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Exact and Approximate Solving of the Aircraft Collision Resolution Problem via Turn Changes

Author

Listed:
  • Antonio Alonso-Ayuso

    (Área de Estadística e Investigación Operativa, Universidad Rey Juan Carlos, 28933 Madrid, Spain)

  • Laureano F. Escudero

    (Área de Estadística e Investigación Operativa, Universidad Rey Juan Carlos, 28933 Madrid, Spain)

  • F. Javier Martín-Campo

    (Departamento de Estadística e Investigación Operativa II (Métodos de decisión), Universidad Complutense de Madrid, 28223 Madrid, Spain)

Abstract

The aircraft conflict detection and resolution problem in air traffic management consists of deciding the best strategy for an arbitrary aircraft configuration such that all conflicts in the airspace are avoided. A conflict situation occurs if two or more aircraft do not maintain the minimum safety distance during their flight plans. A two-step approach is presented. The first step consists of a nonconvex mixed integer nonlinear optimization (MINLO) model based on geometric constructions. The objective is to minimize the weighted aircraft angle variations to obtain the new flight configuration. The second step consists of a set of unconstrained quadratic optimization models where aircraft are forced to return to their original flight plan as soon as possible once there is no aircraft in conflict with any other. The main results of extensive computation are reported by comparing the performance of state-of-the-art nonconvex MINLO solvers and an approximation by discretizing the possible angles of motion for solving a sequence of integer linear optimization (SILO) models in an iterative way. Minotaur, one of the nonconvex MINLO solvers experimented with, gives better solutions but requires more computation time than the SILO approach, which requires only a short time to obtain a good, feasible solution. Its value in the objective function has a reasonable goodness gap compared with the Minotaur solution. Given the need to solve the problem in almost real time, the approximate SILO approach is favored because of its short computation time and solution quality for the testbeds used in the experiment, which include both small- and real-sized instances. However, Minotaur is useful in this particular case for simulation purposes and for calibrating the SILO approach.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:50:y:2016:i:1:p:263-274
    DOI: 10.1287/trsc.2014.0557
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    References listed on IDEAS

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    1. Antonio Alonso-Ayuso & Laureano Escudero & F. Martín-Campo & Nenad Mladenović, 2015. "A VNS metaheuristic for solving the aircraft conflict detection and resolution problem by performing turn changes," Journal of Global Optimization, Springer, vol. 63(3), pages 583-596, November.
    2. Dell'Olmo, Paolo & Lulli, Guglielmo, 2003. "A new hierarchical architecture for Air Traffic Management: Optimisation of airway capacity in a Free Flight scenario," European Journal of Operational Research, Elsevier, vol. 144(1), pages 179-193, January.
    3. 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.
    4. A. Alonso-Ayuso & L. Escudero & P. Olaso & C. Pizarro, 2013. "Conflict avoidance: 0-1 linear models for conflict detection & resolution," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 485-504, October.
    5. 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.
    6. A. Alonso-Ayuso & L. Escudero & F. Martín-Campo, 2014. "On modeling the air traffic control coordination in the collision avoidance problem by mixed integer linear optimization," Annals of Operations Research, Springer, vol. 222(1), pages 89-105, November.
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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. 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.
    3. 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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