbs sampler method to generate new points. We present an extensive empirical validation of the algorithm on problems with complex interactions, comparing its performance with other EDAs that use higher order interactions. We extend the analysis to other functions with discrete representation, where EDA results are scarce, comparing the algorithm with state of the art EDAs that use marginal product factorisations.

Distribution Estimation Using Markov network (DEUM) algorithm is a class of estimation of distribution algorithms that uses Markov networks to model and sample the distribution. Several different versions of this algorithm have been proposed and are shown to work well in a number of different optimisation problems. One of the key similarities between all of the DEUM algorithms proposed so far is that they all assume the interaction between variables in the problem to be pre given. In other words, they do not learn the structure of the problem and assume that it is known in advance. Therefore, they may not be classified as full estimation of distribution algorithms. This work presents a fully multivariate DEUM algorithm that can automatically learn the undirected structure of the problem, automatically find the cliques from the structure and automatically estimate a joint probability model of the Markov network. This model is then sampled using Monte Carlo samplers. The proposed DEUM algorithm can be applied to any general optimisation problem even when the structure is not known.

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.