This paper presents a strategy for designing noise abatement procedures aimed at reducing the global annoyance perceived by the population living around the airports. A non-linear multi-objective optimal control problem is implemented and numerically solved obtaining minimal annoyance trajectories. Annoyance criteria are treated as non-linear functions that can be obtained by using fuzzy logic modelling techniques. Here, a basic implementation is shown where the annoyance is expressed in function of the maximum perceived noise level, the period of the day when the trajectory takes place and the type of area over-flown. Then, lexicographic optimisation techniques are used to deal with the multi-criteria nature of the problem. Finally, an illustrative example is given concerning a hypothetical scenario with five different noise sensitive locations and where different optimal trajectories are obtained for different hours of the day.