Mixed integer nonlinear programming for the three-dimensional aircraft conflict avoidance problem

In this paper, the problem of aircraft conflict avoidance is studied arising in Air Traffic Management systems. The initial configuration of all aircraft including position, velocities, heading angles, altitude and flight trajectories are known, and they are assumed to fly within a shared three-dimensional airspace. The aim of the problem is to find an optimal conflict avoidance strategy for the aircraft so that various conflicts situations can be avoided. A conflict occurs when the relative distance between any pairs of aircraft is less than the minimal safe separation during their flights. In order to ensure the safety of aircraft flight, a Mixed Integer Nonlinear Programming model (MINLP) for solving the three-dimensional conflict avoidance problem involving multiple aircrafts is proposed in this paper, where the aircraft are allowed to change simultaneously heading angle and velocity to achieve the separation. The illustration verifies the effectiveness of the method. The optimal solution of the problem can be obtained easily in a small computational time by using a standard global optimization solver to solve the proposed MINLP model.