# A Hyper Heuristic Algorithm to Solve the Low-Carbon Location Routing Problem
## 5 Simulation Experiment and Analysis
### Efficient Analysis of High-Level Strategies  
Experiments in this section used the Barreto [42] example for LCLRP and the \(W\) class of the CLAM and YLBAM instance library [43] for the capacitated location-routing problem with simultaneous pickup and delivery (CLRPSPD). The N in the example was between 21 and 150, and the M was between 5 and 15.  
The experimental results are shown in Table 3, where the BKS is the best-known solution, Gap1 and Gap2 are the optimal solution and the percentage difference between the average and the BKS, SD and MT are the optimal solution standard deviation and average running time (seconds). The average value, Av., and the median value, Md., are given at the end (the black body indicates that the number is equal to the BKS, black body and italic indicate new BKS). This section sets \(T_{\text{max}}=\min(5\times(M+N+K)^{2},8\times 10^{4})\), and the number of independent running is \(OI=10\).  
It can be seen from Table 3 that SESMAM-HH obtained the optimal solution for all LCLRP examples, and the optimal solution for 12 CLRPSPD examples. Three new BKSs were obtained with an improvement rate of 0.8%, 6.7%, and 4.4%. This experiment proves the effectiveness of the proposed algorithm in solving the CLRPSPD/LCLRP.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{3}{c}{**CPLEX**} & \multicolumn{3}{c}{**HH-SESMAM-AA**} & \multirow{2}{*}{**Instance**} & \multicolumn{3}{c}{**CPLEX**} & \multicolumn{3}{c}{**HH-SESMAM-AA**} \\ \cline{2-11}  & **TC** & **MT** & **Gap** & **SD** & **MT** & & **TC** & **MT** & **Gap** & **SD** & **MT** \\ \hline L10 \(\times\) 2 - 1 & 441.54 & 3.61 & 0.0 & 0.0 & 0.37 & L15 \(\times\) 3 - 4 & 461.54 & 5.59 & 0.0 & 0.0 & 1.53 \\ L10 \(\times\) 2 - 2 & 425.41 & 2.15 & 0.0 & 0.0 & 0.35 & L15 \(\times\) 3 - 5 & 472.86 & 12.64 & 0.0 & 0.0 & 1.59 \\ L10 \(\times\) 2 - 3 & 529.95 & 0.87 & 0.0 & 0.0 & 0.37 & L20 \(\times\) 5 - 1 & 788.76 & 890.45 & 0.0 & 0.0 & 3.74 \\ L10 \(\times\) 2 - 4 & 549.78 & 0.65 & 0.0 & 0.0 & 0.36 & L20 \(\times\) 5 - 2 & 894.56 & 501.18 & 0.0 & 0.0 & 3.46 \\ L10 \(\times\) 2 - 5 & 424.88 & 1.12 & 0.0 & 0.0 & 0.39 & L20 \(\times\) 5 - 3 & 746.06 & 1061.27 & 0.0 & 0.0 & 3.75 \\ L15 \(\times\) 3 - 1 & 484.02 & 15.37 & 0.0 & 0.0 & 1.37 & L20 \(\times\) 5 - 4 & 950.89 & 1667.13 & 0.0 & 0.0 & 0.3 & 3.84 \\ L15 \(\times\) 3 - 2 & 683.62 & 10.26 & 0.0 & 0.0 & 1.39 & L20 \(\times\) 5 - 5 & 916.30 & 476.24 & 0.0 & 0.0 & 0.3 & 3.53 \\ L15 \(\times\) 3 - 3 & 545.40 & 7.94 & 0.0 & 0.0 & 1.64 & & & & & & \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Av.**} & \multicolumn{3}{c}{**Av.**} & \multicolumn{3}{c}{618.04} & \multicolumn{3}{c}{310.43} & \multicolumn{3}{c}{0.0} & \multicolumn{3}{c}{0.0} & \multicolumn{3}{c}{1.85} \\ \cline{2-11}  & **BKS** [43] & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of small instances.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**BKS [44]**} & \multicolumn{3}{c}{**LCLRP**} & \multirow{2}{*}{**BKS [43]**} & \multicolumn{3}{c}{**CLRPSPD**} \\ \cline{3-10}  & & **Gap\({}_{1}\)** & **Gap\({}_{2}\)** & **SD** & **MT** & & **Gap\({}_{1}\)** & **Gap\({}_{2}\)** & **SD** & **MT** \\ \hline G21 \(\times\) 5 & 424.9 & **0.00** & 0.00 & 0.00 & 0.75 & 528.42 & **0.00**