Constraint Handling in Flight Planning

  • Anders Nicolai Knudsen
  • Marco Chiarandini
  • Kim S. Larsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10416)


Flight routes are paths in a network, the nodes of which represent waypoints in a 3D space. A common approach to route planning is first to calculate a cheapest path in a 2D space, and then to optimize the flight cost in the third dimension. We focus on the problem of finding a cheapest path through a network describing the 2D projection of the 3D waypoints. In European airspaces, traffic flow is handled by heavily constraining the flight network. The constraints can have very diverse structures, among them a generalization of the forbidden pairs type. They invalidate the FIFO property, commonly assumed in shortest path problems. We formalize the problem and provide a framework for the description, representation and propagation of the constraints in path finding algorithms, best-first, and A\(^*\) search. In addition, we study a lazy approach to deal with the constraints. We conduct an experimental evaluation based on real-life data and conclude that our techniques for constraint propagation work best together with an iterative search approach, in which only constraints that are violated in previously found routes are introduced in the constraint set before the search is restarted.


  1. 1.
    Knudsen, A.N., Chiarandini, M., Larsen, K.S.: Vertical optimization of resource dependent flight paths. In: Twentysecond European Conference on Artificial Intelligence (ECAI). Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 639–645. IOS Press (2016)Google Scholar
  2. 2.
    Bast, H., Delling, D., Goldberg, A., Müller-Hannemann, M., Pajor, M., Sanders, T., Wagner, D., Werneck, R.F.: Route planning in transportation networks. Technical report. arXiv:1504.05140 [cs.DS] (2015)
  3. 3.
    Olivares, A., Soler, M., Staffetti, E.: Multiphase mixed-integer optimal control applied to 4D trajectory planning in air traffic management. In: Proceedings of the 3rd International Conference on Application and Theory of Automation in Command and Control Systems (ATACCS), pp. 85–94. ACM (2013)Google Scholar
  4. 4.
    de Jong, H.M.: Optimal Track Selection and 3-Dimensional Flight Planning: Theory and Practice of the Optimization Problem in air Navigation Under Space-Time Varying Meteorological Conditions. Staatsuitgeverij, Madison (1974)Google 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), pp. 12:1–12:15. Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2016)Google Scholar
  6. 6.
    Yinnone, H.: On paths avoiding forbidden pairs of vertices in a graph. Discret. Appl. Math. 74(1), 85–92 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kováč, J.: Complexity of the path avoiding forbidden pairs problem revisited. Discret. Appl. Math. 161(10–11), 1506–1512 (2013)MathSciNetzbMATHGoogle Scholar
  8. 8.
    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
  9. 9.
    Hooker, J.N., Ottosson, G.: Logic-based benders decomposition. Math. Program. 96(1), 33–60 (2003)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Anders Nicolai 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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