An effective approach for learning Bayesian network structures is to perform a local search on the space of topological orderings, followed by a systematic search of compatible parent sets. Typically, the local search is initialized with an ordering generated uniformly at random. This can lead to poor local optima, slow down convergence and hurt the performance of the method. In this work we develop two informed heuristics for generating initial solutions to order-based structure learning. Both

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... heuristics rely on the solution of a relaxed version of the problem in which cycles are permitted. The heuristics remove less relevant arcs of the relaxed solution in order to produce a directed acyclic graph, which is then used to produce topological orderings. Experiments with a large collection of real-world data sets demonstrate that our heuristics increase the quality of the solutions found with a negligible overhead.