A Boltzmann based estimation of distribution algorithm

This paper introduces a new approach for estimation of distribution algorithms called the Boltzmann Univariate Marginal Distribution Algorithm (BUMDA). It uses a Normal-Gaussian model to approximate the Boltzmann distribution, hence, formulae for computing the mean and variance parameters of the Gaussian model are derived from the analytical minimization of the Kullback–Leibler divergence. The resulting formulae explicitly introduces information about the fitness landscape for the Gaussian parameters computation, in consequence, the Gaussian distribution obtains a better bias to sample intensively the most promising regions than simply using the maximum likelihood estimator of the selected set. In addition, the BUMDA formulae needs only one user parameter. Accordingly to the experimental results, the BUMDA excels in its niche of application. We provide theoretical, graphical and statistical analysis to show the BUMDA performance contrasted with state of the art EDAs.

► Using the Boltzmann distribution as a base of an EDA.
► Approximate the Boltzmann with a Normal via the Kullback–Leibler divergence.
► The Boltzmann Univariate Marginal Distribution Algorithm needs one user parameter.
► Comparison of the BUMDA versus Univariate and Multivariate Normal-based EDAs.
► Convergence to the elite individual is ensured.