This study investigates a new aircraft flight trajectory optimisation method, derived from the Non-dominated Sorting Genetic Algorithm II method used for multi-objective optimisations. The new method determines, in parallel, a set of optimal flight plan solutions for a flight. Each solution is optimal (requires minimum fuel) for a Required Time of Arrival constraint from a set of candidate time constraints selected for the final waypoint of the flight section under optimisation. The set of candidate time constraints is chosen so that their bounds are contiguous, i.e. they completely cover a selected time domain. The proposed flight trajectory optimisation method may be applied in future operational paradigms, such as Trajectory-Based Operations/free flight, where aircraft do not need to follow predetermined routes. The intended application of the proposed method is to support Decision Makers in the planning phase when there is a time constraint or a preferred crossing time at the final point of the flight section under optimisation. The Decision Makers can select, from the set of optimal flight plans, the one that best fits their criteria (minimum fuel burn or observes a selected time constraint). If the Air Traffic Management system rejects the flight plan, then they can choose the next best solution from the set without having to perform another optimisation. The method applies for optimisations performed on lateral and/or vertical flight plan components. Seven proposed method variants were evaluated, and ten test runs were performed for each variant. For five variants, the worst results yielded a fuel burn less than 90kg (0.14%) over the ‘global’ optimum. The worst variant yielded a maximum of 321kg (0.56%) over the ‘global’ optimum.
