A comparison of formulations for aircraft deconfliction
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912183787454464 |
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| author | Trindade, Renan Spencer D'Ambrosio, Claudia |
| author_facet | Trindade, Renan Spencer D'Ambrosio, Claudia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17403 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A comparison of formulations for aircraft deconfliction Trindade, Renan Spencer D'Ambrosio, Claudia Optimization and Control 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. |
| title | A comparison of formulations for aircraft deconfliction |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.17403 |