The Limits of Estimation of Distribution Algorithms

In this paper, we study the ability limit of EDAs to effectively solve problems in relation to the number of interactions among the variables. More in particular, we numerically analyze the learning limits that different EDA implementations encounter to solve problems on a sequence of additively decomposable functions (ADFs) in which new sub-functions are progressively added. The study is carried out in a worst-case scenario where the sub-functions are defined as deceptive functions. We argue that the limits for this type of algorithm are mainly imposed by the probabilistic model they rely on. Beyond the limitations of the approximate learning methods, the results suggest that, in general, the use of bayesian networks can entail strong computational restrictions to overcome the limits of applicability.