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Aircraft conflict resolution with trajectory recovery using mixed-integer programming

Author

Listed:
  • Fernando Dias

    (Aalto University)

  • David Rey

    (Université Côte d’Azur)

Abstract

To guarantee the safety of flight operations, decision-support systems for air traffic control must be able to improve the usage of airspace capacity and handle increasing demand. This study addresses the aircraft conflict avoidance and trajectory recovery problem. The problem of finding the least deviation conflict-free aircraft trajectories that guarantee the return to a target waypoint is highly complex due to the nature of the nonlinear trajectories that are sought. We present a two-stage iterative algorithm that first solves initial conflicts by manipulating their speed and heading control and then identifying each aircraft’s optimal time to recover its trajectory towards their nominal one. We extend existing mixed-integer programming formulations by modelling speed and heading control as continuous variables while recovery time is treated as a discrete variable. We develop a novel iterative approach which shows that the trajectory recovery costs can be anticipated by inducing avoidance trajectories with higher deviation, therefore obtaining earlier recovery time within a few iterations. Numerical results on benchmark conflict resolution problems show that this approach can solve instances with up to 30 aircraft within 10 min.

Suggested Citation

  • Fernando Dias & David Rey, 2024. "Aircraft conflict resolution with trajectory recovery using mixed-integer programming," Journal of Global Optimization, Springer, vol. 90(4), pages 1031-1067, December.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:4:d:10.1007_s10898-024-01393-1
    DOI: 10.1007/s10898-024-01393-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Nourelhouda Dougui & Daniel Delahaye & Stéphane Puechmorel & Marcel Mongeau, 2013. "A light-propagation model for aircraft trajectory planning," Journal of Global Optimization, Springer, vol. 56(3), pages 873-895, July.
    4. 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.
    5. 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.
    6. 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.
    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. 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.
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