文章基本信息

标题：Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind
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作者：Marco Blanco ; Ralf Bornd{\"o}rfer ; Nam-Dung Hoang 等
期刊名称：OASIcs : OpenAccess Series in Informatics
电子版ISSN：2190-6807
出版年度：2016
卷号：54
页码：1-15
DOI：10.4230/OASIcs.ATMOS.2016.12
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：shortest path problem; A*; flight trajectory optimization; preprocessing; contraction hierarchies; time-dependent shortest path problem