In the past, travel routes for civil passenger and cargo air traffic were aligned to the air traffic network (ATN). To resolve the network congestion problem, the free-flight system has recently been introduced in more and more regions around the globe, allowing flight operations to make full use of the four space-and-time dimensions. For the numerical computation of optimal flight trajectories under free-flight conditions, we separate the problem into a horizontal and a vertical optimization problem, and develop mixed integer nonlinear programs for both. It turns out that both models have second-order cones (SOC) as substructures. We use different modelling strategies for dealing with the SOC and other nonlinear structures, so that after a linear approximation we are able to apply a mixed-integer linear solver to compute global optimal free-flight trajectories.

## Citation

Angewandte Mathematik und Optimierung Schriftenreihe / Applied Mathematics and Optimization Series AMOS#21(2015), Helmut Schmidt University / University of the Federal Armed Forces Hamburg, Germany