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Graph Coloring for Air Traffic Flow Management

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  • Nicolas Barnier
  • Pascal Brisset

Abstract

The aim of Air Traffic Flow Management (ATFM) is to enhance the capacity of the airspace while satisfying Air Traffic Control constraints and airlines requests to optimize their operating costs. This paper presents a design of a new route network that tries to optimize these criteria. The basic idea is to consider direct routes only and vertically separate intersecting ones by allocating distinct flight levels, thus leading to a graph coloring problem. This problem is solved using constraint programming after having found large cliques with a greedy algorithm. These cliques are used to post global constraints and guide the search strategy. With an implementation using FaCiLe, our Functional Constraint Library, optimality is achieved for all instances except the largest one, while the corresponding number of flight levels could fit in the current airspace structure. This graph coloring technique has also been tested on various benchmarks, featuring good results on real-life instances, which systematically appear to contain large cliques. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Nicolas Barnier & Pascal Brisset, 2004. "Graph Coloring for Air Traffic Flow Management," Annals of Operations Research, Springer, vol. 130(1), pages 163-178, August.
    • Handle: RePEc:spr:annopr:v:130:y:2004:i:1:p:163-178:10.1023/b:anor.0000032574.01332.98
    DOI: 10.1023/B:ANOR.0000032574.01332.98
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    Citations

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    Cited by:

    1. Casado, Silvia & Laguna, Manuel & Pacheco, Joaquín & Puche, Julio C., 2020. "Grouping products for the optimization of production processes: A case in the steel manufacturing industry," European Journal of Operational Research, Elsevier, vol. 286(1), pages 190-202.
    2. Stefano Gualandi & Federico Malucelli, 2012. "Exact Solution of Graph Coloring Problems via Constraint Programming and Column Generation," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 81-100, February.
    3. Xiao-Feng Xie & Jiming Liu, 2009. "Graph coloring by multiagent fusion search," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 99-123, August.
    4. Lehouillier, Thibault & Omer, Jérémy & Soumis, François & Desaulniers, Guy, 2017. "Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 696-712.
    5. Ghoneim, Ayman & Abbass, Hussein A., 2016. "A multiobjective distance separation methodology to determine sector-level minimum separation for safe air traffic scenarios," European Journal of Operational Research, Elsevier, vol. 253(1), pages 226-240.
    6. Laurent Moalic & Alexandre Gondran, 2018. "Variations on memetic algorithms for graph coloring problems," Journal of Heuristics, Springer, vol. 24(1), pages 1-24, February.
    7. Prot, D. & Rapine, C. & Constans, S. & Fondacci, R., 2010. "Using graph concepts to assess the feasibility of a sequenced air traffic flow with low conflict rate," European Journal of Operational Research, Elsevier, vol. 207(1), pages 184-196, November.
    8. Salman Arif & Jason Atkin & Geert Maere, 2023. "Analysing the benefits of trajectory deviations for planar trajectory optimisation," Annals of Operations Research, Springer, vol. 326(1), pages 537-560, July.
    9. Severino F. Galán, 2017. "Simple decentralized graph coloring," Computational Optimization and Applications, Springer, vol. 66(1), pages 163-185, January.
    10. 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.

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