Flight Planning in Free Route Airspaces

We consider the problem of finding cheapest flight routes through free route airspaces in a 2D setting. We subdivide the airspace into regions determined by a Voronoi subdivision around the points from a weather forecast. This gives rise to a regular grid of rectangular regions (quads) with every quad having an associated vector-weight that represents the wind magnitude and direction. Finding a cheapest path in this setting corresponds to finding a piece-wise linear path determined by points on the boundaries of the quads. In our solution approach, we discretize such boundaries by introducing border points and only consider segments connecting border points belonging to the same quad. While classic shortest path graph algorithms are available and applicable to the graphs originating from these border points, we design an algorithm that exploits the geometric structure of our scenario and show that this algorithm is more efficient in practice than classic graph-based algorithms. In particular, it scales better with the number of quads in the subdivision of the airspace, making it possible to find more accurate routes or to solve larger problems.