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Mixed-integer nonlinear and continuous optimization formulations for aircraft conflict avoidance via heading and speed deviations

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  • Cafieri, Sonia
  • Conn, Andrew R.
  • Mongeau, Marcel

Abstract

We introduce two new optimization models for the aircraft conflict avoidance problem that aims at issuing decisions on both speed and heading-angle deviations to keep aircraft pairwise separated by a given separation distance. The first model is a new mixed-integer nonlinear formulation. The second model is a continuous optimization formulation, less typical in aircraft conflict avoidance. The advantages of the two models are combined within a three-phase method that we propose to solve the problem to global optimality. Computational experiments on various instances from the literature yield very promising results, and show the effectiveness of the proposed models and of the three-phase solution approach.

Suggested Citation

  • Cafieri, Sonia & Conn, Andrew R. & Mongeau, Marcel, 2023. "Mixed-integer nonlinear and continuous optimization formulations for aircraft conflict avoidance via heading and speed deviations," European Journal of Operational Research, Elsevier, vol. 310(2), pages 670-679.
    • Handle: RePEc:eee:ejores:v:310:y:2023:i:2:p:670-679
    DOI: 10.1016/j.ejor.2023.03.002
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    References listed on IDEAS

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    1. Josef Kallrath & Steffen Rebennack, 2014. "Cutting ellipses from area-minimizing rectangles," Journal of Global Optimization, Springer, vol. 59(2), pages 405-437, July.
    2. 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.
    3. Pietro Belotti & Pierre Bonami & Matteo Fischetti & Andrea Lodi & Michele Monaci & Amaya Nogales-Gómez & Domenico Salvagnin, 2016. "On handling indicator constraints in mixed integer programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 545-566, December.
    4. Peyronne, Clément & Conn, Andrew R. & Mongeau, Marcel & Delahaye, Daniel, 2015. "Solving air traffic conflict problems via local continuous optimization," European Journal of Operational Research, Elsevier, vol. 241(2), pages 502-512.
    5. Dias, Fernando H.C. & Hijazi, Hassan & Rey, David, 2022. "Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution," European Journal of Operational Research, Elsevier, vol. 296(2), pages 520-538.
    6. Lehouillier, Thibault & Omer, Jérémy & Soumis, François & Desaulniers, Guy, 2017. "Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 696-712.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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