Bi-level Cross Entropy Method and Optimal Control for Air Traffic Sequencing and Trajectory Optimization

In the paper presented a bi-level algorithmis introduced to determine the optimal sequence of arriving aircraft, assuming each aircraft follows an optimal trajectory. The objective func- tion, which can be chosen individually for each level, is set to minimize the combined fuel consumption of all aircraft combined in the upper level, which leads to an unconstrained com- binatorial optimization problem. Each of the lower level problems are defined to determine the trajectories granting the lowest individual fuel consumption for each aircraft, which can be formulated as an optimal control problem. Two algorithms are combined to solve the resulting bi-level problem, where the upper level objective is a function of the solutions of the lower level while the lower level problems include constraints dependening on the upper level optimization variables. The combinatorial sequencing problem is solved using the cross entropy method proposed by Rubinstein [1]. The solution of the lower level optimal control problems are obtained by applying a direct collocationmethod implemented in the optimal control tool FAL- CON.m[2]. The efficiency of the combined algorithmis enhanced by the implementation of an intelligent memory system to avoid unnecessary computations. The algorithm is validated by implementing a test case and benchmarked against the bi-level genetic algorithm presented in [3], showing superior performance.     «

In the paper presented a bi-level algorithmis introduced to determine the optimal sequence of arriving aircraft, assuming each aircraft follows an optimal trajectory. The objective func- tion, which can be chosen individually for each level, is set to minimize the combined fuel consumption of all aircraft combined in the upper level, which leads to an unconstrained com- binatorial optimization problem. Each of the lower level problems are defined to determine the trajectories granting the l...     »