# Drone Arc Routing Problems and Metaheuristic Solution Approach
## 5 Computational Results
### Performance of the Simulated Annealing Algorithm Components
DARP-6 was solved considering the algorithm's initial temperature values as 50, 100, 150, and 200 and the number of iterations at each temperature as 2000, 2500, 3000, and 3500, and the obtained results of these experiments are presented in Table 9. The algorithm was run 10 times for each initial temperature and the number of iterations. Table 9 presents the minimum deviation value, average deviation value, and computation times of each experiment. The deviation values were calculated using the objective function value of 6916.44 units as the basis. This objective function value, which is shown in the convergence graph, was obtained by setting the initial temperature value to 100 and the number of iterations to 2500. Table 9 shows that the best obtained solution (the solution having objective function value of 6916.44 units) for the DARP-6 problem was reached when the initial temperature values were 100, 150, and 200 and the number of iterations at each temperature was 2500, 3000, and 3500. Consequently, the initial temperature value of 100 and the number of iterations at each temperature of 2500 provide the shortest computation time among the parameter values enabling the best solution to be obtained. That is why the initial temperature value was set to 100 and the number of iterations performed at each temperature was set to 2500. Figure 9 shows the performance of the neighbor search operators used in the structure of the algorithm whose convergence graph is drawn in Figure 8. The performance of the neighbor search operators is evaluated with regard to the number of times they improve the current solution. Regarding Figure 9, the edge postpone operator (F) demonstrates the highest performance with regard to the number of improvements to the current solution and contributes the greatest to obtaining high-quality solutions. The edge postpone operator (F) improved the current solution value 66 times. Another operator with high performance is the \(k\)-route shorten operator (E). The \(k\)-route shorten operator (E) contributes to improving the current solution 40 times. Apart from the \(k\)-route shorten (E) and edge postpone operators (F), the other operators that contribute the most to obtaining quality solutions are smart reverse (C), edge direction and smart edge direction change (G), and route-repairing operators (H). \begin{table}
\begin{tabular}{c c c c c} \hline
**Initial** & **Number of** & **Minimum Gap** & **Average Gap** & **Computation** \\
**Temperature** & **Iteration** & **Minimum Gap** & **Average Gap** & **Times (Seconds)** \\ \hline \multirow{4}{*}{50} & 2000 & 0.012 & 0.025 & 850 \\  & 2500 & 0.008 & 0.016 & 1100 \\  & 3000 & 0.007 & 0.016 & 1423 \\  & 3500 & 0.007 & 0.015 & 1542 \\ \hline \multirow{4}{*}{100} & 2000 & 0.005 & 0.015 & 1024 \\  & 2500 & - & 0.012 & 1319 \\  & 3000 & - & 0.01 & 1619 \\  & 3500 & - & 0.009 & 1825 \\ \hline \multirow{4}{*}{150} & 2000 & 0.005 & 0.013 & 1044 \\  & 2500 & - & 0.011 & 1391 \\  & 3000 & - & 0.01 & 1698 \\  & 3500 & - & 0.009 & 1918 \\ \hline \multirow{4}{*}{200} & 2000 & 0.004 & 0.011 & 1105 \\  & 2500 & - & 0.01 & 1458 \\ \cline{1-1}  & 3000 & - & 0.009 & 1805 \\ \cline{1-1}  & 3500 & - & 0.009 & 2008 \\ \hline \end{tabular}
\end{table} 
Table 9: Parameter analysis for the DARP-6 problem. The following comments can be made considering the temperature values at which the neighbor search operators improve the current solution. It is seen that the edge postpone operator (F), which has the highest performance in improving the solution, contributes to reaching quality solutions from the initial temperature to the final temperature of the algorithm. The \(k\)-route shorten operator (E), which is the second highest performing operator, has improved the current solution at several temperature values similar to the edge postpone operator (F). The final temperature value at which the \(k\)-route shorten operator (E) improves the current solution is approximately 10.