# Time-Dependent Vehicle Routing Problem with Drones Under Vehicle Restricted Zones and No-Fly Zones
## 6 Numerical Experiments
### Sensitivity Analysis  
#### 6.4.1 Comparison on Different Vehicle Speeds  
In Section 6.3, four examples are selected, and three different vehicle speed cases are compared for analysis. Case 1 is consistent with the settings in Figure 3 of Section 3.3; case 2 follows the settings from reference [38], using a continuous piecewise function (as shown in Figure 9); and case 3 is set to a constant speed of 45 km/h. Table 4 presents the results obtained under these different vehicle speed cases. The metrics in Table 4 have the same meaning as those in Table 2. From Table 4, it is observed that the deviation between case 1 and case 2 ranges from \(-\)3.7% to 1.7%, while the deviation between case 1 and case 3 ranges from \(-\)5.2% to \(-\)1.4%. A comprehensive analysis shows that under the conditions of temporary restricted zones and no-fly zones, higher vehicle speed can reduce costs. At the same time, significant deviations are observed in vehicle routes, drone routes, delivery distances, and delivery costs under different vehicle speeds. This highlights the necessity for businesses to consider actual vehicle speeds when designing delivery plans to avoid resource waste. In the future, we will further explore the costs related to customer time windows and satisfaction.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**TN**} & \multirow{2}{*}{**N/N/1/N2**} & \multicolumn{4}{c}{**HGAVNS-LM**} & \multicolumn{4}{c}{**GAVNS**} & \multicolumn{2}{c}{**HGA**} & \multicolumn{2}{c}{**Des/\%**} \\ \cline{2-11}  & & **KI/K2** & **DI/D2** & **CI/C2/C** & **KI/K2** & **DI/D2** & **CI/C2/C** & **KI/K2** & **DI/D2** & **CI/C2/C** & **GAVNS** & **HGA** \\ \hline C01 & 30/3/2 & 2/7 & 217.9/75.71 & 785.6/15.8007 & 2/6 & 278.6/69.1 & 803.9/139/817.8 & 2/6 & 382.7/65.6 & 835.2/13.2/848.4 & 2.1 & 6.0 \\ C02 & 30/2/3 & 2/7 & 177.3/72.67 & 773.4/14.67920 & 2/7 & 321.5/66.6 & 816.8/13.4/80.32 & 2/7 & 350.9/63.62 & 825.7/17.8384.8 & 4.8 & 5.9 \\ C03 & 50/4/2 & 2/9 & 298.3/89.80 & 810.1/19.7/29.82 & 2/12 & 317.1/27.82 & 80.5/257.846.2 & 2/12 & 342.8/12.88 & 529.7/24.98546. & 2.0 & 3.0 \\ C04 & 50/4/3 & 2/10 & 302.0/19.3 & 816.4/22.0/38.4 & 2/13 & 334.3/141.4 & 821.3/28.6/849.9 & 2/12 & 416.18/127.7 & 846.7/25.7/872.4 & 1.4 & 4.1 \\ C05 & 75/8/4 & 3/20 & 397.3/211.49 & 419.6/25.4/124.1 & 3/2 & 449.7/286.3 & 12154.5/47.1237.3 & 4/18 & 390.1/235.7 & 1532.7/41.0/1573.7 & 2.5 & 26.7 \\ C06 & 75/10/6 & 3/23 & 519.3/28.126 & 135.4/97.28 & 1284.2/34.0 & 3/2 & 640.3/20.17 & 1272.8/45.4/1337.3 & 3/25 & 649.8/37.86 & 1289.2/77.9/1367.1 & 4.1 & 6.5 \\ C07 & 100/4/10 & 3/2 & 678.4/31.9 & 1284.2/62.7/134.6 & 3/2 & 789.4/353.0 & 1317.7/71.3/1389.0 & 4/23 & 627.6/295.5 & 1628.3/59.4/1687.7 & 3.1 & 25.3 \\ C08 & 100/10/8 & 5/33 & 520.3/276.4 & 1596.6/56.1/2012.7 & 6/27 & 465.3/358.0 & 2299.5/71.4/2370.9 & 6/24 & 719.4/278.1 & 2376.6/55.9/2432.5 & 17.8 & 20.9 \\ Avg & - & - & - & - & - & - & - & - & - & 4.7 & 12.3 \\ \hline \hline \end{tabular} Note: dev = (C(GAVNS/GA) - CHGAVNS-LM)/C(HGAVNS-LM) \(\times\) 100%.  
\end{table}
Table 3: Algorithm validation results.