Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

We address the aircraft conflict resolution problem in air traffic control. introduce new mixed-integer programming formulations for with speed, heading and altitude control which are based on disjunctive linear separation conditions. first examine two-dimensional speed represented as continuous decision variables. show that proposed conditions equivalent to classical nonlinear separation. Further, we characterise conflict-free trajectories velocity bounds propose a simple pre-processing algorithm identify pairs either always conflict-free, or cannot be separated using only. then incorporate lexicographic optimisation formulation aims minimise number of flight level changes before resolving outstanding conflicts via The nonconvex, convex relaxations, decomposition methods constraint generation algorithms solve guaranteed optimality. Numerical experiments four types benchmarking instances conducted test performance formulations. method is compared against two benchmarks state-of-the-art approaches problem. Our numerical results largely outperforms both terms runtime able significantly more global