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Mixed-integer nonlinear programming for aircraft conflict avoidance by sequentially applying velocity and heading angle changes

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  • Cafieri, Sonia
  • Omheni, Riadh

Abstract

We consider the problem of aircraft conflict avoidance in Air Traffic Management systems. Given an initial configuration of a number of aircraft sharing the same airspace, the main goal of conflict avoidance is to guarantee that a minimum safety distance between each pair of aircraft is always respected during their flights. We consider aircraft separation achieved by heading angle deviations, and propose a mixed 0–1 nonlinear optimization model, that is then combined with another one which is based on aircraft speed regulation. A two-step solution approach is proposed, where the two models are sequentially solved using a state-of-the-art mixed-integer nonlinear programming solver. Numerical results validate the proposed approach and clearly show the benefit of combining the two considered separation maneuvers.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:1:p:283-290
    DOI: 10.1016/j.ejor.2016.12.010
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    References listed on IDEAS

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    1. David Rey & Christophe Rapine & Rémy Fondacci & Nour-Eddin El Faouzi, 2016. "Subliminal Speed Control in Air Traffic Management: Optimization and Simulation," Transportation Science, INFORMS, vol. 50(1), pages 240-262, February.
    2. 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.
    3. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    4. 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.
    5. Michael R. Bussieck & Arne Stolbjerg Drud & Alexander Meeraus, 2003. "MINLPLib—A Collection of Test Models for Mixed-Integer Nonlinear Programming," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 114-119, February.
    6. 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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    Cited by:

    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. Md Saiful Islam & Md Sarowar Morshed & Md. Noor-E-Alam, 2022. "A Computational Framework for Solving Nonlinear Binary Optimization Problems in Robust Causal Inference," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3023-3041, November.
    3. Li, Xin & Pan, Yanchun & Jiang, Shiqiang & Huang, Qiang & Chen, Zhimin & Zhang, Mingxia & Zhang, Zuoyao, 2021. "Locate vaccination stations considering travel distance, operational cost, and work schedule," Omega, Elsevier, vol. 101(C).
    4. 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.
    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. 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.
    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.

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