eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2017-09-04
15:1
15:14
10.4230/OASIcs.ATMOS.2017.15
article
Cost Projection Methods for the Shortest Path Problem with Crossing Costs
Blanco, Marco
Borndörfer, Ralf
Dung Hoàng, Nam
Kaier, Anton
Casas, Pedro M.
Schlechte, Thomas
Schlobach, Swen
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 transforms crossing costs into shadow costs on individual arcs, thus approximating the SPPCC by a standard shortest path problem. We evaluate all algorithms' performance on real-world flight trajectory optimization instances, obtaining very good à posteriori error bounds.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol059_atmos2017/OASIcs.ATMOS.2017.15/OASIcs.ATMOS.2017.15.pdf
shortest path problem
resource constrained shortest path
crossing costs
flight trajectory optimization
overflight fees
cost projection