{
  "id": "2406.17403",
  "version": "v1",
  "published": "2024-06-25T09:25:08.000Z",
  "updated": "2024-06-25T09:25:08.000Z",
  "title": "A comparison of formulations for aircraft deconfliction",
  "authors": [
    "Renan Spencer Trindade",
    "Claudia D'Ambrosio"
  ],
  "categories": [
    "math.OC"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-25T09:25:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mixed integer nonlinear program",
      "formulation",
      "integer nonlinear programming method",
      "sequential convex mixed integer nonlinear",
      "minlp solvers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}