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Broadcasting in wireless networks, unlike wired networks, inherently reaches several nodes with a single transmission. For an omnidirectional wireless broadcast to a node, all nodes closer to the transmitting node are also reached. This property can be used to compute routing trees which minimize the sum of the transmitter powers. We present a mixed integer programming formulation and a simulated annealing algorithm for the problem. Extensive experimental results for the heuristic approach are presented. They show that the proposed algorithm is capable of improving the results of state-of-the-art algorithms for most of the problems considered. The solutions provided by the simulated annealing algorithm can be improved by applying a very fast post-optimization procedure. This leads to the best known mean results for the problems considered.