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arXiv · 2406.17403

A comparison of formulations for aircraft deconfliction

Renan Spencer Trindade·Claudia D'Ambrosio
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Abstract

In this work, we aim to compare different methods and formulations to solve a problem in air traffic management to global optimality. In particular, we focus on the aircraft deconfliction problem, where we are given n aircraft, their position at time 0, and their (straight) trajectories. We wish to identify and solve potential pairwise conflict by temporarily modifying the aircraft's trajectory. A pair of aircraft is in conflict when they do not respect a minimum, predefined safety distance. In general, conflicts could be solved both varying the aircraft's speed or trajectory, but in this paper we only consider the latter, more precisely heading-angle deviations. The problem has been formulated as a mixed integer nonlinear program (MINLP). We compare this formulation, solved by open-source MINLP solvers for global optimization, against a reformulation that shows a larger number of variables and constraints but only separable nonconvexities. We solve such a separable formulation with the same MINLP solvers or the Sequential Convex Mixed Integer Nonlinear Programming method. The separable formulation, despite being larger, facilitates some solvers in finding good-quality solutions.

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Renan Spencer Trindade, Claudia D'Ambrosio. 2024-06-25. A comparison of formulations for aircraft deconfliction. https://doi.org/10.1007/978-3-031-81241-5_15

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