Journal of Global Optimization

, Volume 58, Issue 4, pp 613–629 | Cite as

Aircraft deconfliction with speed regulation: new models from mixed-integer optimization

  • Sonia Cafieri
  • Nicolas Durand


Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact solver. Since the problem is very difficult to solve, we also propose a heuristic procedure where the problem is decomposed and it is locally exactly solved. Computational results show that the proposed approach provides satisfactory results.


Air Traffic Management Conflict avoidance  Nonconvex mixed-integer nonlinear programming MINLP Modeling  Global exact solution Locally-optimal heuristic 



The authors are grateful to the anonymous referees for their constructive comments that helped improving the paper. The first author gratefully acknowledges financial support under grant ANR 12-JS02-009-01 “ATOMIC”.


  1. 1.
    Alonso-Ayuso, A., Escudero, L.F., Martín-Campo, F.J.: Collision avoidance in air traffic management: a mixed-integer linear optimization approach. IEEE Trans. Intell. Transp. Syst. 12(1), 47–57 (2011)CrossRefGoogle Scholar
  2. 2.
    Alonso-Ayuso, A., Escudero, L.F., Martín-Campo, F.J.: A mixed 01 nonlinear optimization model and algorithmic approach for the collision avoidance in ATM: velocity changes through a time horizon. Comput. Oper. Res. 39(14), 3136–3146 (2012)Google Scholar
  3. 3.
    Belotti, P., Lee, J., Liberti, L., Margot, F., Wächter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods Softw. 24(4), 597–634 (2009)CrossRefGoogle Scholar
  4. 4.
    Bonini, D., Dupré, C., Granger, G.: How ERASMUS can support an increase in capacity in 2020. In: Proceedings of the 7th International Conference on Computing, Communications and Control Technologies: CCCT 2009, Orlando, Florida (2009)Google Scholar
  5. 5.
    Durand N., Alliot J.M.: Optimal resolution of en-route conflict. In: Proceedings of the Eurocontrol/FAA ATM Seminar. Eurocontrol/FAA, (1997)Google Scholar
  6. 6.
    Durand, N., Alliot, J.M.: Ant-colony optimization for air traffic conflict resolution. In: Proceedings of the Eighth USA/Europe Air Traffic Management Research and Development Seminar. Eurocontrol/FAA (2009)Google Scholar
  7. 7.
    Durand, N., Alliot, J.M., Noailles, J.: Automatic aircraft conflict resolution using genetic algorithms. In: Proceedings of the Symposium on Applied Computing, Philadelphia. ACM (1996)Google Scholar
  8. 8.
    Durand, N., Granger, G.: Modeling the controller’s conflict detection task using fast time simulation. In: 30th Digital Avionics Systems Conference (DASC), Seattle, USA (2011)Google Scholar
  9. 9.
    EUROCONTROL: Eurocontrol long-term forecast : IFR Flight Movements 2010–2030. Technical report, Eurocontrol–Air Traffic Statistics and Forecasts (2010)Google Scholar
  10. 10.
    Fortet, R.: Application de l’algèbre de boole en recherche opérationelle. Revue Française de Recherche Opérationelle 4, 17–26 (1960)Google Scholar
  11. 11.
    Fourer, R., Gay, D.: The AMPL Book. Duxbury Press, Pacific Grove (2002)Google Scholar
  12. 12.
    Granger, G., Durand, N.: A traffic complexity approach through cluster analysis. In: Proceedings of the 5th ATM R &D Seminar, Budapest (2003)Google Scholar
  13. 13.
    Hammer, P.L., Rudeanu, S.: Boolean Methods in Operations Research and Related Areas. Springer, Berlin (1968)CrossRefGoogle Scholar
  14. 14.
    Kuchar, J., Yang, L.: A review of conflict detection and resolution modeling methods. IEEE Trans. Intell. Transp. Syst. 1(4), 179–189 (2000)CrossRefGoogle Scholar
  15. 15.
    Liberti, L., Cafieri, S., Tarissan, F.: Reformulations in mathematical programming: a computational approach. In: Abraham, A., Hassanien, A.-E., Siarry, P., Engelbrecht, A. (eds.) Foundations of Computational Intelligence (Global Optimization: Theoretical Foundations and Applications), vol. 203 of Studies in Computational Intelligence, pp. 153–234. Springer, Berlin (2009)Google Scholar
  16. 16.
    Martín-Campo, F.J.: The collision avoidance problem: methods and algorithms. Ph.D. thesis, Rey Juan Carlos University, Madrid (2010)Google Scholar
  17. 17.
    Pallottino, L., Feron, E., Bicchi, A.: Conflict resolution problems for air traffic management systems solved with mixed integer programming. IEEE Trans. Intell. Transp. Syst. 3(1), 3–11 (2002)CrossRefGoogle Scholar
  18. 18.
    Rey, D., Constans, S., Fondacci, R., Rapine, C.: A mixed integer linear model for potential conflict minimization by speed modulations. In: Proceedings of the International Conference on Research in Air Transportation, Budapest (2010)Google Scholar
  19. 19.
    Rey, D., Rapine, C., Fondacci, R., El Faouzi, N.-E.: Minimization of potential air conflicts through speed regulation. Transp. Res. Rec. J. Transp. Res. Board. 2300(1), 59–67(2012)Google Scholar
  20. 20.
    Richards, A., How, J.P.: Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In: American Control Conference, Anchorage, Alaska, (2002)Google Scholar
  21. 21.
    SESAR consortium: The european ATM master plan. Technical Report 1, European Commission and EUROCONTROL, (2009)Google Scholar
  22. 22.
    Vela, A., Solak, S., Singhose, W., Clarke, J.-P.: A mixed-integer program for flight-level assignment and speed control for conflict resolution. In: Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai (2009)Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Laboratoire MAIAAÉcole Nationale de l’Aviation CivileToulouseFrance

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