## 5 Numerical Example  
### Data Preparation  
In order to verify the effectiveness of the model and the accuracy of the algorithm, based on the existing research in relevant references [40], a case of a multimodal transport  
Figure 10: The process of IWOA.  
network with 14 nodes and 37 transport routes is constructed. The network is chosen to balance model complexity and computational feasibility, incorporating real-world multi-modal features while aligning with benchmark scales in prior research for comparability. Assuming that the freight transportation demand is 20 TEU, it is transported from node 1 to node 14. The values of relevant parameters are shown in Tables 3-6, and the structure of the multimodal transport network is shown in Figure 11. It is set that the transfer capacity of each node is the same, which is 50 TEU/h, the transfer and connection speed within the node is 40 km/h, the average connection distance is 10 km, and the goods need to complete the transportation task within 150 h. This study parameterizes the departure time for all transport modes at Node 1 as 8:00 AM, establishing a unified temporal reference point. Given that inter-nodal transit duration is mathematically determined by the quotient of transportation distance and velocity, we operationalize fuzzy transit duration calculation through modal-specific fuzzy velocity parameters under fixed geographical distances.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Transportation Route** & **Road (km)** & **Railway (km)** & **Waterway (km)** \\ \hline
1 & 1-2 & 332 & 735 & — \\
2 & 1-3 & 306 & 786 & — \\
3 & 1-4 & 281 & 540 & 638 \\
4 & 2-3 & 814 & 606 & — \\
5 & 2-5 & 56  
To systematically analyze transportation pricing dynamics, this study constructs 16 distinct freight rate scenario combinations to investigate the impact of cost volatility on route optimization outcomes, with detailed scenario parameterization presented in Table 7.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Type of Cargo**} & \multirow{2}{*}{**Name of Cargo**} & **Price of** & **Average Daily** \\  & & & **Cargo (10\({}^{4}\)** & **Depreciation** \\  & & & **USD/TEU)** & **Rate (\%)** \\ \hline \(n=1\) & High value-added and & Mobile phones, & & \\  & timeliness-strong cargo & tablets, etc. & & 40 & 0.043 \\ \(n=2\) & High value-added and & Precious metals, etc. & 30 & 0.0012 \\ \(n=3\) & Low value-added and & Flowers, fruits, etc. & 10 & 0.1 \\  & timeliness-strong cargo & & & \\ \(n=4\) & Low value-added and & Ore raw materials, etc. & 5 & 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Full load value and average daily depreciation rate of different categories of cargo.  
Figure 11: Multimodal transport network structure.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode of**} & \multirow{2}{*}{**Speed (km/h)**} & \multirow{2}{*}{**Transportation**} & **Transport** & \multirow{2}{*}{**Depature**} \\
**Transport** & & **(CNY/TEU\(\cdot\)km)** & & **Emissions** & **Interval (h)** \\ \hline Road & (40,90,100) & 4.74 & 3.73 & — \\ Railway & (45,50,75) & 1.84 & 1.27 & 1 \\ Waterway & (20,25,40) & 0.89 & 0.42 & 1 \\ \hline \hline \end{tabular} note—indicates that it does not exist.  
\end{table}
Table 4: Transportation parameters of different transportation modes.