A comparison of formulations for aircraft deconfliction

TL;DR

This paper compares different mathematical formulations for aircraft deconfliction, focusing on trajectory adjustments to ensure safety, and evaluates their effectiveness using open-source solvers to achieve global optimality.

Contribution

It introduces and compares a mixed integer nonlinear program and a separable reformulation for aircraft deconfliction, highlighting their relative advantages in solver performance.

Findings

Separable formulation facilitates better solutions despite larger size.

Open-source MINLP solvers can effectively solve the formulations.

Separable formulation shows promise for real-time air traffic management.

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.