Efficient trajectory parameterization for environmental optimization of departure flight paths using a genetic algorithm

Abstract

In this study, a genetic optimization algorithm is applied to the design of environmentally friendly aircraft departure trajectories. The environmental optimization has been primarily focused on noise abatement and local NO x emissions, whilst taking fuel burn into account as an economical criterion. In support of this study, a novel parameterization approach has been conceived for discretizing the lateral and vertical flight profiles, which reduces the need to include nonlinear side constraints in the multiparameter optimization problem formulation, while still permitting to comply with the complex set of operational requirements pertaining to departure procedures. The resulting formulation avoids infeasible solutions and hence significantly reduces the number of model evaluations required in the genetic optimization process. The efficiency of the developed approach is demonstrated in a case study involving the design of a noise abatement departure procedure at Amsterdam Airport Schiphol in The Netherlands.

An Efficient Application of the MOEA/D Algorithm for Designing Noise Abatement Departure Trajectories

“…To model an aircraft during departure operations, an intermediate point-mass model [19] is used in this paper. The model is based on several assumptions: (1) there is no wind present; (2) the Earth is flat and non-rotating; and (3) the flight is coordinated.…”

“…In trajectory optimization problems, operational constraints in different flight phases can cause the violation of new solutions found by an optimization algorithm, and hence there will be a large amount of computation time for evaluating these solutions while they are not potential candidates for an optimal solution. Recognizing this problem, Hartjes and Visser [19] introduced a novel trajectory parameterization that can handle operational constraints in the problem formulation, thus reducing the computational cost significantly. This technique aims to decompose a trajectory into a separate vertical path and ground track.…”

“…SEL indoor is the indoor sound exposure level in decibel (dB) and is evaluated by using a replica of the integrated noise model (INM) that has been the Federal Aviation Authorities' (FAA) standard regulatory noise model since the late 1970s [19]. Because SEL obtained from INM represents an outdoor value, an amount of 15 dB is subtracted to obtain SEL indoor , accounting for the sound absorption of an average house with an open window [28].…”

“…For both departures, the optimized trajectory starts at 35 ft, a take-off safety speed of V 2 + 10 kts, with the landing gear retracted and departure flaps selected and is terminated at an altitude of 6000 ft and an equivalent airspeed (EAS) of 250 kts. The ground tracks are constructed by three straight legs and two turns, as shown in Figure 2, which results in five design variables, while the vertical path is subdivided into 10 segments and parameterized as the study in [19], which results in an additional 18 design variables. For the reference case, the ground track is fixed to conform to the current SID, while the vertical path is optimized for fuel burn after finishing the NADP-1.…”

“…These include an adaptive replacement strategy [23], a stopping condition criterion [24], and a constraint-handling technique [25]. Also, to reduce redundant evaluations of infeasible solutions derived from operational constraints during different flight phases, the new trajectory parameterization technique recently proposed in [19] is also applied. The robustness and reliability of the proposed method are validated through two numerical examples at Schiphol Airport in The Netherlands.…”