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A VNS metaheuristic for solving the aircraft conflict detection and resolution problem by performing turn changes

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Abstract

The aircraft Conflict Detection and Resolution (CDR) problem in air traffic management consists of finding a new configuration for a set of aircraft such that conflict situations between them are avoided. A conflict situation arises if two or more aircraft violate the safety distances that they must maintain in flight. In this paper we propose a Variable Neighborhood Search approach for solving the CDR by turn changes. This metaheuristic compares favorably with previous best known methods for solving the Mixed Integer Nonlinear Programming (MINLP) model proposed elsewhere. It is worth pointing out the astonishingly short time in which the first feasible solution is obtained. This is crucial for this specific problem, where a response must be provided almost in real time if it is to be useful in a real-life problem. A comparative study between the performance of the new approach, a state-of-the-art MINLP solver and our Sequential Integer Linear Optimization approach proposed elsewhere is reported, using a testbed of instances with up to 25 aircraft.

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Acknowledgments

The authors are grateful for the help of Sven Leyffer of the Mathematics and Computer Science Division, National Laboratory, Chicago, USA, for making available to us his nonconvex MINLP Minotaur engine. This research has been partially supported by the projects MTM2012-36163-C06-06 by the Ministerio de Economía y Competitividad, Spain, RIESGOS CM by the Regional Community of Madrid, Spain, and 174010 by the Serbian Ministry of Sciences.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad Rey Juan Carlos, Madrid, Spain

    Antonio Alonso-Ayuso & Laureano F. Escudero

  2. Departamento de Estadística e Investigación Operativa II, Universidad Complutense de Madrid, Madrid, Spain

    F. Javier Martín-Campo

  3. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Nenad Mladenović

Authors
  1. Antonio Alonso-Ayuso
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  2. Laureano F. Escudero
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  3. F. Javier Martín-Campo
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  4. Nenad Mladenović
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Correspondence to F. Javier Martín-Campo.

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Alonso-Ayuso, A., Escudero, L.F., Martín-Campo, F.J. et al. A VNS metaheuristic for solving the aircraft conflict detection and resolution problem by performing turn changes. J Glob Optim 63, 583–596 (2015). https://doi.org/10.1007/s10898-014-0144-8

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  • DOI: https://doi.org/10.1007/s10898-014-0144-8

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