# The Electric Vehicle Routing Problem with Time Windows, Partial Readers, and Parcel Lockers
## 5 Experimental Results
### Results on EVRPTW-PR-PL  
This section presents an analysis of the effectiveness of our proposed ALNS for solving EVRPTW-PR-PL instances. We first find solutions to the EVRPTW-PR-PL instances by solving the model presented in Section 3 using a commercial solver (i.e., GUROBI). While optimal solutions are found for small-sized instances, no feasible solution is obtained after 2 h for large-sized instances. Our ALNS is then implemented to solve these instances, especially large ones. Tables A8-A10 present the results obtained by both GUROBI and ALNS for small-sized instances with 5, 10, and 15 customers, respectively. Here, optimal solutions are provided by GUROBI. Our ALNS algorithm also provides optimal solutions for all instances within an average computational time of 0.51 seconds. For large-sized instances, the detailed results of subsets C-1, C-2, R-1, R-2, RC-1, and RC-2 are in Tables A11-A16, respectively. Each table presents the best solutions \(f_{b}\) and the average solutions \(f_{a}\) after 10 runs. To assess the algorithm's performance, we calculate the gap between the average cost value (\(f_{a}\)) and the best cost value (\(f_{b}\)), denoted by \(\Delta f_{(a-b)}\). This gap indicates the algorithm's stability in finding solutions. Our ALNS performs stability and efficiency analyses when solving large EVRPTW-PR-PL instances with an average gap \(\Delta f_{(a-b)}\) of 3.33%. Figure 4: Comparison results on EVRPTW-PR instances among algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Subset**} & \multicolumn{4}{c}{**Average of the Best Solution of 10 Runs (\(\tilde{f_{b}}\))**} & \multicolumn{4}{c}{**Average Gap (\(\Delta\tilde{f}[\%]\))**} & \multirow{2}{*}{\(\tilde{I}\)**(min)**} \\ \cline{2-2} \cline{5-11}  & **BKS** & **KC** & **SW** & **HGA** & **ALNS** & **BKS** & **KC** & **SW** & **HGA** & **ALNS** \\ \hline C-1 & 994.57 & 1004.04 & 994.99 & 1002.25 & 1005.62 & 1.13 & 0.20 & 0.73 & \(-\)0.34 & 0.00 & 12.64 \\ C-2 & 629.82 & 629.95 & 629.82 & 640.99 & 629.82 & 0.00 & \(-\)0.02 & 0.00 & \(-\)1.77 & 0.00 & 5.78 \\ R-1 & 1199.67 & 1221.70 & 1213.96 & 1239.72 & 1222.96 & 1.88 & 0.09 & 1.57 & \(-\)1.41 & 0.00 & 15.17 \\ R-2 & 909.69 & 927.76 & 923.09 & 914.76 & 918.90 & 0.98 & 0.32 & 0.86 & 0.40 & 0.00 & 11.06 \\ RC-1 & 1365.25 & 1403.33 & 1321.07 & 1389.71 & 1404.22 & 2.70 & 0.52 & 2.66 & 1.05 & 0.00 & 15.73 \\ RC-2 & 1130.90 & 1140.07 & 1134.66 & 1142.61 & 1142.23 & 0.98 & 0.19 & 0.66 & 0.06 & 0.00 & 10.74 \\ \hline Average & 1038.32 & 1054.48 & 1036.27 & 1055.01 & 1053.96 & 1.28 & 0.22 & 1.08 & \(-\)0.33 & 0.00 & 11.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the results of the large-sized EVRPTW-PR instances among algorithms. We also evaluate the impacts of _lockerRemovallInsertion_() operators by varying the value of \(\delta_{L}\) within a range of \(\{0.1,0.2,\ldots,1.0\}\) for solving large-sized instances. Table 4 presents the results from ALNS with different \(\delta_{L}\) values. The table includes the overall best objective values obtained for all instances after 10 runs (\(\tilde{f}_{b}\)) and the average computational time (\(\tilde{f}\)). For each value of \(\delta_{L}\), the gap between \(\tilde{f}_{b}\) and the minimum of all \(\tilde{f}_{b}\) values is calculated by \(\Delta\tilde{f}_{b}=\frac{\tilde{f}_{b}-\min(\tilde{f}_{b})}{\min(\tilde{f}_{ b})}\). Based on these results, Figure 5 shows that the _lockerRemovallInsertion_() operators significantly improve the performance of our ALNS in solving EVRPTW-PR-PL. In particular, ALNS without using the _lockerRemovallInsertion_() (i.e., \(\delta_{L}=0\)) provides the worst results among all cases, with a gap of 1.02%. It is worth noting that the best performance of ALNS is achieved at \(\delta_{L}=0.3\).