Incorporating a Metropolis method in a distribution estimation using Markov random field algorithm

Markov random field (MRF) modelling techniques have been recently proposed as a novel approach to probabilistic modelling for estimation of distribution algorithms (EDAs) (S. K. Shakya et al., 2004). An EDA using this technique was called distribution estimation using Markov random fields (DEUM). DEUM was later extended to DEUM/sub d/ (S. Shakya et al., 2005). DEUM and DEUM/sub 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/sub d/ to incorporate a simple Metropolis method and empirically shows that for linear univariate problems the proposed univariate MRF models are very effective. In particular, the proposed DEUM/sub d/ algorithm can find the solution in O(n) fitness evaluations. Furthermore, we suggest that the Metropolis method can also be used to extend the DEUM approach to multivariate problems.