# Solving the Air Conflict Resolution Problem under Uncertainty using an Iterative Bi-Objective Mixed Integer Programming Approach

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Abstract : In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision on the aircraft speed prediction, and the delay in the execution of maneuvers. Using a geometrical approach, we derive an analytical expression for the minimum distance between aircraft, along with the corresponding probability of conflict. These expressions are incorporated into an existing deterministic model for conflict resolution. This model solves the problem as a maximum clique of minimum weight in a graph whose vertices represent possible maneuvers and where edges link conflict-free maneuvers of different aircraft. We then present a solution procedure focusing on two criteria, namely fuel efficiency and the probability of re-issuing maneuvers in the future: we iteratively generate solutions of the Pareto front to provide the controller with a set of possible solutions where he/she can choose the one corresponding the most to his/her preferences. Intensive Monte-Carlo simulations validate the expressions derived for the minimum distance and the probability of conflict. Computational results highlight that up to 10 different solutions for instances involving up to 35 aircraft are generated within three minutes.
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Cited literature [30 references]

https://hal-insa-rennes.archives-ouvertes.fr/hal-01353978
Contributor : Jérémy Omer <>
Submitted on : Thursday, October 3, 2019 - 11:21:33 AM
Last modification on : Tuesday, March 30, 2021 - 10:28:50 AM

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Thibault Lehouillier, Moncef Ilies Nasri, Jérémy Omer, François Soumis, Guy Desaulniers. Solving the Air Conflict Resolution Problem under Uncertainty using an Iterative Bi-Objective Mixed Integer Programming Approach. Transportation Science, INFORMS, 2017, 51 (4), pp.1242-1258. ⟨10.1287/trsc.2016.0714⟩. ⟨hal-01353978v3⟩

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