The future traffic management systems will be time-based. Under this context, flight reference trajectories require a time of arrival constraint at a given waypoint to guarantee safety and an improved traffic management. Algorithms that compute the most economical trajectory taking into account the time based constraint are required. In this paper, an algorithm that fulfills the time of arrival constraint and computes the most economical vertical reference trajectory was developed. The time constraint was optimized by using the golden search section to find the most economical combinations of Mach numbers that complies with the required time of arrival. The combination of altitudes that provide the most economical vertical reference trajectory was computed by using the Artificial Bee Colony optimization algorithm. To avoid unnecessary Mach number variations, the solution provided by the developed algorithm was post-treated to obtain as many consecutive flight segments with the same Mach number as possible. Results showed that the RTA constraint was fulfilled while reducing the flight cost of the optimized trajectory with respect to the flight cost of the reference trajectory, Nomenclature ETA = Estimated Time of Arrival EW = Efficiency Weight Flight Time = Time required to fly between two waypoints fitness = Trajectory fitness Mach = Mach Number RTA = Required Time of Arrival WD = Wind Direction WS = Wind Speed V sound = Speed of Sound
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