A bi-level algorithm is developed to determine the optimal arrival sequence w.r.t a specific upper level objective function, e.g. minimizing pollutant emissions or maximizing runway throughput. Within a sequence it is assumed that all aircraft are operated optimally (lower level optimization), minimizing individual fuel consumption. However, all aircraft trajectories adhere to constraints imposed by the upper level, such as time and distance separation. The algorithm combines a direct optimal control method for solving the lower level problem with a genetic algorithm, which is applied to the upper level combinatorial problem. The lower level problems are fully discretized by applying a trapezoidal collocation scheme provided by FALCON.m [1] and subsequently solved utilizing the interior point NLP solver IPOPT [2]. The discretization is performed during initialization of the algorithm and reused during execution to minimize computational effort. For the upper level problem an efficient mutation operator is introduced, which exploits the information contained within the Lagrange multiplier of the discretized arrival time constraint. The algorithm is validated against a test case scenario comprising five aircraft destined for runway 08L of Munich airport, which en- ter the terminal maneuvering area within four minutes at multiple way points. Aircraft dynamics are represented by a model derived from BADA 3. The performance of the algorithm allows the application on a pre-tactical level for a limited number of arriving aircraft.     «

A bi-level algorithm is developed to determine the optimal arrival sequence w.r.t a specific upper level objective function, e.g. minimizing pollutant emissions or maximizing runway throughput. Within a sequence it is assumed that all aircraft are operated optimally (lower level optimization), minimizing individual fuel consumption. However, all aircraft trajectories adhere to constraints imposed by the upper level, such as time and distance separation. The algorithm combines a direct optimal co...     »