We address the issue of multi-aircraft cooperative strategic trajectory planning in free-route airspace (FRA) in this study, taking into consideration the impact of time-varying and altitude-varying wind forecast uncertainty. A bi-level planning model was established in response to the properties of the wind. The upper level focused on minimizing the flight time, while the lower level aimed to reduce potential conflicts. Meanwhile, a heuristic approach based on conflict severity (CS) within the framework of a cooperative co-evolution evolutionary algorithm (CCEA) was proposed to accelerate the convergence speed in view of the complexity of this optimization issue. In order to conduct the experiments, historical data of 1479 flights over western Chinese airspace were retrieved. The number of conflicts, total flight time, total flight time variance, and deviation were used as indicators to evaluate the safety, efficiency, and predictability of the trajectory. When compared to a trajectory in the structured airspace, the optimal solution was conflict-free and reduced the total flight time by about 17.7%, the variance by 11.7%, and the deviation by 37.5%. Additionally, the contrast with the two-stage model demonstrated that the proposed method was entirely meaningful. The outcome of this survey can provide an effective trajectory-planning method, which is crucial for the sustainable development of future air traffic management (ATM).

The application of Trajectory-Based Operation (TBO) and Free-Route Airspace (FRA) can relieve air traffic congestion and reduce flight delays. However, this new operational framework has higher requirements for the reliability and efficiency of the trajectory, which will be significantly influenced if the analysis of wind uncertainty during trajectory planning is insufficient. In the literature, trajectory planning models considering wind uncertainty are developed based on the time-invariant condition (i.e., three-dimensional), which may potentially lead to a significant discrepancy between the predicted flight time and the real flight time. To address this problem, this study proposes a trajectory planning model considering time-variant wind uncertainty (i.e., four-dimensional). This study aims to optimize a reliable and efficient trajectory by minimizing the Mean-Excess Flight Time (MEFT). This model formulates wind as a discrete variable, forming the foundation of the proposed time-variant predicted method that can calculate the segment flight time accurately. To avoid the homogeneous assumption of distributions, we specifically apply the first four moments (i.e., expectation, variance, skewness, and kurtosis) to describe the stochasticity of the distributions, rather than using the probability distribution function. We apply a two-stage algorithm to solve this problem and demonstrate its convergence in the time-variant network. The simulation results show that the optimal trajectory has 99.2% reliability and reduces flight time by approximately 9.2% compared to the current structured airspace trajectory. In addition, the solution time is only 2.3 min, which can satisfy the requirement of trajectory planning.