  As air traffic volume is continuously increasing, it has become a priority to
improve traffic control algorithms to handle future air travel demand and
improve airspace capacity. We address the conflict resolution problem in air
traffic control using a novel approach for aircraft collision avoidance with
trajectory recovery. We present a two-stage algorithm that first solves all
initial conflicts by adjusting aircraft headings and speeds, before identifying
the optimal time for aircraft to recover towards their target destination. The
collision avoidance stage extends an existing mixed-integer programming
formulation to heading control. For the trajectory recovery stage, we introduce
a novel exact mixed-integer programming formulation as well as a greedy
heuristic algorithm. The proposed two-stage approach guarantees that all
trajectories during both the collision avoidance and recovery stages are
conflict-free. Numerical results on benchmark problems show that the proposed
heuristic for trajectory recovery is competitive while also emphasizing the
difficulty of this optimization problem. The proposed approach can be used as a
decision-support tool for introducing automation in air traffic control.
