# A Hyper Heuristic Algorithm to Solve the Low-Carbon Location Routing Problem
## 5 Simulation Experiment and Analysis
### Experiments and Analyses
#### 5.3.4. The Impact of the Fleets on Costs and Carbon Emissions  
This section analyzes the impact of fleets on logistics costs and carbon emissions by solving the LVEHIC case. The results are shown in Table 7.  
As seen from Table 7, _HF_ can obtain the lowest _TC_ and _CO\({}_{2}\)_. _RC_ of _HF_ is smaller than \(L\)1 and \(M\), but greater than \(L\)2, at approximately 1.3%, mainly reflecting the influence of different fleets and quantities on _RC_. Different fleets have no effect on depots selection. _PF_ and _CWT_ values of \(L\)1 are the  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{6}{c}{**RLCRPTWSPDHF**} & \multicolumn{6}{c}{**RLRPTWSPDHF**} \\ \cline{2-11}  & **TC** & **FC** & **PF** & **CO\({}_{2}\)** & **D** & **CWT** & **MT** & \(\Delta\)**TC** & \(\Delta\)**CO\({}_{2}\)** & \(\Delta\)**D** & \(\Delta\)**CWT** \\ \hline  
d.** & 1789.98 & 351.54 & 97.90 & 106.07 & 139.94 & 169.32 & 106.85 & 1.89 & 14.07 & 11.38 & \(-\)13.90 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Results of two models on LDEPOT.  
Figure 5: The trend in the average value of the six types of parameters.  
smallest, indicating that \(L1\) vehicle plays a key role in customer satisfaction. The reason is that time window parameters may be consistent with \(L1\) vehicle parameters. According to \(D\) value analysis, \(L2\) and \(M\) have smaller \(D\) values, because the vehicle capacity is relatively large and can serve more customers. Figure 6 is a box plot of vehicle capacity utilization. The average full load of HF is 85.92%, which is higher than that of 25.28% and 105.26% for L2 and M, but lower than 4.61% for L1.  
As can be seen from the above, using HF can reduce logistics costs and carbon emissions compared with a single type vehicle, but there is no guarantee of obtaining optimal values of waiting time, service distance, and vehicle full load rate. However, it can still be strongly inferred that the HF has huge advantages over a single car model and can better meet the requirements of practical distribution applications.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{6}{c}{**HF**} & \multicolumn{6}{c}{**L\({}_{1}\)**} \\ \cline{2-13}  & **TC** & **RC** & **PF** & **CO\({}_{2}\)** & **D** & **CWT** & \(\Delta\)**TC** & \(\Delta\)**RC** & \(\Delta\)**PF** & \(\Delta\)**CO\({}_{2}\)** & \(\Delta\)**D** & \(\Delta\)**CWT** \\ \hline
25-1 & 843.0 & 561.1 & 82.7 & 60.1 & 81.0 & 150.3 & 1.54 & 4.42 & \(-\)39.90 & 10.66 & 21.81 & \(-\)48.95 \\
25-2 & 990.3 & 742.1 & 52.0 & 59.2 & 88.1 & 70.7 & 0.85 & \(-\)0.84 & \(-\)5.59 & 8.95 & 11.73 & 2.57 \\
25-3 & 838.9 & 561.1 & 65.3 & 64.1 & 85.5 & 120.3 & 1.21 & 4.42 & \(-\)18.88 & \(-\)1.10 & 8.61 & \(-\)29.45 \\
50-1 & 1445.1 & 1059.8 & 66.6 & 96.1 & 123.6 & 104.7 & 3.44 & 5.85 & \(-\)53.14 & 7.26 & 14.54 & \(-\)91.94 \\
50-2 & 1582.1 & 1209.8 & 79.9 & 88.2 & 120.7 & 132.4 & 1.56 & 2.05 & \(-\)14.12 & 3.83 & 9.19 & \(-\)28.99 \\
50-3 & 1552.7 & 1178.8 & 95.1 & 84.1 & 114.7 & 156.9 & 2.19 & 4.73 & \(-\)47.24 & 8.28 & 16.89 & \(-\)69.46 \\
75-1 & 1850.0 & 1383.8 & 74.8 & 118.1 & 171.6 & 102.9 & 2.87 & 3.58 & 11.25 & \(-\)12.3 & 5.15 & \(-\)18.78 \\
75-2 & 1928.7 & 1396.2 & 88.2 & 134.1 & 183.4 & 118.2 & 1.52 & 2.66 & \(-\)28.78 & 3.94 & 5.68 & \(-\)47.61 \\
75-3 & 1524.9 & 1027.6 & 106.8 & 117.8 & 158.1 & 166.2 & 3.40 & 5.43 & \(-\)23.64 & 5.47 & 11.02 & \(-\)40.65 \\
100-1 & 27