A constraint-programming formulation for dynamic airspace sectorization

In this paper we consider the dynamic airspace sectorization problem (DASP) where airspace is partitioned into a number of sectors, each sector being assigned to a team of air traffic controllers. The objective of DASP is to balance the controllers' workload among the sectors and to simultaneously minimize the coordination workload between adjacent sectors. This problem is closely related to the graph partitioning problems. However, some specific constraints have to be taken into account (e.g., aircraft can not enter twice the same sector; aircraft have to stay in each crossed sector at least a given amount of time, etc.) and they make it difficult to use the most popular graph partitioning techniques of the literature. To solve the DASP, we introduce a constraint-programming formulation that can compute optimal solution for "small" instances of problem. A heuristic based on the notion of gain of Kernighan/Lin algorithm for graph partitioning is also introduced for finding a reasonable good initial solution for large size instances in a small amount of time. We also show how the constraint-programming formulation is used to re-optimize locally this initial solution.