We present a framework to generate, in a multi-aircraft environment, 4D optimized trajectories in a scenario with several weather constraints obtained with advanced weather prediction models. We focus on the trajectory optimization module of this framework, which is based on a point-mass representation of the aircraft. By tuning some of the parameters of this module, we compute several alternative trajectories avoiding these constraints both laterally and vertically. The experiment conducted involves flights crossing the North Atlantic region, while in the en-route phase. This preliminary framework is also used to run the experiments in multiple cycles or consecutive time periods, assuming different update times for the weather constraints, and choosing the best trajectory per flight and per cycle. The ultimate goal of the framework is to develop innovative procedures in the air traffic management system to reduce the climate and environmental impact of aviation, while increasing the resilience of air operations to weather phenomena.