Lexicographic optimisation for optimal departure aircraft trajectories

This paper presents a strategy for designing noise abatement procedures, aimed at reducing the exposure to noise of the population living around the airports. Noise optimal departing routes are computed for a specific aircraft type and for a given scenario (airport and airspace configuration, local geography, etc.). Hence, a non-linear multi-objective optimal control problem is formally identified and detailed. Lexicographic optimisation is presented as an alternative optimisation technique to the common used weighting methods. This approach establishes a hierarchical order among all the optimisation objectives instead of giving them a specific (and most of the time, arbitrary) weight. In this work, the optimisation criteria are chosen as the maximum perceived noise levels at different sensitive locations as well as some criteria associated with the operation of the aircraft. A practical example is given, in a hypothetical scenario, showing how the proposed optimisation technique may help aircraft procedure designers when dealing with departing routes.