TY - CONF
A1 - Blanco, Marco
A1 - Borndörfer, Ralf
A1 - Hoang, Nam-Dung
A1 - Kaier, Anton
A1 - Maristany de las Casas, Pedro
A1 - Schlechte, Thomas
A1 - Schlobach, Swen
A2 - D'Angelo, Gianlorenzo
A2 - Dollevoet, Twan
T1 - Cost Projection Methods for the Shortest Path Problem with Crossing Costs
T2 - 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)
N2 - 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.
Y1 - 2017
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6489
VL - 59
ER -