Aircraft Vertical Route Optimization by Beam Search and Initial Search Space Reduction

Abstract

This paper describes an optimization algorithm that provides an economical vertical navigation profile by finding the combinations of climb, cruise, and descent speeds, as well as altitudes, for an aircraft to minimize flight costs. The computational algorithm takes advantage of a space search reduction methodology to reduce the initial number of available speed and altitude combinations. The optimal solution was found by implementing the beam search algorithm. A bounding function that correctly estimates the flight cost by considering step climbs was developed to reduce the number of calculations required by the beam search algorithm. The full-flight fuel burn cost was obtained using a performance database-based method. The algorithm uses a numerical performance model instead of equations of motion to compute fuel burn. The database was developed by using flight experimental data. To validate the algorithm, its results were compared to those of three other algorithms: an exhaustive search, beam search, and search space reduction. The solution provided by the algorithm was also compared to the solution provided by a flight management system. Following this comparison, the algorithm systematically found the optimal solutions, which were better in terms of flight cost than those provided by the flight management system.