New flight trajectory optimisation method using genetic algorithms

Abstract This paper presents a new flight trajectory optimisation method, based on genetic algorithms, where the selected optimisation criterion is the minimisation of the total cost. The candidate flight trajectories evaluated in the optimisation process are defined as flight plans with two components: a lateral flight plan (the set of geographic points that define the flight trajectory track segments) and a vertical flight plan (the set of data that define the altitude and speed profiles, as well as the points where the altitude and/or speed changes occur). The lateral components of the candidate flight plans are constructed by selecting a set of adjacent nodes from a routing grid. The routing grid nodes are generated based on the orthodromic route between the flight trajectory’s initial and final points, a selected maximum lateral deviation from the orthodromic route and a selected grid node step size along and across the orthodromic route. Two strategies are investigated to handle invalid flight plans (relative to the aircraft’s flight envelope) and to compute their flight performance parameters. A first strategy is to assign a large penalty total cost to invalid flight profiles. The second strategy is to adjust the invalid flight plan parameters (altitude and/or speed) to the nearest limit of the flight envelope, with priority being given to maintaining the planned altitude. The tests performed in this study show that the second strategy is computationally expensive (requiring more than twice the execution time relative to the first strategy) and yields less optimal solutions. The performance of the optimal profiles identified by the proposed optimisation method, using the two strategies regarding invalid flight profile performance evaluation, were compared with the performance data of a reference flight profile, using identical input data: initial aircraft weight, initial and final aircraft geographic positions, altitudes and speed, cost index, and atmospheric data. The initial and final aircraft geographic positions, and the reference flight profile data, were retrieved from the FlightAware web site. This data corresponds to a real flight performed with the aircraft model used in this study. Tests were performed for six Cost Index values. Given the randomness of the genetic algorithms, the convergence to a global optimal solution is not guaranteed (the solution may be non-optimal or a local optima). For a better evaluation of the performance of the proposed method, ten test runs were performed for each Cost Index value. The total cost reduction for the optimal flight plans obtained using the proposed method, relative to the reference flight plan, was between 0.822% and 3.042% for the cases when the invalid flight profiles were corrected, and between 1.598% and 3.97% for the cases where the invalid profiles were assigned a penalty total cost.