This paper addresses a multiple depot, multiple unmanned vehicle routing problem with fuel constraints. The objective of the problem is to find a tour for each vehicle such that all the specified targets are visited at least once by some vehicle, the tours satisfy the fuel constraints, and the total travel cost of the vehicles is a minimum. We consider a scenario where the vehicles are allowed to refuel by visiting any of the depots or fuel stations. This is a difficult optimization problem that involves partitioning the targets among the vehicles and finding a feasible tour for each vehicle. The focus of this paper is on developing fast variable neighborhood descent (VND) and variable neighborhood search (VNS) heuristics for finding good feasible solutions for large instances of the vehicle routing problem. Simulation results are presented to corroborate the performance of the proposed heuristics on a set of 23 large instances obtained from a standard library. These results show that the proposed VND heuristic, on an average, performed better than the proposed VNS heuristic for the tested instances.