Finding most probable explanations (MPEs) in graphical models, such as Bayesian belief networks, is a fundamental problem in reasoning under uncertainty, and much effort has been spent on developing effective algorithms for this N P-hard problem. Stochastic local search (SLS) approaches to MPE solving have previously been explored, but were found to be not competitive with state-of-theart branch & bound methods. In this work, we identify the shortcomings of earlier SLS algorithms for the MPE

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... blem and demonstrate how these can be overcome, leading to an SLS algorithm that substantially improves the state-of-the-art in solving hard networks with many variables, large domain sizes, high degree, and, most importantly, networks with high induced width.