# Two-Stage Metaheuristic Algorithms for Order-Batching and Routing Problems
## 5 Computational Experiment
### Algorithm Parameters  
Regarding the VNS algorithm, the perturbation frequency equaled the perturbation factors, and the perturbation frequency was derived as follows: perturbation factor \(\times\) order number. A test was performed in all scenarios involving 40 orders and various perturbation factors (Table 6). Regarding the SA algorithm, the starting temperature was set at 10,000 \({}^{\circ}\)C, the annealing parameter was 0.001, and the unimproved number of iterations was 100. A test was performed in all scenarios involving 40 orders and different \(L_{max}\) values (Table 6).  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **SO** & **FFD** & **RB** & **BF** & **BFD** \\ \hline Mean & 1603.9 & 721.1 & 1197.0 & 724.6 & 710.0 \\ Std. & 1202.1 & 557.8 & 906.5 & 566.4 & 542.1 \\ \hline \end{tabular}
\end{table}
Table 4: Mean value and standard deviation of initial solutions (unit: m).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**Initial Batch** & \multicolumn{4}{c}{**FFD**} & \multicolumn{4}{c}{**BF**} & \multicolumn{4}{c}{**BFD**} \\ \cline{2-13}
**Solution \#** & \multicolumn{4}{c}{**Number of Orders**} & \multicolumn{4}{c}{**Number of Orders**} & \multicolumn{4}{c}{**Number of Orders**} \\ \cline{2-13}
**Scenario \#** & **10** & **20** & **40** & **80** & **10** & **20** & **40** & **80** & **10** & **20** & **40** & **80** \\ \hline
1 & 152 & 341 & 685 & 1311 & 183 & 325 & 665 & 1339 & 17  
First, we focused on two parent groups--those involving chains with lengths of 10 and 15--to test whether the variance was the same. \(H_{0}:\sigma_{1}=\sigma_{2}\); \(H_{1}:\sigma_{1}\
eq\sigma_{2}\); mean value \(\overline{X}_{L10}=600.2\); \(\overline{X}_{L15}=618.7\); standard deviation \(S^{2}_{L10}=16,702.9\); \(S^{2}_{L15}=17,618.7\); rejection region \(C=F_{0.025}(7,7)\)_or_\(1/F_{0.025}(7,7)\); and \(F=0.948\
otin\) C; moreover, \(H_{0}:\sigma_{10}^{2}=\sigma_{15}^{2}\). Subsequently, we continued to test the average of the two parent groups, \(H_{0}\): \(\mu_{1}-\mu_{2}\leq 0\) and \(H_{1}\): \(\mu_{1}-\mu_{2}>0\), where \(\mu_{1}\) represents the average of a chain with a length of 10, \(\mu_{2}\) is the average of a chain with a length of 15, and \(t=0.291\), C[\(t\,|\,t>t_{0.05}\) (14) = 1.761], and \(t\
otin C\). Hence, \(H_{0}\) was not rejected, and consequently, the average influence of the chain with \(L_{max}=10\) on the objective value was nonsignificant.  
The test results revealed that the chain length influenced the objective value of the solution to only a small degree and that no significant difference in the solving speed existed under the various perturbation factors. Moreover, Table 6 demonstrates no apparent significant difference. Consequently, we adopted \(L_{max}=10\) as the parameter setting.  
When the perturbation factors were 0.2 and 0.4 (Table 7), the factors demonstrated the same objective value and did not influence the solving value; moreover, the solving speed did not differ notably. However, in the example of scenario 5, a relative difference was apparent.  
Regardless of whether the perturbation factor was 0.2 or 0.4, the objective value was the same. Therefore, we set the parameter of the perturbation factor at 0.2, a value that reduced the computation time. Moreover, because a few parameters in each scenario, such as order item, order capacity, and vehicle capacity, were generated randomly through a uniform distribution, merely comparing the influences and correlations of these items can hardly yield meaningful results.