To sustain the continuously increasing air traffic demand, the future air traffic management system will rely on a so-called trajectory based operations concept that will increase air traffic capacity by reducing the controllers’ workload. This will be achieved by transferring tactical conflict detection and resolution tasks to the strategic planning phase. In this future air traffic management paradigm context, this paper presents a methodology to address such trajectory planning at nation-wide and continent scale. The pro-posed methodology aims at minimizing the global interaction between aircraft trajectories by allocating alternative departure times, alternative horizontal flight paths, and alternative flight levels to the trajectories involved in the interaction. To improve robustness of the strategic trajectory planning, un-certainty of aircraft position and aircraft arrival time to any given position on the trajectory are considered. This paper presents a mathematical formulation of this strategic trajectory planning problem leading to a mixed-integer optimization problem, whose objective function relies on the new concept of interaction between trajectories. A computationally efficient algorithm to compute interaction between trajectories for large-scale applications is presented and implemented. Resolution method based on hybrid-metaheuristic algorithm have been developed to solve the above large-scale optimization problems. Finally, the overall methodology is implemented and tested with real air traffic data taking into account uncertainty over the French and the European airspace, involving more than 30,000 trajectories. Conflict-free and robust 4D trajectory planning are produced within computational time acceptable for the operation context, which shows the viability of the approach.