Abstract
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.
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Lehouillier, T., Omer, J., Soumis, F., Desaulniers, G. (2015). A New Variant of the Minimum-Weight Maximum-Cardinality Clique Problem to Solve Conflicts between Aircraft. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-18161-5_1
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DOI: https://doi.org/10.1007/978-3-319-18161-5_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18160-8
Online ISBN: 978-3-319-18161-5
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