Combining NLP and MILP in Vertical Flight Planning

Abstract

Vertical flight planning of commercial aircrafts can be formulated as a Mixed-Integer Linear Programming (MILP) problem and solved with branch-and-cut based solvers. For fuel-optimal profiles, speed and altitude must be assigned to the corresponding segments in such a way that the fuel consumed throughout the flight is minimized. Information about the fuel consumption of an aircraft is normally given by the aircraft manufacturers as a black box function, where data is only available on a grid points depending on speed, altitude and weight. Hence, some interpolation technique must be used to adequate this data to the model. Using piecewise linear interpolants for this purpose is suitable for the MILP approach but computationally expensive, since it introduces a significant amount of binary variables. The aim of this work is to investigate reductions of the computation times by using locally optimal solutions as initial solutions for a MILP model which is, thereafter solved to global optimality. Numerical results on test instances are presented.