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Cost Projection Methods for the Shortest Path Problem with Crossing Costs

  • Real world routing problems, e.g., in the airline industry or in public and rail transit, can feature complex non-linear cost functions. An important case are costs for crossing regions, such as countries or fare zones. We introduce the shortest path problem with crossing costs (SPPCC) to address such situations; it generalizes the classical shortest path problem and variants such as the resource constrained shortest path problem and the minimum label path problem. Motivated by an application in flight trajectory optimization with overflight costs, we focus on the case in which the crossing costs of a region depend only on the nodes used to enter or exit it. We propose an exact Two-Layer-Dijkstra Algorithm as well as a novel cost-projection linearization technique that approximates crossing costs by shadow costs on individual arcs, thus reducing the SPPCC to a standard shortest path problem. We evaluate all algorithms’ performance on real-world flight trajectory optimization instances, obtaining very good à posteriori error bounds.

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Author:Marco Blanco, Ralf BorndörferORCiD, Nam-Dung Hoang, Anton Kaier, Pedro Maristany de las CasasORCiD, Thomas Schlechte, Swen Schlobach
Editor:Gianlorenzo D'Angelo, Twan Dollevoet
Document Type:In Proceedings
Parent Title (German):17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)
Year of first publication:2017
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
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