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Detecting and solving aircraft conflicts using bilevel programming

Author

Listed:
  • Martina Cerulli

    (École Polytechnique)

  • Claudia D’Ambrosio

    (École Polytechnique)

  • Leo Liberti

    (École Polytechnique)

  • Mercedes Pelegrín

    (École Polytechnique)

Abstract

We present two bilevel programming formulations for the aircraft deconfliction problem: one based on speed regulation in k dimensions, the other on heading angle changes in 2 dimensions. We propose three reformulations of each problem based on KKT conditions and on two different duals of the lower-level subproblems. We also propose a cut generation algorithm to solve the bilevel formulations. Finally, we present computational results on a variety of instances.

Suggested Citation

  • Martina Cerulli & Claudia D’Ambrosio & Leo Liberti & Mercedes Pelegrín, 2021. "Detecting and solving aircraft conflicts using bilevel programming," Journal of Global Optimization, Springer, vol. 81(2), pages 529-557, October.
    • Handle: RePEc:spr:jglopt:v:81:y:2021:i:2:d:10.1007_s10898-021-00997-1
    DOI: 10.1007/s10898-021-00997-1
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    References listed on IDEAS

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    1. Sonia Cafieri & Claudia D’Ambrosio, 2018. "Feasibility pump for aircraft deconfliction with speed regulation," Journal of Global Optimization, Springer, vol. 71(3), pages 501-515, July.
    2. M. Hosein Zare & Juan S. Borrero & Bo Zeng & Oleg A. Prokopyev, 2019. "A note on linearized reformulations for a class of bilevel linear integer problems," Annals of Operations Research, Springer, vol. 272(1), pages 99-117, January.
    3. Antonio Alonso-Ayuso & Laureano F. Escudero & F. Javier Martín-Campo, 2016. "Exact and Approximate Solving of the Aircraft Collision Resolution Problem via Turn Changes," Transportation Science, INFORMS, vol. 50(1), pages 263-274, February.
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    5. Cafieri, Sonia & Omheni, Riadh, 2017. "Mixed-integer nonlinear programming for aircraft conflict avoidance by sequentially applying velocity and heading angle changes," European Journal of Operational Research, Elsevier, vol. 260(1), pages 283-290.
    6. C. Audet & P. Hansen & B. Jaumard & G. Savard, 1997. "Links Between Linear Bilevel and Mixed 0–1 Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 273-300, May.
    7. Sonia Cafieri & Nicolas Durand, 2014. "Aircraft deconfliction with speed regulation: new models from mixed-integer optimization," Journal of Global Optimization, Springer, vol. 58(4), pages 613-629, April.
    8. Co, Christine G. & Tanchoco, J. M. A., 1991. "A review of research on AGVS vehicle management," Engineering Costs and Production Economics, Elsevier, vol. 21(1), pages 35-42, February.
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    Cited by:

    1. Mercedes Pelegrín & Martina Cerulli, 2023. "Aircraft Conflict Resolution: A Benchmark Generator," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 274-285, March.

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