Established flight planning using  on shortest path algorithms on airway networks face a performance challenge in growing free-flight zones, which lead to excessively large graphs. In theses situations, continuous optimal control techniques promise shorter run times, but provide only local optima. In this project, we investigate the structural relations between discrete and continuous optima and develop efficient hybrid algorithms.

Established flight planning involves shortest path selection in a pre-defined airway network, where effective edge lengths depend also on the wind speed at the time the plane passes that edge. In order to reduce fuel costs and air pollution, free flight zones are increasingly discussed. Removing the restriction of following the pre-defined airways allows taking better routes and exploiting advantageous wind situations more effectively. Achieving this flexibility with established graph-based optimization methods requires a massive refinement of the graph leading to significantly increased computing times.

A 2D flight directory in spatially inhomogeneous wind. Continuous optimal control techniques based on discretization of ordinary differential equations scale much better than global graph-based approaches, i.e. the run time complexity in terms of the desired accuracy is much lower. Unfortunately, they compute only local optima.

The project therefore aims at

  • a theoretical understanding of the approximation and convergence properties of discrete and continuous approaches in form of error bounds,
  • the derivation of hybrid algorithms in form of a switch from discrete global to continuous local optimization at an optimal accuracy threshold, and
  • the integration of continuous optimization as a building block in more general flight planning problems including traffic flight restrictions.