# Drone Arc Routing Problems and Metaheuristic Solution Approach
## 5 Computational Results
### Computational Results for DARP-DD
Therefore, the proposed algorithm provided a 9.9% better result for DARP-1 than the URL algorithm. For the large-sized DARP-7 problem, the proposed algorithm achieved an 18.4% better result than the URL algorithm. For the other test problems in Table 6, the proposed algorithm obtained an average of 14% higher quality results. Meanwhile, since the URL algorithm is a heuristic method, it is quite fast, and the results presented in Table 6 were obtained in less than three seconds for each test problem. The DARP-1 and DARP-6 problems are taken into consideration to display the drone routes that correspond to the obtained solution shown in Table 6. The drone routes for the DARP-1 problem are shown in Figure 6 while the drone routes for the DARP-6 problem are presented in Appendix A. As shown in Figure 6, 17 required edges were serviced by using four drones with an energy capacity of 500 Joules. The edges in each drone's route are shown in a different color. Dashed edges indicate deadheading on the relevant edge. Drone routes were obtained as follows:  
_First drone route (blue-colored route):_\(\text{d}(\text{depot}-10)-(10-8)-(8-7)-(7-9)-(9-10)\)\(-\)\(\text{d}(10-\text{depot})\). _Second drone route (red-colored route):_\(\text{d}(\text{depot}-16)-(16-15)-\text{d}(15-1)-(1-3)-\)\(\text{d}(3-6)-(6-5)-(5-4)-\text{d}(4-\text{depot})\). _Third drone route (green-colored route):_\(\text{d}(\text{depot}-2)-(2-1)-\text{d}(1-11)-(11-12)-\)\(\text{d}(12-6)-(6-4)-\text{d}(4-\text{depot})\). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & & **Proposed Simulated Annealing Algorithm** & \multicolumn{2}{c}{**URL Algorithm**} \\ \cline{5-10}
**Test** & **Number of** & **Number of** & **Number of** & **Number of** & **Results** & **Computation** & **Number of** & **Results** \\
**Problems** & **Components** & **Edges** & **Non-Required** & **Drones** & **(Objective** & **Times** & **Drones** & **(Objective** \\  & & & & & **Capacity)** & **Values)** & **(Seconds)** & **(Drone** & **Function** \\  & & & & & & **Capacity)** & **Values)** & **(Seconds)** & **Values)** \\ \hline DARP-1 & 5 & 17 & 171 & 4 (500 J) & 1204.46 & 30.4 & 5 (500 J) & 1324.12 \\ DARP-2 & 6 & 28 & 406 & 4 (1000 J) & 2429.58 & 66.1 & 5 (1000 J) & 2704.21 \\ DARP-3 & 10 & 44 & 1035 & 6 (1000 J) & 3287.91 & 190.7 & 6 (1000 J) & 3661.5 \\ DARP-4 & 11 & 64 & 2016 & 5 (1500 J) & 3915.78 & 554.3 & 5 (1500 J) & 4546.78 \\ DARP-5 & 19 & 84 & 3741 & 7 (1500 J) & 6238.37 & 810.6 & 8 (1500 J) & 7296.33 \\ DARP-6 & 17 & 100 & 4753 & 8 (1500 J) & 6916.44 & 1319.8 & 10 (1500 J) & 8033.11 \\ DARP-7 & 34 & 200 & 18915 & 21 (1500 J) & 20137.39 & 3651.3 & 24 (1500 J) & 23845.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The obtained results for the DARP-DD test problems. Analyzing the drone routes reveals that some components on the graph are serviced by the same drone, while other components are serviced by different drones. In addition, because the energy capacity of the drones is consumed during deadheading, deadheading was made at the edges that give the shortest possible connection between the components. The capacity utilization rates of the drones are 75%, 99%, 96%, and 97%, respectively. The objective function value, the total distance traveled by the drones, was obtained as 1204.46 units.