## 4 Validation of Algorithm Effectiveness  
Assuming there are 30 nodes in the network, including 10 unmanned aerial vehicles, 10 unmanned surface vessels, and 10 unmanned underwater vehicles, the performance parameters of each type of node are the same. The movement speed of air nodes in the entire network remains consistent based on the benchmark of water surface and underwater nodes. The entire network is based on a reference point group movement model, and it moves in a specific direction at a certain speed with a maximum movement speed of 10 m/s. The maximum number of iterations for the whale algorithm is 50. During the simulation process, the positions of each node in the network are shown in Figure 5.  
Figure 4: Algorithmic process for path selection.  
Using a plane of z = 500 m as the sea surface, its initial topological structure is shown in Figure 6.  
We conducted simulation experiments on the failure of multiple nodes in air-sea cross-domain communication networks, assuming the set of failed nodes is \(V_{lapse}\) and the set of affected nodes that need to be restored is \(V_{recover}\). When a network node fails, the node that needs to be restored sends a link establishment request to neighboring nodes, and each node in the network learns the set of nodes that need to be restored through sharing. The network topology with multiple node failures is shown in Figure 7. Here, the red nodes represent failed nodes, \(V_{lapse}=\{16,22,23\}\); the green nodes represent the nodes that need to be restored, \(V_{recover}=\{10,15,17,24,28\}\); the red dashed line represents the interrupted link. We restored the failed nodes and used the minimum communication cost algorithm described in the previous section to find the minimum communication cost path. The nodes in \(V_{recover}\) find the minimum communication cost path based on the predicted value of link quality, as shown in Table 1.  
Figure 5: Node location map of air–sea cross-domain communication network.  
Figure 6: Initial network topology diagram of air–sea cross-domain communication network (top view).  
The topology of the network is restored using the minimum communication cost algorithm, as shown in Figure 8a, where the green dashed line represents the restored links. After using the minimum communication cost algorithm to restore the network, connectivity is restored, and then load optimization is performed on it, as shown in Table 2. The optimized network topology is shown in Figure 8b.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Start** & **End** & **Shortest Path** & **Path Quality** \\ \hline
10 & 15 & 10\(\rightarrow\)15 & 17.33 \\
10 & 17 & 10\(\rightarrow\)17 & 10.40 \\
10 & 24 & 10\(\rightarrow\)17\(\rightarrow\)24 & 20.28 \\
10 & 28 & 10\(\rightarrow\)17\(\rightarrow\)28 & 26.99 \\
15 & 17 & 15\(\rightarrow\)17 & 11.92 \\
15 & 24 & 15\(\rightarrow\)24 & 20.04 \\
15 & 28 & 15\(\rightarrow\)28 & 16.35 \\
17 & 24 & 17\(\rightarrow\)24 & 9.88 \\
17 & 28 & 17\(\rightarrow\)28 & 16.59 \\
24 & 28 & 24\(\rightarrow\)28 & 16.21 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Path quality table between nodes in \(V_{recover}\).  
Figure 8: The restored network topology diagram: (**a**) minimum communication cost algorithm; (**b**) load-balancing algorithm.  
Figure 7: Network topology diagram after multi-node failure.  
As shown in Figure 8b, the nodes that need to be restored in the figure have undergone network repair based on the minimum communication cost and load-balancing algorithm. Through load-balancing algorithms, the number of links is reduced, communication costs are lowered, and the load is restored more evenly compared to using only the minimum communication cost algorithm.