## 4 Experimental Setup
### Case Study Description  
To evaluate the practical effectiveness of the proposed IGWOHHO algorithm, a case study is constructed based on a 35-node urban intermodal transport network. This case is adapted from the city arithmetic example network developed by [PERSON] and [PERSON] [51], with further reference to the experimental framework used in multimodal transport scheduling optimization by [PERSON] and [PERSON] [52]. The network serves as a realistic and structured platform for validating the proposed model and algorithm. The network structure is illustrated in Figure 10, reflecting an urban transport layout with multiple intermodal transfer possibilities. Between each pair of adjacent nodes, up to three transport modes are available in the fixed order of roads, rail, and inland waterways. Table 1 provides the transport distances for each mode and section. A blank entry indicates that a specific transport mode is not available for the corresponding segment. Figure 9: Three-dimensional graphs of functions. (**a**) Schwefel 2.22 function; (**b**) Rosenbrock function; (**c**) Ackley function; (**d**) Penalized function; (**e**) Foxholes function; (**f**) Kowalik function. The 35 nodes in the network consist of origin points, destination terminals, and intermediate transshipment hubs. Transport demand is defined for selected node pairs based on typical container flow patterns in inland logistics systems. Each node is associated with a soft time window, within which early or late arrivals are allowed but incur penalty costs. According to Table 2, soft time window constraints are applied to intermediate nodes, whereas a hard time window (25, 50) is enforced at the destination node D. The penalty cost is 100 CNY/TEU\(\cdot\)h for early arrival and 200 CNY/TEU\(\cdot\)h for delayed arrival. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Sections** & **Transport Distance** & **Sections** & **Transport Distance** & **Sections** & **Transport Distance** \\ \hline O–1 & (110, 101, 129) & 12–18 & (103, \(-\), \(-\)) & 22–24 & (133, 115, 142) \\ O–2 & (134, 164, \(-\)) & 12–23 & (128, 138, 132) & 23–24 & (133, 135, \(-\)) \\ O–3 & (75, 83, 107) & 13–14 & (143, 146, 146) & 23–29 & (150, \(-\), \(-\)) \\
1–6 & (148, 161, 166) & 13–16 & (63, \(-\), \(-\)) & 23–30 & (135, 145, 161) \\
1–7 & (120, 133, 112) & 13–17 & (107, \(-\), \(-\)) & 24–25 & (94, 98, \(-\)) \\
2–5 & (103, 80, \(-\)) & 13–19 & (130, 136, 145) & 24–28 & (138, \(-\), \(-\)) \\
2–6 & (85, \(-\), \(-\)) & 14–15 & (103, 87, 111) & 24–29 & (146, 136, 153) \\
3–4 & (117, 125, 137) & 14–16 & (132, 141, \(-\)) & 25–26 & (73, \(-\), 96) \\
4–5 & (75, \(-\), \(-\)) & 15–20 & (100, 73, 114) & 25–28 & (107, 82, \(-\)) \\
4–11 & (150, 166, 173) & 16–19 & (129, \(-\), \(-\)) & 26–27 & (132, 120, 150) \\
5–10 & (101, 86, \(-\)) & 16–20 & (81, \(-\), \(-\)) & 27–28 & (137, \(-\), \(-\)) \\
6–9 & (144, 167, 162) & 16–21 & (\(-\), 80, \(-\)) & 27–32 & (110, 104, \(-\)) \\
6–10 & (133, \(-\), \(-\)) & 17–19 & (67, \(-\), \(-\)) & 27–D & (117, 129, 143) \\
7–8 & (128, 119, 134) & 18–19 & (110, \(-\), \(-\)) & 28–29 & (76, \(-\), \(-\)) \\
7–9 & (105, \(-\), \(-\)) & 18–22 & (76, \(-\), \(-\)) & 28–31 & (130, \(-\), \(-\)) \\
8–12 & (112, 84, 115) & 18–23 & (115, \(-\), \(-\)) & 28–32 & (104, 96, \(-\)) \\
8–13 & (113, 112, 124) & 19–21 & (119, \(-\), \(-\)) & 29–30 & (141, \(-\), \(-\)) \\
9–10 & (126, \(-\), \(-\)) & 19–22 & (125, 114, 138) & 29–31 & (129, 140, \(-\)) \\
9–13 & (135, 149, 140) & 20–21 & (95, \(-\), \(-\)) & 30–31 & (95, 89, 118) \\
10–11 & (88, \(-\), \(-\)) & 20–26 & (110, 97, 119) & 31–33 & (106, 106, 114) \\
10–14 & (120, 136, \(-\)) & 21–22 & (73, \(-\), \(-\)) & 32–33 & (120, 125, \(-\)) \\
11–15 & (90, 74, 90) & 21–25 & (111, 89, \(-\)) & 32–D & (117, 84, \(-\)) \\
12–17 & (55, \(-\), \(-\)) & 21–26 & (65, \(-\), \(-\)) & 33–D & (108, \(-\), \(-\)) \\ \hline \end{tabular}
\end{table} 
Table 1: Distance traveled by different modes of transport. Figure 10: Network structure of the arithmetic example.