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

Zhi Yuan(yuanz***at***hsu-hh.de)
Liana Amaya Moreno(lamayamo***at***hsu-hh.de)
Armin Fügenschuh(fuegenschuh***at***hsu-hh.de)
Anton Kaier(anton.kaier***at***lhsystems.com)
Amina Mollaysa(maolaaia***at***hsu-hh.de)
Swen Schlobach(swen.schlobach***at***lhsystems.com)

Abstract: 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.

Keywords: Free-flight planning, second-order cone programming, mixed-integer linear programming

Category 1: Applications -- OR and Management Sciences (Airline Optimization )

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

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

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Entry Submitted: 08/04/2015
Entry Accepted: 08/05/2015
Entry Last Modified: 08/04/2015

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