# Drone Arc Routing Problems and Metaheuristic Solution Approach
## 6 Conclusions and Future Works  
This study focused on the routing of surveillance drones considering their energy capacities, which are consumed during both servicing and deadheading. The DARP-DD and its special case, the MS-DARP-DD, were discussed. The simulated annealing algorithm was used to solve these problems. The components of the simulated annealing algorithm, including solution representation, neighbor search operators, constraint handling strategy, and parameter values, were designed in accordance with the problems. The solution representation was developed as a two-dimensional list based on the required edges. The \(k\)-route shorten, smart edge direction change, and smart reverse operators were introduced to the literature as neighbor search operators to be applied in other ARPs. In addition, it is the first time an edge postpone operator, which is employed to improve the tour of the RPP, was used as a neighbor search operator with merge and split procedure. A dynamic penalty function was developed and used in the structure of the algorithm as a constraint-handling strategy. Figure 9: The number of times the neighbor search operators improve the current solution for the DARP-6 problem. The letters A, B, C, D, E, F, G, and H represent \(k\)-reverse, \(n\)-reverse, smart reverse, intra-route reverse, \(k\)-route shorten, edge postpone, edge direction and smart edge direction change, route-repairing operators, respectively. The proposed algorithm was initially applied to solve the CARP using 20 differently sized test problems. The optimal solution of the bmcv-d18 instance (121 required and 133 total edges) was obtained in 1345 s. For the Hefei-4 instance (485 required, 727 non-required, and 1212 total edges), the algorithm achieved a high-quality result within 2.5 h, deviating only 4% from the best known result. This demonstrates the algorithm's capability to solve large-sized problems efficiently. Considering the ability of the proposed algorithm to achieve high-quality results for the CARP, the proposed algorithm was applied to solve the DARP-DD and MS-DARP-DD. Differently sized test problems were generated for the DARP-DD and MS-DARP-DD to test the performance of the proposed algorithm. The largest-sized test problem (DARP-7) had 34 components, 195 nodes, 200 required edges, and 18,915 non-required edges. The computational results show that the proposed metaheuristic algorithm was capable of solving differently sized problems within reasonable computation times. Considering the DARP-7 problem for the DARP-DD, the solution was obtained in about 1 h by using 21 drones with an energy capacity of 1500 Joules. The total traveled distance by the drones was obtained as 20137.3 units. Furthermore, the obtained drone routes reveal that the capacity utilization rates of the drones are quite high, and deadheading was made at the edges that give the shortest possible connection between the components. These results demonstrate that the proposed algorithm can solve these particular instances within reasonable computing times. However, it is important to note that the scope of these results is confined to the defined problem sizes and scenarios. The algorithm's performance may vary with different problem characteristics. Since the MS-DARP-DD has more edges than the DARP-DD, it needs more drones to service the required edges in most test problems. Furthermore, the total distance traveled by the drones and computation times increased in the MS-DARP-DD. When the drone routes for the MS-DARP-DD are analyzed, it is revealed that the required edges that need to be serviced more than once can be served by the same drones or by different drones. Therefore, this problem does not require the same drone to perform multiple services. The performance of the neighbor search operators was evaluated with regard to the number of times that they improved the current solution.