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In this paper, an approach to aircraft trajectory optimization is presented in which integer and continuous variables are considered. Integer variables model decision-making processes, and continuous variables describe the state of the aircraft, which evolves according to differential-algebraic equations. The problem is formulated as a multiphase mixed-integer optimal control problem. It is transcribed into a mixed-integer nonlinear programming problem by applying a fifth degree Gauss&-Lobatto direct collocation method and is then solved using a nonlinear- programming-based branch-and-bound algorithm. The approach is applied to the following en route flight planning problem: Given an aircraft point mass model, a wind forecast, an airspace structure, and the relevant flying information regions with their associated overflying costs, find the control inputs that steer the aircraft from the initial fix to the final fix, following a route of waypoints while minimizing the fuel consumption and overflying costs during the flight. The decision-making process arises in determining the optimal sequence of waypoints. The optimal times at which the waypoints are to be overflown are also to be determined. Numerical results are presented and discussed, showing the effectiveness of the approach.