Multi-Level Elliptic Dijkstra's Algorithm for Finding Optimal Trajectory of Aircrafts

We propose a multi-level elliptic Dijkstra's algorithm for flight planning in free flight airspaces. We exploit a multi-level decomposition of a given graph into a sequence of containing subgraphs. The algorithm alternates between running the forward and backward search on those subgraphs, starting from the smallest one to the original graph using a modification of Dijkstra's algorithm. The distances obtained by earlier searches help to reduce the search space of the later ones significantly. Computational results show that our algorithm requires at most 0.06s to find the cheapest route in a graph of more than 130,000 nodes and 17.5 million arcs, and is about 7 times faster than Dijkstra's algorithm on average.