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Solving air traffic conflict problems via local continuous optimization

Author

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  • Peyronne, Clément
  • Conn, Andrew R.
  • Mongeau, Marcel
  • Delahaye, Daniel

Abstract

This paper first introduces an original trajectory model using B-splines and a new semi-infinite programming formulation of the separation constraint involved in air traffic conflict problems. A new continuous optimization formulation of the tactical conflict-resolution problem is then proposed. It involves very few optimization variables in that one needs only one optimization variable to determine each aircraft trajectory. Encouraging numerical experiments show that this approach is viable on realistic test problems. Not only does one not need to rely on the traditional, discretized, combinatorial optimization approaches to this problem, but, moreover, local continuous optimization methods, which require relatively fewer iterations and thereby fewer costly function evaluations, are shown to improve the performance of the overall global optimization of this non-convex problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:2:p:502-512
    DOI: 10.1016/j.ejor.2014.08.045
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    References listed on IDEAS

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    1. 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.
    2. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
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    Cited by:

    1. 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.
    2. Sadeque Hamdan & Oualid Jouini & Ali Cheaitou & Zied Jemai & Tobias Andersson Granberg, 2023. "On the binary formulation of air traffic flow management problems," Annals of Operations Research, Springer, vol. 321(1), pages 267-279, February.
    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.
    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.

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