The most common way of automatically learning Bayesian networks from data is the combination of a scoring metric, the evaluation of the fitness of any given candidate network to the data base, and a search procedure to explore the search space. Usually, the search is carried out by greedy hill-climbing algorithms, although other techniques such as genetic algorithms, have also been used.

A recent metaheuristic, Ant Colony Optimisation (ACO), has been successfully applied to solve a great variety of problems, being remarkable the performance achieved in those problems related to path (permutation) searching in graphs, such as the Traveling Salesman Problem. In two previous works [13,12], the authors have approached the problem of learning Bayesian networks by means of the search+score methodology using ACO as the search engine.

As in these articles the search was performed in different search spaces, in the space of orderings [13] and in the space of directed acyclic graphs [12]. In this paper we compare both approaches by analysing the results obtained and the differences in the design and implementation of both algorithms.