## 3 Hybrid Algorithm--RSO-IGA
The fitness function is defined as in Equation (23):

\[F=-\lambda_{1}u+\lambda_{2}V \tag{23}\]

#### 3.2.3 Crossover

This paper employs an improved order crossover method. The specific steps are as follows:

1. Select the same region on two parent chromosomes, \(P_{1}\) and \(P_{2}\);
2. Copy the genes from the selected region of \(P_{1}\) and \(P_{2}\) to the end of \(P_{1}\) and \(P_{2}\), respectively, resulting in \(P_{1^{\prime}}\) and \(P_{2^{\prime}}\);
3. Exchange the genes in the selected regions of \(P_{1^{\prime}}\) and \(P_{2^{\prime}}\), resulting in \(P_{1^{\prime}}\) and \(P_{2^{\prime}}\);
4. Remove the duplicate genes outside the selected regions in \(P_{1^{\prime}}\) and \(P_{2^{\prime}}\), yielding two offspring chromosomes, \(F_{1}\) and \(F_{2}\). The specific operation is illustrated in Figure 3:0

In Figure 9, the red arrow represents the segmentation of chromosome fragments, and the white arrow represents the change process of chromosome. After completing the crossover operation, it is necessary to verify whether the loading plan of the delivery vehicle satisfies the three-dimensional constraints. If not, the crossover operation is repeated. #### 3.2.4 Mutation

A chromosome is randomly selected from the population generated after the crossover operation for mutation. The mutation process is illustrated in Figure 10, the red arrow indicates the exchange of fragments of two chromosomes, and the white arrow indicates the change process of the whole chromosome. The steps are as follows:

1. Select some chromosomes from the parent generation based on the mutation probability;
2. Randomly select two genes from the parent chromosome and exchange them to produce a new offspring chromosome;

Figure 3:1 Crossing. (3) Verify whether the loading plan of the delivery vehicle after the mutation operation satisfies the three-dimensional constraints. If not, the mutation operation is repeated. The offspring generated after crossover and mutation are validated using the residual space-optimized three-dimensional bin packing algorithm to determine whether the plan can accommodate all parcels along the route. If successful, subsequent operations are performed; otherwise, the crossover and mutation operations are repeated. ### Algorithm Comparison

This paper further modifies the experimental data based on the following instances designed by [PERSON]:

(1) The number of customer points is increased;

(2) The types of boxes are expanded;

(3) Time windows are removed, and the modified data are shown in Figure 3:2 \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Serial** \\ **Number** \\ \end{tabular} } & \multirow{3}{*}{**Data ID**} & \multirow{3}{*}{\
\begin{tabular}{c} **Number** \\ **of Distri-** \\ **bution** \\ **Centers** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Number** \\ **of Customer** \\ **Points** \\ \end{tabular} } & \multicolumn{6}{c}{**Demand Quantity at Customer Points**} \\ \cline{4-10}  & & & & **First** & **Second** & **Third** & **Fourth** & **Fifth** & **Sixth** & **Total** \\  & & & **Type of** & **Type of** & **Type of** & **Type of** & **Type of** & **Type of** & **Number** \\  & & & **Points** & **Box** & **Box** & **Box** & **Box** & **Box** & **Box** & **Box** & **Box** & **of Boxes** \\ \hline



\hline \hline \end{tabular}
\end{table} 
Table 2: Experimental data. Figure 10: Mutation. ### Statistical Significance Analysis

In order to better reflect the evaluation effect of the RSO-IGA algorithm, ABC algorithm, and GA-TS algorithm, the Wilcoxon test is carried out, and the evaluation index includes the transportation distance (\(f\)) and loading rate (\(V\)). The test results are shown in Table 3, and the detailed analysis Table 4, is as follows: