Solving the Air Conflict Resolution Problem Under Uncertainty Using an Iterative Biobjective Mixed Integer Programming Approach
研究了在风效应、速度预测误差和机动执行延迟等不确定性下，如何通过几何方法推导最小距离和冲突概率，并利用迭代双目标混合整数规划生成帕累托前沿解，为空中交通管制员提供兼顾燃油效率和未来机动调整概率的多种解决方案。
In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuvers. Using a geometrical approach, we derive an analytical expression for the minimum distance between aircraft, along with the corresponding probability of conflict. These expressions are incorporated into an existing deterministic model for conflict resolution. This model solves the problem as a maximum clique of minimum weight in a graph whose vertices represent possible maneuvers and where edges link conflict-free maneuvers of different aircraft. We then present a solution procedure focusing on two criteria, namely, fuel efficiency and the probability of reissuing maneuvers in the future: we iteratively generate Pareto front solutions to provide the controller with a set of possible solutions where she can choose the one corresponding the most to her preferences. Intensive Monte Carlo simulations validate the expressions derived for the minimum distance and the probability of conflict. Computational results highlight that up to 10 different solutions for instances involving up to 35 aircraft are generated within 3 minutes.