Blanco, Marco ;
Borndörfer, Ralf ;
Hoang, NamDung ;
Kaier, Anton ;
Schienle, Adam ;
Schlechte, Thomas ;
Schlobach, Swen
Solving Time Dependent Shortest Path Problems on Airway Networks Using SuperOptimal Wind
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 timedependent shortest path problem with piecewise linear travel time functions, and a timedependent shortest path problem with piecewise differentiable travel time functions.
The shortest path problem and its timedependent 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 applicationspecific "superoptimal 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.
BibTeX  Entry
@InProceedings{blanco_et_al:OASIcs:2016:6536,
author = {Marco Blanco and Ralf Bornd{\"o}rfer and NamDung Hoang and Anton Kaier and Adam Schienle and Thomas Schlechte and Swen Schlobach},
title = {{Solving Time Dependent Shortest Path Problems on Airway Networks Using SuperOptimal Wind}},
booktitle = {16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)},
pages = {12:112:15},
series = {OpenAccess Series in Informatics (OASIcs)},
ISBN = {9783959770217},
ISSN = {21906807},
year = {2016},
volume = {54},
editor = {Marc Goerigk and Renato Werneck},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6536},
URN = {urn:nbn:de:0030drops65360},
doi = {10.4230/OASIcs.ATMOS.2016.12},
annote = {Keywords: shortest path problem, A*, flight trajectory optimization, preprocessing, contraction hierarchies, timedependent shortest path problem}
}
2016
Keywords: 

shortest path problem, A*, flight trajectory optimization, preprocessing, contraction hierarchies, timedependent shortest path problem 
Seminar: 

16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)

Issue date: 

2016 
Date of publication: 

2016 