We provide a general and malleable heuristic for the air conflict resolution problem. This heuristic is based on a new neighborhood structure for searching the solution space of trajectories and flight-levels. Using unsupervised learning, the core idea of our heuristic is to cluster the conflict points and disperse them in various flight levels. Our first algorithm is called Cluster & Disperse and in each iteration it assigns the most problematic flights in each cluster to another flight-level. In effect, we shuffle them between the flight-levels until we achieve a well-balanced configuration. The Cluster & Disperse algorithm then uses any horizontal plane conflict resolution algorithm as a subroutine to solve these well-balanced instances. Nevertheless, we develop a novel algorithm for the horizontal plane based on a similar idea. That is we cluster and disperse the conflict points spatially in the same flight level using the gradient descent and a social force. We use a novel maneuver making flights travel on an arc instead of a straight path which is based on the aviation routine of the Radius to Fix legs. Our algorithms can handle a high density of flights within a reasonable computation time. We put their performance in context with some notable algorithms from the literature. Being a general framework, a particular strength of the Cluster & Disperse is its malleability in allowing various constraints regarding the aircraft or the environment to be integrated with ease. This is in contrast to the models for instance based on mixed integer programming.

翻译：本文提出了一种通用且灵活的空中冲突解决启发式方法。该启发式方法基于一种新的邻域结构，用于搜索轨迹与飞行高度的解空间。其核心思想是利用无监督学习对冲突点进行聚类，并将其分散至不同飞行高度。我们的首个算法称为Cluster & Disperse，在每次迭代中，它将每个聚类中最具问题的航班重新分配至另一飞行高度。实际上，我们通过在飞行高度间调整航班分配，直至获得均衡的配置。随后，Cluster & Disperse算法可调用任意水平面冲突解决算法作为子程序来处理这些均衡化实例。尽管如此，我们基于相似思想开发了一种新颖的水平面冲突解决算法：通过梯度下降法与社会力模型，在同一飞行高度内对冲突点进行空间聚类与分散。我们采用了一种创新机动策略，使航班沿圆弧而非直线飞行，该策略基于航空惯例中的Radius to Fix航段设计。我们的算法能够在合理计算时间内处理高密度航班流，并将其性能与文献中若干经典算法进行了对比分析。作为一个通用框架，Cluster & Disperse的突出优势在于其灵活性，能够轻松整合各类航空器或环境约束，这与基于混合整数规划等模型形成鲜明对比。