A heuristic algorithm for aircraft 4D trajectory optimization based on bezier curve

In this study, we propose an aircraft 4D trajectory optimization model based on Bezier curve. Many real-world factors (such as winds, obstacles, uncertainties) and actions (the modification of departure time, the trajectory shape, aircraft speed and altitude) are taken into account. To solve the model, an improved simulated annealing algorithm with two phases was proposed: the first phase for reducing the number of conflicts and the second phase for decreasing the total flight time. A national-size dataset for France which is provided by a fast time simulator (ΠRATS) is used as a case study. The experimental results show that the algorithm provides conflict-free trajectories within a very short time for all instances. For the objective to deconflict aircraft, the algorithm is almost linearly scalable for large-scale instances. For a given limited run time (such as 6 hours), the algorithm provides good solutions with small values of objective function (total flight time, changes of aircraft speed and obstacles encounters).