## 3 Experiment
### Detailed Analysis and Comparison
The MOMTA-HN algorithm exhibits enhanced flexibility and reliability in path selection, and its multi-objective optimization strategy enables it to adapt to diverse network environments, ensuring the successful completion of transmission tasks. In contrast, the SPFA and Dijkstra algorithms demonstrate superior path selection capabilities under specific conditions. However, they lack the flexibility and robustness of the MOMTA-HN algorithm when confronted with network attacks and complex network environments. As illustrated in Figure 11, this study presents a comprehensive comparison experiment among the MOMTA-HN algorithm, the multipath algorithm with the first type of simplification (MOMTA-I), and the multipath algorithm with the second type of simplification (MOMTA-II). The experiment is designed to evaluate the performance of these algorithms under attack scenarios, focusing on their ability to maintain successful transmissions. In Figure 9(a), the source and destination nodes are node 9 and node 18, respectively. At this juncture, the MOMTA-HN algorithm needs to perform only the first type of simplification, which involves deleting all nodes in the sub-network where the transmission node of the first link is located. This simplification aims to derive a second path for redundant transmission. The multipath algorithm that employs only the first type of simplification can also compute the same result. The deletion method of multipath algorithms using only the second type of simplification is simpler compared to the first type. After the optimization filtering of the multi-objective optimization algorithm, the second path calculated is identical for all the algorithms mentioned, causing the three lines in the figure to overlap. This scenario demonstrates that under certain conditions, both types of simplifications can achieve similar results. In Figure 9(b), the source and destination nodes are node 18 and node 22, respectively. In this scenario, the initial simplification approach of the MOMTA-HN algorithm proves ineffective, necessitating the use of the second type of simplification. This method involves deleting all nodes associated with the initial link to derive a second path for redundant transmission. The algorithm that performs only the first type of simplification is unable to compute the second path. However, the algorithm that performs only the second type of simplification can calculate the same second path as the MOMTA-HN algorithm after the required deletions, resulting in the two lines in the figure overlapping. This demonstrates the effectiveness of the second type of simplification when the first type fails. In Figure 11c, the source and destination nodes are node 1 and node 9, respectively. At this juncture, both Type I and Type II simplification methods of the MOMTA-HN algorithm are ineffective in deriving a second path for redundant transmission. Consequently, Type III  
Figure 11: Transmission success rate of MOMTA-HN, MOMTA-I, and MOMTA-II encountering attacks with different types of simplifications. (**a**) Comparison of the number of successful transmissions from node 9 to node 18 encountering an attack; (**b**) comparison of the number of successful transmissions from node 18 to node 22 encountering an attack; (**c**) comparison of the number of successful transmissions from node 1 to node 9 encountering an attack. simplification is required. This advanced method involves a more sophisticated approach to ensure a new independent path is found, thereby enhancing the system's robustness. Both the algorithms that use only the first type of simplification and those that use only the second type are unable to compute the second path, causing the lines in the figure to overlap. This highlights the necessity of the third type of simplification in more complex scenarios where traditional methods fail.