License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.ATMOS.2022.2
URN: urn:nbn:de:0030-drops-171068
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17106/
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Borndörfer, Ralf ; Danecker, Fabian ; Weiser, Martin

A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization

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OASIcs-ATMOS-2022-2.pdf (0.7 MB)

Abstract

We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen’s algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage.

BibTeX - Entry

@InProceedings{borndorfer_et_al:OASIcs.ATMOS.2022.2,
  author =	{Bornd\"{o}rfer, Ralf and Danecker, Fabian and Weiser, Martin},
  title =	{{A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization}},
  booktitle =	{22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)},
  pages =	{2:1--2:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-259-4},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{106},
  editor =	{D'Emidio, Mattia and Lindner, Niels},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17106},
  URN =		{urn:nbn:de:0030-drops-171068},
  doi =		{10.4230/OASIcs.ATMOS.2022.2},
  annote =	{Keywords: shortest path, flight planning, free flight, discretization error bounds, optimal control, discrete optimization, global optimization}
}

Keywords: shortest path, flight planning, free flight, discretization error bounds, optimal control, discrete optimization, global optimization
Collection: 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)
Issue Date: 2022
Date of publication: 06.09.2022

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