An efficient algorithm for vertical free-flight optimization in air transportation

Air transportation plays a vital role in driving global economic growth, job creation, and enhancing international connectivity. Central to this infrastructure is flight planning, where the priority is to ensure safe and efficient aircraft trajectories. This paper focuses on optimizing flight paths in Free Route Airspaces, addressing the challenge of finding minimal fuel consumption trajectories in three-dimensional space. We introduce a novel approach that utilizes nonlinear programming to find efficient solutions, balancing computational efficiency with the quality of the results. Our work develops an algorithm to identify near-optimal solutions and establishes upper bounds through a mixed-integer program. Numerical results indicate that the relative optimality gap is no greater than 0.001% and the absolute optimality gap does not exceed 5.0554 kg. Computational experiments further demonstrate that our approach achieves up to 3.2% fuel savings compared to the traditional flight scenario on a segment for Airbus A380. It is significant to note that a 1% reduction in global aviation fuel consumption could translate into annual savings of billions of dollars in operational costs. Our evaluation across 11 different aircraft types consistently shows meaningful fuel-saving benefits. These results suggest that the proposed algorithm has strong potential for broad applicability across a wide range of aircraft.