Particle Swarm Optimization with Required Time of Arrival Constraint for Aircraft Trajectory

Global warming has motivated the aeronautical industry to develop new technologies that will reduce polluting emissions. A direct way to achieve this goal is to reduce fuel consumption. Reference trajectory optimization contributes to this goal by guiding aircraft to zones where meteorological conditions are favorable to execute their required missions and thereby to reduce flight costs. In this article, the reference trajectory was optimized in terms of geographical position, altitude, and speed, by taking into account a Required Time of Arrival (RTA) constraint and weather conditions. The algorithm assumes that there is no traffic and that the aircraft can fly anywhere in the search space. The search space was modeled in the form of a unidirectional weighted graph, fuel burn was computed using a numerical model, and the weather forecast was taken into account. The methodology utilized in this article to determine the most economical combinations of parameters that delivered the optimal trajectory was inspired by the Particle Swarm Optimization (PSO) algorithm. Results showed that the algorithm provided acceptable solutions under traffic management constraints. It was observed that the developed algorithm was able to save up to 9.1% (6,800 kg) of fuel burn when there was no RTA constraint for flight trajectories and up to 1.8% (600 kg) of fuel against real, as-flown trajectories with an RTA constraint of ±30 seconds. Because of the nature of the PSO Algorithm, the local best trajectories are extracted and provided as a Trajectory Option Set (TOS), which is similar in cost as the optimal trajectory.