Abstract The Multi-Sector Planning (MSP) concept, adopted in both the SESAR and NextGen projects, promotes the control of aircraft and resolution of conflicts over a medium time horizon to reduce and balance controller workload. In the context of MSP, we propose a first formulation of the complexity resolution problem that allows trajectory modifications using both speed and heading changes assuming exact knowledge of aircraft positions. This model is also the first to have the capacity to ensure workload balancing among sectors in a Multi-Sector Area (MSA). The number of crossing conflicts in a sector is used as a measure of controller workload. This problem is formulated as a mixed integer linear programming model that allows obtaining optimal solutions. This model ensures neighbor trajectory recovery and minimal delays. This model was tested on a set of conflict detection and resolution benchmark test problems with up to 300 simultaneous conflicts. Conflict-free solutions were obtained in less than 1.4 seconds. The model was also tested on several distinct sets of randomly generated problems with an MSA of four sectors and up to 150 aircraft. The number of crossing conflicts was reduced by more than 99 % with a computation time smaller than four seconds. It was found that it is beneficial to allow the use of both speed and heading changes in high traffic situations. It was also found that considering workload balancing allows the minimization of the total workload in the MSA while preventing overloading some sectors.

中文翻译：

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使用速度和航向变化的多部门规划混合整数线性规划模型

摘要 SESAR 和 NextGen 项目均采用多部门规划 (MSP) 概念，促进飞机控制和冲突解决在中等时间范围内，以减少和平衡控制器的工作量。在 MSP 的背景下，我们提出了复杂性解决问题的第一个公式，假设飞机位置的准确知识，允许使用速度和航向变化来修改轨迹。该模型也是第一个能够确保多扇区区域 (MSA) 中的扇区之间的工作负载平衡的模型。扇区中交叉冲突的数量用作控制器工作量的度量。这个问题被表述为允许获得最佳解决方案的混合整数线性规划模型。该模型确保邻居轨迹恢复和最小延迟。该模型在一组冲突检测和解决基准测试问题上进行了测试，同时冲突多达 300 个。在不到 1.4 秒的时间内获得了无冲突的解决方案。该模型还在几组不同的随机生成问题上进行了测试，MSA 有四个扇区，最多 150 架飞机。交叉冲突的数量减少了 99% 以上，计算时间小于 4 秒。发现允许在高交通情况下同时使用速度和航向变化是有益的。还发现考虑工作负载平衡允许最小化 MSA 中的总工作负载，同时防止某些扇区过载。在不到 1.4 秒的时间内获得了无冲突的解决方案。该模型还在几组不同的随机生成问题上进行了测试，MSA 有四个扇区，最多 150 架飞机。交叉冲突的数量减少了 99% 以上，计算时间小于 4 秒。发现允许在高交通情况下同时使用速度和航向变化是有益的。还发现考虑工作负载平衡允许最小化 MSA 中的总工作负载，同时防止某些扇区过载。在不到 1.4 秒的时间内获得了无冲突的解决方案。该模型还在几组不同的随机生成问题上进行了测试，MSA 有四个扇区，最多 150 架飞机。交叉冲突的数量减少了 99% 以上，计算时间小于 4 秒。发现允许在高交通情况下同时使用速度和航向变化是有益的。还发现考虑工作负载平衡允许最小化 MSA 中的总工作负载，同时防止某些扇区过载。发现允许在高交通情况下同时使用速度和航向变化是有益的。还发现考虑工作负载平衡允许最小化 MSA 中的总工作负载，同时防止某些扇区过载。发现允许在高交通情况下同时使用速度和航向变化是有益的。还发现考虑工作负载平衡允许最小化 MSA 中的总工作负载，同时防止某些扇区过载。