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Documents authored by Schlobach, Swen

Document
DOI: 10.4230/OASIcs.ATMOS.2017.15
Cost Projection Methods for the Shortest Path Problem with Crossing Costs

Authors: Marco Blanco, Ralf Borndörfer, Nam Dung Hoàng, Anton Kaier, Pedro M. Casas, Thomas Schlechte, and Swen Schlobach

Published in: OASIcs, Volume 59, 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)

Abstract
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.
Cite as

Marco Blanco, Ralf Borndörfer, Nam Dung Hoàng, Anton Kaier, Pedro M. Casas, Thomas Schlechte, and Swen Schlobach. Cost Projection Methods for the Shortest Path Problem with Crossing Costs. In 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017). Open Access Series in Informatics (OASIcs), Volume 59, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{blanco_et_al:OASIcs.ATMOS.2017.15,
  author =	{Blanco, Marco and Bornd\"{o}rfer, Ralf and Dung Ho\`{a}ng, Nam and Kaier, Anton and Casas, Pedro M. and Schlechte, Thomas and Schlobach, Swen},
  title =	{{Cost Projection Methods for the Shortest Path Problem with Crossing Costs}},
  booktitle =	{17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)},
  pages =	{15:1--15:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-042-2},
  ISSN =	{2190-6807},
  year =	{2017},
  volume =	{59},
  editor =	{D'Angelo, Gianlorenzo and Dollevoet, Twan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2017.15},
  URN =		{urn:nbn:de:0030-drops-78939},
  doi =		{10.4230/OASIcs.ATMOS.2017.15},
  annote =	{Keywords: shortest path problem, resource constrained shortest path, crossing costs, flight trajectory optimization, overflight fees, cost projection}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2016.12
Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind

Authors: Marco Blanco, Ralf Borndörfer, Nam-Dung Hoang, Anton Kaier, Adam Schienle, Thomas Schlechte, and Swen Schlobach

Published in: OASIcs, Volume 54, 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)

Abstract
We study the Flight Planning Problem for a single aircraft, which deals with finding a path of minimal travel time in an airway network. Flight time along arcs is affected by wind speed and direction, which are functions of time. We consider three variants of the problem, which can be modeled as, respectively, a classical shortest path problem in a metric space, a time-dependent shortest path problem with piecewise linear travel time functions, and a time-dependent shortest path problem with piecewise differentiable travel time functions. The shortest path problem and its time-dependent variant have been extensively studied, in particular, for road networks. Airway networks, however, have different characteristics: the average node degree is higher and shortest paths usually have only few arcs. We propose A* algorithms for each of the problem variants. In particular, for the third problem, we introduce an application-specific "super-optimal wind" potential function that overestimates optimal wind conditions on each arc, and establish a linear error bound. We compare the performance of our methods with the standard Dijkstra algorithm and the Contraction Hierarchies (CHs) algorithm. Our computational results on real world instances show that CHs do not perform as well as on road networks. On the other hand, A* guided by our potentials yields very good results. In particular, for the case of piecewise linear travel time functions, we achieve query times about 15 times shorter than CHs.
Cite as

Marco Blanco, Ralf Borndörfer, Nam-Dung Hoang, Anton Kaier, Adam Schienle, Thomas Schlechte, and Swen Schlobach. Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind. In 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016). Open Access Series in Informatics (OASIcs), Volume 54, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{blanco_et_al:OASIcs.ATMOS.2016.12,
  author =	{Blanco, Marco and Bornd\"{o}rfer, Ralf and Hoang, Nam-Dung and Kaier, Anton and Schienle, Adam and Schlechte, Thomas and Schlobach, Swen},
  title =	{{Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind}},
  booktitle =	{16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)},
  pages =	{12:1--12:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-021-7},
  ISSN =	{2190-6807},
  year =	{2016},
  volume =	{54},
  editor =	{Goerigk, Marc and Werneck, Renato F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2016.12},
  URN =		{urn:nbn:de:0030-drops-65360},
  doi =		{10.4230/OASIcs.ATMOS.2016.12},
  annote =	{Keywords: shortest path problem, A*, flight trajectory optimization, preprocessing, contraction hierarchies, time-dependent shortest path problem}
}
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