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This book proposes some novel approaches for finding unmanned aerial vehicle trajectories to reach targets with unknown location in minimum time. At first, it reviews probabilistic search algorithms that have been used for dealing with the minimum time search (MTS) problem, and discusses how metaheuristics, and in particular the ant colony optimization algorithm (ACO), can help to find high-quality solutions with low computational time. Then, it describes two ACO-based approaches to solve the discrete MTS problem and the continuous MTS problem, respectively. In turn, it reports on the evaluation of the ACO-based discrete and continuous approaches to the MTS problem in different simulated scenarios, showing that the methods outperform in most all the cases over other state-of-the-art approaches. In the last part of the thesis, the work of integration of the proposed techniques in the ground control station developed by Airbus to control ATLANTE UAV is reported in detail, providing practical insights into the implementation of these methods for real UAVs.