## 4 Example Experiments
### Algorithm Performance Testing  
Based on the multimodal transport network presented in Section 3.1, twenty-two examples were designed. The quantities of equipment at the twenty origins (see Table 8, ranging between 400 and 900 units) and the transshipment efficiencies of eight upstream stations (see Table 9, ranging between 2 and 30 units/h) and three downstream stations (see Table 10, ranging between 2 and 30 units/h) were randomly generated. Then, twelve small-scale examples (tests 1 to 12, see columns 1 to 4 in Table 11) and ten larger-scale examples (tests 13 to 22, see columns 1 to 4 in Table 12) were designed. Test 1 selected origins 1 to 5, upstream stations TL and LZ, as well as downstream stations AKS and KEL. As the scale of the examples gradually increased, the origins were added sequentially according to the rows in Table 5, and upstream and downstream stations were added sequentially according to the columns in Tables 6 and 7, respectively. For example, test 2 added upstream station NJ to test 1, test 3 added origin 6 to test 1, and so on. The GA_GA was used to solve these examples with each calculated ten times. The results are shown in columns 5 and 6 of Tables 11 and 12, where Obj and Cpu represent the average objective value and average computation time of a single experiment, respectively (in all subsequent experiments, Obj and Cpu are the averages of ten repeated calculations). The parameters of GA_GA were set as follows. The outer layer has a population size of 10, a crossover probability of 0.9, a mutation probability of 0.1, and a maximum number of generations of 100. The inner layer has a population size of 20, a crossover probability of 0.9, a mutation probability of 0.1, and a maximum number of generations of 50. Additionally, other solution methods were also designed. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Downstream**} & \multicolumn{8}{c}{**Upstream Station**} \\ \cline{2-10}  & **NJ** & **FY** & **ZZ** & **YT** & **KM** & **HEB** & **TL** & **LZ** & **JC** & **XA** \\ \hline KS & 5176 & 4573 & 4168 & 5057 & 6047 & 5893 & 5265 & 3030 & 5605 & 3687 \\ AKS & 4714 & 4111 & 3572 & 4595 & 5585 & 5431 & 4803 & 2568 & 5143 & 3225 \\ KEL & 4177 & 3585 & 3047 & 4069 & 4444 & 4905 & 4278 & 2042 & 4876 & 2699 \\ LS & 3989 & 3670 & 3295 & 4157 & 4460 & 4906 & 4503 & 2153 & 4784 & 2787 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The distances (km) between upstream and downstream stations. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Destination**} & \multicolumn{3}{c}{**Downstream Station**} \\ \cline{2-4}  & **KS** & **AKS** & **KEL** & **LS** \\ \hline BGH & 1176 & 1447 & 1989 & 1665 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The distances (km) between upstream stations and the destination. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Origin Number**} & \multirow{2}{*}{**Quantity**} & \multirow{2}{*}{**Origin Number**} & \multirow{2}{*}{**Quantity**} \\ \hline
1 & 780 & 11 & 782 \\
2 & 400 & 12 & 651 \\
3 & 620 & 13 & 940 \\
4 & 545 & 14 & 365 \\
5 & 760 & 15 & 550 \\
6 & 535 & 16 & 535 \\
7 & 855 & 17 & 845 \\
8 & 670 & 18 & 520 \\
9 & 718 & 19 & 765 \\
10 & 739 & 20 & 425 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The equipment quantities (unit). 1. CPLEX. Using the CPLEX solver to solve the above tests. The results are shown in columns 7, 8, and 9 of Tables 11 and 12, where Gap represents the percentage difference of Obis between GA_GA and the algorithm compared with GA_GA_GA_. \(Gap=(Obj_{*}-Obj_{GA\_GA})/Obj_{*}\)-100, where \(Obj_{GA\_GA}\) is the Obj of GA_GA_(e.g., column 7 in Table 11), and \(Obj_{*}\) is the Obj of the algorithm being compared with GA_GA_GA. For example, in Table 11 for test 12, the Gap between CPLEX and GA_GA is calculated as \((732.46-739.29)/732.46\times 100=-0.93\%\). Hereafter, each Gap is calculated in this manner.