Mixed Integer Second-Order Cone Programming for the Horizontal and Vertical Free-flight Planning Problem

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.

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

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