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An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution


An exact mixed integer nonlinear optimization (MINO) model is presented for tackling the aircraft conflict detection and resolution problem in air traffic management. Given a set of flights and their configurations, the aim of the problem was to provide new configurations such that all conflict situations are avoided, with conflict situation understood to mean an event in which two or more aircraft violate the minimum safety distances that must be maintained in flight. The proposed model solves the problem using both horizontal (velocity and angle turn change) and vertical (altitude level change) maneuvers. As a special case, another model is presented in which only horizontal maneuvers are used. The models proposed are based on a geometric construction which involves trigonometric functions, so the constraint system is included via a large set of trigonometric and nonconvex inequalities. A multicriteria approach is presented to provide useful information to air traffic control officers about the maneuvers to be performed. The main results of an extensive computational experiment are reported in which the performance of the state-of-the-art nonconvex MINO solver Minotaur is studied.

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The authors gratefully acknowledge the help of Sven Leyffer of the Mathematics and Computer Science Division of the National Laboratory, Chicago, USA, in making available to us the latest version of his nonconvex MINO Minotaur engine. They would like to express their thanks to the two anonymous reviewers for their helpful and constructive comments and suggestions which clearly improved the final version of the paper. This research is partially supported by the projects OPTIMOS3 MTM2012-36163-C06-06 and PCDASO MTM2012-31514, both funded by the Spanish Ministry of Economy Affairs and Competitiveness.

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Correspondence to F. Javier Martín-Campo.

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Alonso-Ayuso, A., Escudero, L.F. & Martín-Campo, F.J. An exact multi-objective mixed integer nonlinear optimization approach for aircraft conflict resolution. TOP 24, 381–408 (2016).

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  • Collision avoidance problem
  • Air traffic management
  • Mixed 0–1 nonlinear optimization
  • Multicriteria functions
  • Goal programming

Mathematics Subject Classification

  • 90C11
  • 90C29
  • 90C30