## 3 Hybrid Algorithm--RSO-IGA
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **Comparison** & \(p\)**-Value** \\ \hline Distance (\(f\)) & RSO-IGA and ABC algorithm & \(2.384\times 10^{-6}\) \\ Distance (\(f\)) & RSO-IGA and GA-TS algorithm & \(2.384\times 10^{-6}\) \\ Average loading rate (\(V\)) & RSO-IGA and ABC algorithm & \(1.6689\times 10^{-6}\) \\ Average loading rate (\(V\)) & RSO-IGA and GA-TS algorithm & \(5.7363\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(p\) value comparison between different algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Serial**} & \multirow{2}{*}{**Data ID**} & \multirow{2}{*}{
\begin{tabular}{c} **Number** \\ **of Distribution** \\ **Centers** \\ \end{tabular} } & \multicolumn{3}{c}{**Number**} & \multicolumn{6}{c}{**Demand Quantity at Customer Points**} \\ \cline{4-11}  & & & **First** & **Second** & **Third** & **Fourth** & **Fifth** & **Sixth** & **Total** \\ \cline{2-11}
**Number** & & **\begin{tabular}{c} **[-1.0**]** **bution** \\ **Centers** \\ \end{tabular} & \begin{tabular}{c} **[-1.0**]** **tomer** \\ **Points** \\ \end{tabular} & \begin{tabular}{c} **[-1.0**]** **Type of** \\ **Box** \\ \end{tabular} & \begin{tabular}{c} **Type of** \\ **Box** \\ \end{tabular} & \begin{tabular}{c} **Type of** \\ **Box** \\ \end{tabular} & \begin{tabular}{c} **Type of** \\ **Box** \\ \end{tabular} & \begin{tabular}{c} **Type of** \\ **Box** \\ \end{tabular} & \begin{tabular}{c} **Type of** \\ **Box** \\ \end{tabular} & \
\begin{tabular}{c} **Type of** \\ **Box** \\ \end{tabular} &
\begin{tabular}{c} **Number** \\ **of Boxes** \\ \end{tabular} \\ \hline
20 & Pr-20 & 1 & 120 & 213 & 21 & 34 & 52 & 79 & 24 & 535 \\
21 & Pr-21 & 1 & 200 & 159 & 47 & 56 & 21 & 45 & 76 & 581 \\
22 & Pr-22 & 1 & 200 & 54 & 67 & 50 & 43 & 146 & 34 & 581 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(Cont.\)

\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Serial** & \multicolumn{3}{c}{**RSO-IGA**} & \multicolumn{3}{c}{**Artificial Bee Colony Algorithm**} & \multicolumn{3}{c}{**GA-TS Algorithm**} \\ \cline{2-11}
**Number** & \(f\) & \(V\) & \(T\) & \(f\) & \(V\) & \(T\) & \(f\) & \(V\) & \(T\) \\ \hline
1 & 934 & 65.21 & 653 & 1332 & 63.99 & 1055 & 1523 & 68.75 & 975 \\
2 & 852 & 68.56 & 624 & 1248



Based on the Wilcoxon test results, the RSO-IGA algorithm showed statistically significant advantages in both aspects (all \(p<0.01\)): In the optimization of transportation distance, RSO-IGA has extremely significant improvement compared with ABC algorithm and GA-TS algorithm (\(p=2.384\times 10^{-6}\)), indicating that its path planning ability is significantly better than the two comparison algorithms. In terms of loading rate, the difference between RSO-IGA and ABC algorithm was extremely significant (\(p=1.6689\times 10^{-6}\)), while the improvement between RSO-IGA and GA-TS algorithm was small but still significant (\(p=0.0057\)). These results prove that RSO-IGA achieves statistically significant performance improvements on both key metrics of the logistics optimization problem. The distance optimization is more consistent (reaching \(1\times 10^{-6}\) level significance in both comparisons), while the loading rate optimization is significant, but the difference is relatively limited in the GA-TS algorithm comparison. ## 4 Case Validation

### Algorithm Parameter Determination

The case data are derived from the order data delivered on a certain day at H University, comprising a total of 472 parcels. After removing redundant information, details such as \"quantity of goods\", \"box dimensions\", and \"delivery customer points\" are retained. Specific parameters are provided in Table 11.

The delivery vehicle used by H University's Cainiao Station has a cargo compartment size of 1800 mm \(\times\) 1000 mm \(\times\) 1200 mm. Based on the algorithm's packing performance and practical considerations, the correction coefficient is set to 80%.