## 3 Numerical Evaluations and Experimental Analyses
### Simulation Results and Analysis
In Figure 7, With 45 underwater sensor nodes deployed as the research object, figure (a1-a3), (b1-b3), (c1-c3) and (d1-d3) shows the moving trajectories, final node positions, and final node coverage effects of the four algorithms: BES, 3D-IVFA, DABVF, and proposed algorithm. In the figure, dots represent the random distribution positions of nodes, pentagons represent the positions of nodes after optimization, the line between the point and the five-pointed star represents the movement trajectory of nodes from the random distribution position to the optimized position, and the area shaped by the ball represents the perception range of underwater nodes. We can see that the proposed algorithms show excellent performance of nodes distributed uniformly compared with the other three methods. This is because the proposed algorithm uses an adaptive position update mechanism that can autonomously choose the most suitable strategy to update the particle positions. The global exploration ability of the algorithm is enhanced while at the same time, the local development ability of the algorithm is ensured. In addition, the VFA algorithm is used to drive nodes to the optimal position using the force between nodes, which reduces the coverage blind area of the network and optimizes the coverage effect of the network. In Figure 8, 3D-IVFA has the best average iteration step performance. Because 3D-IVFA extends the traditional law of virtual force, the use of the center of gravity and balance force makes the deployment of sensor nodes more reasonable, reducing the movement of large distances between nodes. The proposed algorithm has worse performance in the average iteration step than the BES, 3D-IVFA, and DABVF algorithms. This is because the algorithm constantly updates the node position in the running process and adopts the greedy strategy to select the node position again through the global interference mechanism in the late iteration, resulting in large moving distances between nodes. This is because of the constant update of node positions constantly seeking the optimal position, improving the balance of distribution density, and achieving the best coverage effect. In Figure 9, moving displacements of 45 underwater sensor nodes are projected from three mutually perpendicular directions. The dots represent the random distribution positions, the pentagrams represent the optimized positions, and the lines between the points and the pentagrams represent the 3D views of the moving displacements from the random distribution position to the optimized position. Figure (a1), (b1), (c1), and (d1) shows the front views of the node motion trajectories of BES, 3D-IVFA, DABVF, and the proposed algorithm, respectively. Figure (a2), (b2), (c2), and (d2) shows the right elevations of the node motion trajectories of BES, 3D-IVFA, DABVF, and the proposed algorithm, respectively. Figure (a3), (b3), (c3), and (d3) shows the top views of the node motion trajectories of BES, 3D-IVFA, DABVF, and the proposed algorithm, respectively. We can see that, compared  
Figure 6: The relationship between coverage efficiency and node number in the four algorithms. with the other three algorithms, the proposed algorithm is better when an equal distribution of nodes is considered from a three-dimensional perspective. This is because the proposed algorithm uses strategies such as improved PSO and global interference mechanism to constantly update the location of nodes to make their distribution more uniform and realize optimal deployment of the network. Figure 10 shows the comparison of \(k\)-coverage before and after the optimization of the proposed algorithm using different node numbers. After optimization of the proposed algorithm, the coverage of multiple repetitions decreases while the coverage of low repetitions increases. For example, with 45 underwater sensor nodes deployed as the research object, the 1-coverage and 2-coverage during the initial deployment are only 43.09% and 22.14%, respectively, and the coverage hole is 27%.