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Chapitre D'ouvrage Année : 2015

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

Résumé

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 minimiz- ing 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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Dates et versions

hal-02099567 , version 1 (04-02-2022)

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Thibault Lehouillier, Jérémy Omer, François Soumis, Guy Desaulniers. A New Variant of the Minimum-Weight Maximum-Cardinality Clique Problem to Solve Conflicts between Aircraft. Modelling, Computation and Optimization in Information Systems and Management Sciences, pp.3-14, 2015, Advances in Intelligent Systems and Computing, ⟨10.1007/978-3-319-18161-5_1⟩. ⟨hal-02099567⟩
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