Currently large passenger and cargo airplanes cannot fly freely through the three-dimensional space. Their routes have to follow the air traffic network (ATN), which is an imaginary road network around the globe. Following the ATN routes has the disadvantage that sometimes detours from the best-possible routes have to be taken, which leads to a higher-than-necessary fuel consumption. A relatively new idea to reduce these cost and environmental burden is to change to free flight routes that do not follow given ATN routes any longer. However, airplanes cannot always follow the direct line of sight. The main obstacles are restricted airspaces, weather conditions (wind, temperature), varying per-nation overflight costs, and further safety regulations (ETOPS).

In order to compute optimal flight trajectories we formulate the problem as discrete-continuous optimization problem. We discretize the equations of motion and apply mixed-integer linear solvers for its numerical solution.

Partners

• Fraunhofer IGD, Darmstadt
• TU Darmstadt

Industrial partners / Funding

• Lufthansa Systems GmbH, Frankfurt.

Related talks

• Solving Discrete-Nonlinear Problems with Linear Mixed-Integer Programming Techniques, Seminar on Algebra and Graph Theory, Warsaw, Poland, 26.9.2007.
• Solving Discrete-Nonlinear Problems with Linear Mixed-Integer Programming Techniques, 13th Czech-French-German Conference 2007, Heidelberg, Germany, 21.9.2007.
• Solving Discrete-Nonlinear Problems with Linear Mixed-Integer Programming Techniques, Sino-German Matheon- Workshop „Nonlinear Integer Programming and Structural Optimization“, Berlin, Germany, 10.7.2007.