The Aircraft Routing with Air Refueling Problem: Exact and Greedy Approaches

We consider the problem of finding the least cost route for an aircraft between a predetermined starting and target location while ensuring either enough fuel is on board or acquired en route via refueling for completion of the route. Other considerations of this problem include adherence to regulations for threat and no-fly zones and to regulations for the minimum fuel needed on an aircraft in the case of an emergency or flawed refueling operation. We prove that this problem is NP-hard, thereby motivating the potential value for a heuristic for larger, operationally-focused problems. Two solution methods are proposed: (i) a greedy heuristic that examines paths of arcs and (ii) an exact algorithm which is a non-polynomial extension of Dijkstra’s shortest path algorithm. These solution methods are computationally tested on a representative set of realistic missions with starting and target locations. The results validate the greedy heuristic as a real-time solution approach which is shown by the speed and accuracy of the solutions found when benchmarked against the exact algorithm and current practice.