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A New Variant of the Minimum-Weight Maximum-Cardinality Clique Problem to Solve Conflicts between Aircraft

  • Thibault LehouillierEmail author
  • Jérémy Omer
  • François Soumis
  • Guy Desaulniers
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 359)

Abstract

In this article, we formulate a new variant of the problem of finding a maximum clique of minimum weight in a graph applied to the detection and resolution of conflicts between aircraft. The innovation of the model relies on the cost structure: the cost of the vertices cannot be determined a priori, since they depend on the vertices in the clique. We apply this formulation to the resolution of conflicts between aircraft by building a graph whose vertices correpond to a set of maneuvers and whose edges link conflict-free maneuvers. A maximum clique of minimal weight yields a conflict-free situation involving all aircraft and minimizing the costs induced. We solve the problem as a mixed integer linear program. Simulations on a benchmark of complex instances highlight computational times smaller than 20 seconds for situations involving up to 20 aircraft.

Keywords

Air Traffic Control Conflict Resolution Maximum Clique Mixed Integer Linear Programming 

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References

  1. 1.
    Lehouillier, T., Omer, J., Soumis, F., Allignol, C.: Interactions between operations and planning in air traffic control. In: Proceedings of the 2nd International Conference of Research in Air Transportation, Istanbul (2014)Google Scholar
  2. 2.
    Campo, M., Javier, F.: The collision avoidance problem: methods and algorithms. Ph.D. dissertation (2010)Google Scholar
  3. 3.
    Omer, J., Farges, J.-L.: Hybridization of nonlinear and mixed-integer linear programming for aircraft separation with trajectory recovery. IEEE Transactions on Intelligent Transportation Systems 14(3), 1218–1230 (2013)CrossRefGoogle Scholar
  4. 4.
    Omer, J.: A space-discretized mixed-integer linear model for air-conflict resolution with speed and heading maneuvers (2014)Google Scholar
  5. 5.
    Pallottino, L., Feron, E.M., Bicchi, A.: Conflict resolution problems for air traffic management systems solved with mixed integer programming. IEEE Transactions on Intelligent Transportation Systems 3(1), 3–11 (2002)CrossRefGoogle Scholar
  6. 6.
    Alonso-Ayuso, A., Escudero, L.F., Martin-Campo, F.J., Javier, F.: Collision avoidance in air traffic management: a mixed-integer linear optimization approach. IEEE Transactions on Intelligent Transportation Systems 12(1), 47–57 (2011)CrossRefGoogle Scholar
  7. 7.
    Durand, N., Alliot, J.-M., Noailles, J.: Automatic aircraft conflict resolution using genetic algorithms. In: Proceedings of the Symposium Applied Computing, Philadelphia (1996)Google Scholar
  8. 8.
    Alonso-Ayuso, A., Escudero, L.F., Martín-Campo, F.J., Mladenović, N.: A vns metaheuristic for solving the aircraft conflict detection and resolution problem by performing turn changes. Journal of Global Optimization, 1–14 (2014)Google Scholar
  9. 9.
    Vela, A.E.: Understanding conflict-resolution taskload: implementing advisory conflict-detection and resolution algorithms in an airspace (2011)Google Scholar
  10. 10.
    Barnier, N., Brisset, P.: Graph coloring for air traffic flow management. Annals of Operations Research 130(1-4), 163–178 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Handbook of combinatorial optimization, pp. 1–74. Springer (1999)Google Scholar
  12. 12.
    Wu, Q., Hao, J.-K.: A review on algorithms for maximum clique problems. European Journal of Operational Research (2014)Google Scholar
  13. 13.
    User manual for the Base of Aircraft Data (BADA), Eurocontrol, Tech. Rep. 11/03/08-08 (2011)Google Scholar
  14. 14.
    Paielli, R.A.: Modeling maneuver dynamics in air traffic conflict resolution. Journal of Guidance, Control, and Dynamics 26(3), 407–415 (2003)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thibault Lehouillier
    • 1
    Email author
  • Jérémy Omer
    • 1
  • François Soumis
    • 1
  • Guy Desaulniers
    • 1
  1. 1.Group on Research in Decision AnalysisMontrealCanada

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