## 4 The Design of Routing Protocol
### Data Packet Forwarding
In general, if the computational complexity is not a main concern, incorporating all future states in the decision value calculation would benefit the optimal routing decision. Second, the impact of the routing pipe radius on the performance of the proposed ASVMR protocol is simulated. Figure 11 shows the impact of the routing pipe radius on the performance of the proposed ASVMR protocol, where the number of sensor nodes is set as 150; the moving velocity of the sensor nodes is set as 0; the discount factor is set as 0.8; and the routing pipe radius changes from \(R/8\) to \(R\). The PDR, the hop count, the end-to-end delay, and the energy tax are shown in Figure 11a-d, respectively. From Figure 11a, one finds that the PDR of the ASVMR protocol increases with an increase in the routing pipe radius. This is because a larger routing pipe radius can provide more neighboring nodes, which reduces the routing void and lowers the packet loss rate. From Figure 11b, we observe that as the routing pipe radius increases, the hop count of the ASVMR protocol decreases. The reason for this is the ability of a larger routing pipe radius to provide a greater number of nodes in the candidate forwarding set, thereby increasing the likelihood of discovering a more optimal route. From Figure 11c,d, we observe that as the routing pipe radius increases, the end-to-end delay and energy tax of the ASVMR protocol decrease. This is because the number of hops from the source node to the destination node decreases, resulting in a reduction in the end-to-end delay and the amount of energy consumed in each packet transmission. Figure 10: Impact of the discount factor on the performance. Therefore, the routing pipe radius affects the performance of the ASVMR protocol significantly. The increase in the routing pipe radius results in a higher PDR, smaller hop count, and lower end-to-end delay and energy tax in the ASVMR protocol, which indicates that a more optimal path is selected. ## 6 Conclusions

In this paper, we proposed an intelligent routing protocol, the ASVMR protocol, for the UASN. In the proposed protocol, various types of node state information are considered to dynamically optimize the routing path in real time. Specifically, the SVM framework for routing is designed to reduce the end-to-end delay and prolong the network lifetime. The decision-making process for the selection of the next hop incorporates the adaptive routing pipe and future states in order to reduce the energy consumption. Moreover, we introduce a waiting time mechanism and routing void recovery mechanism to improve the PDR and reduce the packet loss in dynamic underwater environments. The simulation results show that the proposed ASVMR protocol performs well in terms of the PDR, the hop count, the end-to-end delay, and the energy tax. In the future, other parameters in the UASN, such as the transmission rate and the link quality, should be considered to further enhance the accuracy and effectiveness of the routing decision. Conceptualization, S.Z. and H.C.; methodology, S.Z. and H.C.; software, S.Z. ; validation, S.Z., H.C. and L.X. ; formal analysis, S.Z. and H.C.; investigation, S.Z. ; resources, H.C. and L.X. ; data curation, S.Z. ; writing--original draft preparation, S.Z. ; writing--review and editing, S.Z. and H.C.; visualization, S.Z. ; supervision, H.C.; project administration, H.C. and L.X. ; funding acquisition, H.C. and L.X. All authors have read and agreed to the published version of the manuscript. Figure 11: Impact of the routing pipe radius on the performance. **Funding:** This research was funded by the National Natural Science Foundation of China, grant numbers 42227901 and 62271442, the Science and Technology Department of Zhejiang Province, grant number GG22F019348, and the Natural Science Foundation of Zhejiang Province, grant number LZ23F010006. **Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.