## 5 Experiment Results
### Effectiveness Evaluation against the Known Optimal Solutions  
The main difference between our R-VRPTWLST and the VRPTW lies in the following two aspects: first, survivors at the site are given limited survival time constraints, and second, the transport helicopters can also be used to transfer survivors under given conditions, i.e., when the transport helicopter's load is less than half of its maximum capacity and the survivors' life strength could endure the subsequent journey until they are transported to the rescue center. In these cases, transport helicopters deliver rescue supplies along the way to pick up survivors. Although the travel route of transport helicopters may not be optimal, if several survivors are transported along the way, it reduces the number of sites that medical helicopters need to arrive to, indirectly reducing the travel route of medical helicopters. As we take the sum of the route lengths flown by two types of helicopters as the optimization objective, we present a joint rescue problem involving these two types of helicopters, i.e., R-VRPTWLST. In order to further decouple the R-VRPTWLST problem and evaluate the effectiveness of the IIG, we employed the Solomon instances' best solution to create instances of the R-VRPTWLST, where problem parameters are chosen so that the given route is still feasible. Since the optimal solutions of Solomon instances in the literature are values, rather than the specific route sequence, to simplify this creation process, we removed the constraint of limited survival time for survivors. Specifically, we set the survivor's life strength value to infinity to ensure that limited survival time does not become a condition that affects helicopter path optimization. This rescue path planning problem is named R-VRPTWLST  
Figure 5: ANOVA of the IIG and IIG_NS. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Instances**} & \multirow{2}{*}{**Better Values**} & \multicolumn{2}{c}{**Algorithms**} & \multicolumn{2}{c}{**RPIs**} \\ \cline{3-6}  & & IIG & IIG\_NS & IIG & IIG\_NS \\ \hline rrc104 & 2045.94 & **2045.94** & 2093.10 & **0.00** & 2.31 \\ rrc105 & 2454.70 & **2454.70** & 2540.50 & **0.00** & 3.50 \\ rrc106 & 2333.60 & **2333.60** & 2413.30 & **0.00** & 3.42 \\ rrc107 & 2159.70 & **2159.70** & 2235.99 & **0.00** & 3.53 \\ rrc108 & 2172.61 & **2172.61** & 2252.53 & **0.00** & 3.68 \\ rrc201 & 2741.56 & **2741.56** & 2838.36 & **0.00** & 3.53 \\ rrc202 & 2560.35 & **2560.35** & 2665.13 & **0.00** & 4.09 \\ rrc203 & 2396.92 & **2396.92** & 2515.60 & **0.00** & 4.95 \\ rrc204 & 2245.18 & **2245.18** & 2365.22 & **0.00** & 5.35 \\ rrc205 & 2886.66 & 3165.74 & **2886.66** & 8.82 & **0.00** \\ rrc206 & 2614.92 & **2614.92** & 2746.17 & **0.00** & 5.02 \\ rrc207 & 2380.57 & **2380.57** & 2450.92 & **0.00** & 2.96 \\ rrc208 & 2248.49 & **2248.49** & 2347.66 & **0.00** & 4.41 \\ Mean & 2011.12 & 2018.88 & 2059.98 & 0.45 & 2.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._ILS and the corresponding instance is marked as '****_ILS'. Additional experiments were conducted to solve these instances using the proposed IIG algorithm. Table 6 presents the comparison results of the IIG used to deal with two types of R-VRPTWLST instances. In Table 6, the first two columns provide traditional Solomon instances and their corresponding known optimal values. The third to sixth columns provide the corresponding results of using the IIG to solve the R-VRPTWLST-ILS instances, where THD value represents the traveled distance of the transport helicopters, THD value describes the traveled distance of the medical helicopters, and OD value gives the total distance of the two types of helicopters. The seventh to tenth columns present the results of the IIG solving the R-VRPTWLST problem. Since these R-VRPTWLST-ILS's instances are created based on Solomon instances' best solution, it is simply a VRPTW problem for the rescue route planning of transporting rescue supplies by transport helicopters.