Mathematical optimization methods for aircraft conflict resolution in air traffic control

Abstract

Air traffic control is a very dynamic and heavy constrained environment where many decisions need to be taken over short periods of time and in the context of uncertainty. Adopting automation under such circumstances can be a crucial initiative to reduce controller workload and improve airspace usage and capacity. Traditional methods for air traffic control have been exhaustively used in the last decades and are reaching their limits, therefore automated approaches are receiving a significant and growing attention. In this thesis, the focus is to obtain optimal aircraft trajectories to ensure flight safety in the short-term by solving optimization problems. During cruise stage, separation conditions require a minimum of 5 Nautical Miles (NM) horizontally or 1000 feet (ft) vertically between any pair of aircraft. A conflict between two or more aircraft is a loss of separation among these aircraft. Air traffic networks are organized in flight levels which are separated by at least 1000 ft, hence during cruise stage, most conflicts occur among aircraft flying at the same flight level. This thesis presents several mathematical formulations to address the aircraft conflict resolution problem and its variants. The core contribution of this research is the development of novel mixed integer programming models for the aircraft conflict resolution problem. New mathematical optimization formulations for the deterministic aircraft conflict resolution problem are analyzed and exact methods are developed. Building on this framework, richer formulations capable of accounting for aircraft trajectory prediction uncertainty and trajectory recovery are proposed. Results suggest that the formulations presented in thesis are efficient and competitive enough with the state-of-art models and they can provide an alternative solution to possibly fill some of the gaps currently present in the literature. Furthermore, the results obtained demonstrate the impact of these models in solving very denser air space scenarios and their competitiveness with state-of-the-art formulations without regarding variable discretization or non-linear components