Reformulated Subliminal Speed Regulation Models for Aircraft Deconfliction Problems

The aircraft deconfliction problem focuses on maintaining safe distances between aircraft, a key challenge in air traffic management. Traditionally handled by human controllers, this task is increasingly being explored for automation. One promising approach is subliminal speed control, which subtly adjusts aircraft speeds within restricted areas through automated regulation. These continuous speed adjustments can be naturally modeled as optimization problems, specifically semi-infinite programming problems with an infinite number of constraints that vary continuously over time. In this work, a semi-infinite programming model for speed-based aircraft deconfliction is considered, and several direct methods are applied to its solution. As these methods prove to be inefficient, an equivalent formulation of the problem as a nonlinear programming model with a finite number of constraints is proposed. This reformulation is shown to reduce the model’s complexity and can be efficiently solved using standard solvers. Numerical experiments also demonstrate that this approach improves the quality of the solutions when compared with some heuristics proposed in the literature.