A fully multivariate DEUM algorithm

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.