Two-Stage Greener Four-Dimensional Trajectory Optimisation with Combined Holding Strategies

The rapid growth of air transport demand poses challenges to the development of the global air traffic system, including increased delays and environmental pollution. To alleviate these problems, a two-stage greener 4D trajectory optimisation framework is proposed by integrating air traffic flow management (ATFM) with the trajectory-based operations (TBO). In the first stage, a multi-objective optimisation model is developed for network-wide delay management to minimise delay costs and CO₂ emissions. The combination of ground holding, standard airborne holding and economic airborne holding is adopted to control the controlled time of arrival (CTA) at each critical node along the trajectory. In the second stage, the 4D trajectory optimisation method is conducted based on the CTA constraints of the negotiated solution from the first stage to generate specific “runway-to-runway” 4D trajectory for the individual flight. The method is tested on the Shanghai-Beijing-Guangzhou air traffic network. Results indicate that including the economic airborne holding provides a more flexible trade-off between delay costs and CO₂ emissions, facilitating stakeholder negotiations. Specifically, a 1% increase in delay cost can lead to a reduction in CO₂ emissions by approximately 0.51%. The proposed method presents a promising solution for achieving greener and more precise ATFM within the TBO paradigm.