Analysis of the univariate marginal distribution algorithm modeled by Markov chains

Abstract

This work presents an analysis of the convergence behaviour of the Univariate Marginal Distribution Algorithm (UMDA) when it is used to maximize a number of pseudo-boolean functions. The analysis is based on modeling the algorithm using a reducible Markov chain, whose absorbing states correspond to the individuals of the search space. The absorption probability to the optimum and the expected time of convergence to the set of absorbing states are calculated for each function. This information is used to provide some insights into how the absorption probability to the optimum and the expected absorption times evolve when the size of population increases. The results show the different behaviours of the algorithm in the analyzed functions. © Springer-Verlag Berlin Heidelberg 2003.