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Heuristic Variants of A\(^*\) Search for 3D Flight Planning

  • Anders N. Knudsen
  • Marco Chiarandini
  • Kim S. Larsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)

Abstract

A crucial component of a flight plan to be submitted for approval to a control authority in the pre-flight phase is the prescription of a sequence of airways and airway points in the sky that an aircraft has to follow to cover a given route. The generation of such a path in the 3D network that models the airways must respect a number of constraints. They generally state that if a set of points or airways is visited then another set of points or airways must be avoided or visited. Paths are then selected on the basis of cost considerations. The cost of traversing an airway depends, directly, on fuel consumption and on traversing time, and, indirectly, on weight and on weather conditions.

Path finding algorithms based on A\(^*\) search are commonly used in automatic planning. However, the constraints and the dependency structure of the costs invalidate the classic domination criterion in these algorithms. A common approach to tackle the increased computational effort is to decompose the problem heuristically into a sequence of horizontal and vertical route optimizations. Using techniques recently designed for the simplified 2D context, we address the 3D problem directly. We compare the direct approach with the decomposition approach. We enhance both approaches with ad hoc heuristics that exploit the expected appeal of routes to speed-up the solution process. We show that, on data resembling those arising in the context of European airspaces, the direct approach is computationally practical and leads to results of better quality than the decomposition approach.

References

  1. 1.
    Batz, G.V., Geisberger, R., Sanders, P., Vetter, C.: Minimum time-dependent travel times with contraction hierarchies. ACM J. Exp. Algorithmics 18(1), 1.4:1–1.4:43 (2013). Article no. 1.4MathSciNetMATHGoogle Scholar
  2. 2.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1(1), 269–271 (1959)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)CrossRefGoogle Scholar
  4. 4.
    Yinnone, H.: On paths avoiding forbidden pairs of vertices in a graph. Discrete Appl. Math. 74(1), 85–92 (1997)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Blanco, M., Borndörfer, R., Hoang, N.-D., Kaier, A., Schienle, A., Schlechte, T., Schlobach, S.: 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). OpenAccess Series in Informatics (OASIcs), vol. 54, pp. 12:1–12:15. Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2016)Google Scholar
  6. 6.
    Bast, H., Delling, D., Goldberg, A., Müller-Hannemann, M., Pajor, T., Sanders, P., Wagner, D., Werneck, R.F.: Route planning in transportation networks (2015). arXiv:1504.05140 [cs.DS]
  7. 7.
    Knudsen, A.N., Chiarandini, M., Larsen, K.S.: Constraint handling in flight planning. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 354–369. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66158-2_23CrossRefGoogle Scholar
  8. 8.
    Knudsen, A.N., Chiarandini, M., Larsen, K.S.: Vertical optimization of resource dependent flight paths. In: 22nd European Conference on Artificial Intelligence (ECAI). Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 639–645. IOS Press (2016)Google Scholar
  9. 9.
    Blanco, M., Borndörfer, R., Dung Hoàng, N., Kaier, A., Casas, P.M., Schlechte, T., Schlobach, S.: Cost projection methods for the shortest path problem with crossing costs. In: D’Angelo, G., Dollevoet, T., (eds.) 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS). OpenAccess Series in Informatics (OASIcs), vol. 59, pp. 15:1–15:14. Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2017)Google Scholar
  10. 10.
    Jensen, C.K., Chiarandini, M., Larsen, K.S.: Flight planning in free route airspaces. In: D’Angelo, G., Dollevoet, T., (eds.) 17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS). OpenAccess Series in Informatics (OASIcs), vol. 59, pp. 14:1–14:14. Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2017)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Anders N. Knudsen
    • 1
  • Marco Chiarandini
    • 1
  • Kim S. Larsen
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark

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