Logic-Constrained Shortest Paths for Flight Planning

Abstract: The logic-constrained shortest path problem (LCSPP) combines a one-to-one shortest path problem with satisfiability constraints imposed on the routing graph. This setting arises in flight planning, where air traffic control (ATC) authorities are enforcing a set of traffic flow restrictions (TFRs) on aircraft routes in order to increase safety and throughput. We propose a new branch and bound-based algorithm for the LCSPP. The resulting algorithm has three main degrees of freedom: the node selection rule, the branching rule and the conflict. While node selection and branching rules have been long studied in the MIP and SAT communities, most of them cannot be applied out of the box for the LCSPP. We review the existing literature and develop tailored variants of the most prominent rules. The conflict, the set of variables to which the branching rule is applied, is unique to the LCSPP. We analyze its theoretical impact on the B&B algorithm. In the second part of the paper, we show how to model the flight planning problem with TFRs as an LCSPP and solve it using the branch and bound algorithm. We demonstrate the algorithm's efficiency on a dataset consisting of a global flight graph and a set of around 20000 real TFRs obtained from our industry partner Lufthansa Systems GmbH. We make this dataset publicly available. Finally, we conduct an empirical in-depth analysis of dynamic shortest path algorithms, node selection rules, branching rules and conflicts. Carefully choosing an appropriate combination yields an improvement of an order of magnitude compared to an uninformed choice.