6489
2017
eng
59
conferenceobject
0
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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.
17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)
yes
urn:nbn:de:0297-zib-64817
Creative Commons - CC BY - Namensnennung 4.0 International
Gianlorenzo D'Angelo
Thomas Schlechte
Marco Blanco
Twan Dollevoet
Ralf Borndörfer
Nam-Dung Hoang
Anton Kaier
Pedro Maristany de las Casas
Thomas Schlechte
Swen Schlobach
Mathematical Optimization
Blanco, Marco
Borndörfer, Ralf
Schlechte, Thomas
LHS-ATN
MODAL-RailLab
Maristany de las Casas, Pedro
MODAL-Gesamt