# Variable Neighborhood Search for the Two-Echelon Electric Vehicle Routing Problem with Time Windows
## 5 Computational Experiments
### Numerical Results
Moreover, the superiority of VNS\({}_{\text{full}}\) over VNS\({}_{\text{red}}\) is much more significant in the context of instances with a long scheduling horizon (R2* C2* and RC2*) compared to the instances with a short scheduling horizon (R1* C1* and RC1*); see Figure 8e,f. Finally, when considering all large instances together, VNS\({}_{\text{full}}\) significantly outperforms VNS\({}_{\text{red}}\) (see also Figure 8a). \begin{table}
\begin{tabular}{c c c c|c c c|c c c c|c c c c|c c c c} \hline \hline \multicolumn{1}{c|}{**Instances**} & \multicolumn{1}{c|}{**C\&W Savings Heuristic**} & \multicolumn{1}{c|}{**VNS\({}_{\text{red}}\)**} & \multicolumn{1}{c}{**VNS\({}_{\text{full}}\)**} & \multicolumn{1}{c}{**VNS\({}_{\text{full}}\)**} & \multicolumn{1}{c}{**} \\
**Name** & \(\mathbf{n_{k}}\) & \(\mathbf{n_{v}}\) & **m** & **n** & **Dist** & \(\overline{\mathbf{t(s)}}\) & **m** & **n** & **Dist** & **Avg** & **Imp(\%)** & \(\overline{\mathbf{t(s)}}\) & **m** & **n** & **Dist** & **Avg** & **Imp(\%)** & \(\overline{\mathbf{t(s)}}\) \\ \hline C101\_C21 & 3 & 25 & 3 & 39 & 1941.16 & 0.005 & 3 & 20 & 1513.91 & 1562.77 & 19.49 & 499.70 & 3 & 20 & **1494.18** & **1538.74** & 20.73 & 579.98 \\ C102\_C21 & 3 & 28 & 3 & 33 & 1822.02 & 0.005 & 3 & 21 & 1501.66 & 1506.95 & 17.29 & 537.57 & 3 & 19 & **1447.86** & **1487.11** & 18.38 & 572.03 \\ C103\_C21 & 3 & 26 & 3 & 29 & 1702.89 & 0.005 & 3 & 20 & 1447.98 & 1463.34 & 14.07 & 509.37 & 3 & 19 & **1399.25** & **1425.80** & 16.27 & 656.63 \\ C104\_C21 & 3 & 31 & 3 & 24 & 1580.07 & 0.005 & 3 & 20 & 1435.04 & 1446.17 & 8.47 & 405.19 & 3 & 19 & **1400.52** & **1439.76** & 8.88 & 540.97 \\ C105\_C21 & 4 & 43 & 3 & 36 & 1877.85 & 0.005 & 3 & 20 & 1522.97 & 1541.60 & 17.91 & 359.00 & 3 & 20 & **1493.69** & **1521.13** & 19.00 & 466.13 \\ C106\_C21 & 4 & 37 & 3 & 35 & 1791.74 & 0.004 & 3 & 20 & 1474.74 & 1491.70 & 16.75 & 361.26 & 3 & 20 & **1429.75** & **1476.85** & 17.57 & 536.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Computational results for large-sized clustered instances. \begin{table}
\begin{tabular}{c c c c|c c c c|c c c c|c c c c|c c c c} \hline \hline \multicolumn{1}{c|}{**Instances**} & \multicolumn{1}{c|}{**C\&W Savings Heuristic**} & \multicolumn{1}{c|}{**VNS\({}_{\text{red}}\)**} & \multicolumn{1}{c}{**VNS\({}_{\text{full}}\)**} & \multicolumn{1}{c}{**VNS\({}_{\  
When comparing the algorithms in terms of the average computation times required to find the best solutions of a run, it can be seen that VNS\({}_{\text{red}}\) was able to provide solutions in lower CPU times than VNS\({}_{\text{full}}\). We can infer that destroy and repair type operators help to produce better solutions; however, repairing a destroyed solution prolongs the computation time. Finally, VNS\({}_{\text{red}}\) and VNS\({}_{\text{full}}\) produced comparable results for small problem instances in terms of the number of utilized vehicles. In contrast, the increased effectiveness of VNS\({}_{\text{full}}\) is shown in the context of large problem instances. Even though making use of a lower number of vehicles usually means that a better solution is obtained, note that a smaller fleet size does not always guarantee a better solution. For some of the instances (i.e., C103_C15, R202_C15), even though VNS\({}_{\text{red}}\) provides solutions with a lower fleet size than VNS\({}_{\text{full}}\), the solutions of VNS\({}_{\text{full}}\) are better. The reason for this is that the objective function only minimizes the traveled distance. It is also worth noting that the average improvement rate with respect to the solutions of the C&W savings heuristic for large clustered problem instances is lower than in the context of the random and random-clustered instances. One reason for this is possibly the assignment of each customer to the nearest satellite in the initial solution construction phase, which provides most probably a better customer-satellite assignment than in the context of random instances.