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We start with a brief introduction to Bayesian networks. We provide an overview of learning Bayesian networks from data, and the different variations of this task. We then focus on the particular task of learning Bayesian network structure from fully observed data using a search-and-score approach. We discuss the Bayesian score and its implications, and survey the literature on existing structure-learning ... read morealgorithms. We then develop two genetic algorithms for learning structure. The first algorithm searches over the space of graphs, and uses a specialized representation to ensure that the mutation and crossover operators are closed. The second algorithm searches over the space of node orders, and uses advanced caching and precomputation mechanisms to avoid repeated computations. We analyze the running time of the latter algorithm, including its caching and precomputation steps. Finally, we apply this algorithm to a structure-discovery task in the Genetic-Programming domain.