A mixed integer linear programming model for multi-sector planning using speed and heading changes

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 s. 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.