A New Variant of the Minimum-Weight Maximum-Cardinality Clique Problem to Solve Conflicts between Aircraft

  • Thibault LehouillierEmail author
  • Jérémy Omer
  • François Soumis
  • Guy Desaulniers
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 359)


In this article, we formulate a new variant of the problem of finding a maximum clique of minimum weight in a graph applied to the detection and resolution of conflicts between aircraft. The innovation of the model relies on the cost structure: the cost of the vertices cannot be determined a priori, since they depend on the vertices in the clique. We apply this formulation to the resolution of conflicts between aircraft by building a graph whose vertices correpond to a set of maneuvers and whose edges link conflict-free maneuvers. A maximum clique of minimal weight yields a conflict-free situation involving all aircraft and minimizing the costs induced. We solve the problem as a mixed integer linear program. Simulations on a benchmark of complex instances highlight computational times smaller than 20 seconds for situations involving up to 20 aircraft.


Air Traffic Control Conflict Resolution Maximum Clique Mixed Integer Linear Programming 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thibault Lehouillier
    • 1
    Email author
  • Jérémy Omer
    • 1
  • François Soumis
    • 1
  • Guy Desaulniers
    • 1
  1. 1.Group on Research in Decision AnalysisMontrealCanada

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