We present two bilevel programming formulations for the aircraft deconfliction problem: one based on speed regulation in k dimensions, the other on heading angle changes in 2 dimensions. We propose three reformulations of each problem based on KKT conditions and on two different duals of the lower-level subproblems. We also propose a cut generation algorithm to solve the bilevel formulations. Finally, we present computational results on a variety of instances.

中文翻译：

---

使用双层编程检测和解决飞机冲突

我们针对飞机的冲突问题提出了两种双层编程公式：一种基于k维度的速度调节，另一种基于2维的航向角变化。我们根据KKT条件和较低级别子问题的两个不同对偶，建议对每个问题进行三个重新表述。我们还提出了切割生成算法来解决双层配方。最后，我们给出了各种实例的计算结果。