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Journal articles
Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem
Abstract : In this article, we tackle the conflict resolution problem using a new variant of the minimum-weight maximum-clique model. The problem involves identifying maneuvers that maintain the required separation distance between all pairs of a set of aircraft while minimizing fuel costs. We design a graph in which the vertices correspond to a finite set of maneuvers and the edges connect conflict-free maneuvers. A maximum clique of minimal weight yields a conflict-free situation that involves all the aircraft and minimizes the costs induced. The innovation of the model is its cost structure: the costs of the vertices cannot be determined a priori, since they depend on the vertices in the clique. We formulate the problem as a mixed integer linear program. Since the modeling of the aircraft dynamics and the computation of trajectories is separated from the solution process, the model is flexible. As a consequence, our mathematical framework is valid for any hypotheses. In particular, the aircraft can perform dynamic velocity, heading, and flight-level changes. To solve instances involving a large number of aircraft spread over several flight levels, we introduce two decomposition algorithms. The first is a sequential mixed integer linear optimization procedure that iteratively refines the discretization of the maneuvers to yield a trade-off between computational time and cost. The second is a large neighborhood search heuristic that uses the first procedure as a subroutine. The best solutions for the available set of maneuvers are obtained in less than 10 seconds for instances with up to 250 aircraft randomly allocated to 20 flight levels.
Cited literature [34 references]
https://hal-insa-rennes.archives-ouvertes.fr/hal-01353974
Contributor : Jérémy Omer <>
Submitted on : Monday, August 22, 2016 - 12:02:37 PM
Last modification on : Friday, April 23, 2021 - 2:40:13 PM
Long-term archiving on: : Wednesday, November 23, 2016 - 10:41:52 AM
Contributor : Jérémy Omer <>
Submitted on : Monday, August 22, 2016 - 12:02:37 PM
Last modification on : Friday, April 23, 2021 - 2:40:13 PM
Long-term archiving on: : Wednesday, November 23, 2016 - 10:41:52 AM
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