## 5 Simulation Analysis
### Method Application
The CIPSO algorithm calculated the optimal value as (3.7372, 0.345644), which means this vessel's optimal collision avoidance operation requires it to slow down to 3.737 knots. The vessel decelerated from 13 knots to 3.7 knots, with a reverse deceleration stroke of 1.04 n miles and a stroke time of 8.3 min. After stabilizing to 3.7 knots, the \(d_{CPA}\) values with TG1, TG2, and TG3 were [1.10, 2.57, 1.54], the \(d_{CPA}\) values between OS and each TG were greater than the set \(d_{1}\) value, and the OS could safely navigate the port, avoiding all vessels. Figure 9 shows the change curve of collision risk when the vessel undertakes the deceleration collision avoidance operation; the CRI value of each TG relative to OS is gradually reduced to below 0.3 within 10 min, which reduces the CR. Figure 10 shows the change in the distance between each TG and OS during the collision avoidance process, and the encounter distance between each TG and OS is higher than \(d_{1}\). The value of the closest encounter distance between TG1 and OS is very similar to the value of \(d_{1}\), which also indicates that the speed value given by the speed-varying collision avoidance decision makes the energy loss of the vessel as small as possible, and simultaneously maximizes the safety of the vessel's encounter. The above analysis can \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Target Vessel** & **TG1** & **TG2** & **TG3** \\ \hline Vessel type & Fish boat & LNG & Bulk carrier \\ Course (\({}^{\circ}\)) & 90.0 & 253.0 & 93.0 \\ Direction (\({}^{\circ}\)) & 313.5 & 008.4 & 307.8 \\ Speed (knot) & 7 & 9 & 9 \\ Distance (n mile) & 3.561 & 4.522 & 5.483 \\ \(d_{CPA}\) (n mile) & 0.242 & 0.075 & 0.080 \\ \(t_{CPA}\) (min) & 12.13 & 19.32 & 16.93 \\ Displacement (\(t\)) & 286.0 & 89,634.0 & 23,565.0 \\ Length (m) & 24.4 & 274.3 & 182.9 \\ Breadth (m) & 7.2 & 43.3 & 22.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Target vessels encounter situational parameters. conclude that the speed-varying collision avoidance decision is effective and can feasibly safely avoid all target vessels. To further validate the feasibility and effectiveness of the method, a large-vessel maneuvering simulator was used to conduct multi-vessel simulation experiments. Figure 11 shows the trajectory generated after manipulating collision avoidance in the simulation case in the simulator. In the figure, the green vessel (OS) is the simulated vessel, while the other vessels (TG1, TG2, TG3) are the simulated target vessels. The virtual shadow of the vessel represents the position of the vessel at a certain time. The numbers in the  
Figure 8: Comparison diagram of fitness changes. Figure 10: Change the curve of encounter distance between OS and each TG. Figure 9: Change curve of CRI in the collision avoidance process. figure represent different time points, with 1 being the starting time point, and a time interval of 4 min. From Figure 11, it can be seen that the distance between the trajectories of OS is equal at the third moment, indicating that OS is reversing and decelerating to the predetermined safe speed. At the fourth moment, the TG1 has safely passed the bow of the OS and is a long, safe distance from the OS. At the sixth moment, TG2 and TG3 are also sailing in their respective directions past the bow of the OS. This indicates that the safe speed provided by this decision support method meets the safety requirements of super-large vessel navigation. Figure 12 presents the curves of the \(d_{CPA}\) and \(t_{CPA}\) of each TG relative to OS over time. From the figure, it can be seen that, after driving for about 8 min under the given decision, the \(d_{CPA}\) values of OS and each TG are greater than 1 n miles. This indicates that the speed-varying collision avoidance measures for super-large vessels are highly feasible and in line with the \"substantial\" collision avoidance operation required in COLREGS. Figure 11: Simulation test on the motion trajectories of each vessel.