## 3 Experiments
### Static Route Planning Experiments by SPA*
According to the main scale parameters of the ship, the coefficients \(a_{1}\)-\(a_{4}\) in Equation (2) are taken as 1.08, 0.126, 0.00277, and 2.33 \(\times\) 10\({}^{-7}\), respectively [15; 16; 22; 23; 38]. The experimental risk assessment data were taken from the sea area of latitude \(-\)15\({}^{\circ}\) to 15 and longitude 100\({}^{\circ}\) to 135\({}^{\circ}\). It includes vector data of wind and waves, wave height, wave speed, wave period, sea surface temperature, and sea surface salinity. The time range of the data is 2022-11-1-2022-11-7, and the four time periods recorded each day are 00:00, 06:00, 12:00 and 18:00; spatial resolution: 1/12\({}^{\circ}\); data scale: 421 \(\times\) 361 \(\times\) 28 (longitude-latitude-time). We averaged the data on the first day, and the regions with distinct risk characteristics were constituted into the data sets of 100 \(\times\) 100, 200 \(\times\) 200 and 400 \(\times\) 400 in Figure 5. Each of the above cases was experimented 100 times, and the average value of each indicator obtained was the average value. The relevant experimental results are organized in Table 2. Under different map sizes, the R-VIMO of SPA * and traditional path planning algorithms are all 0. In SI-based path planning, only SSA's R-VIMO is 0 at 100 \(\times\) 100. Compared with other algorithms, SPA * shows obvious advantages in four indicators. Especially for time, even in the size of 400 \(\times\) 400, SPA * still maintains the calculation speed of completing a planning within 1.5 s. In contrast, A * and BA *, which are faster in traditional path planning, need 7.0562 and 22.4825 s to complete a planning, respectively. The fastest SSA in SI-based path planning still needs 13.0777 s to complete a planning. However, the R-VIMO of SSA is 0-27.47%, which means that its planning performance has serious problems and cannot meet the IMO standard. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Indicator**} & \multicolumn{2}{c}{**Our Algorithm**} & \multicolumn{2}{c}{**Traditional Path Planning**} & \multicolumn{2}{c}{**SI-Based Path Planning**} & \multirow{2}{*}{**Map Size**} \\ \cline{2-2} \cline{4-9}  & **SPA* & **Dijkstra** & **A* & **BA* & **ACO** & **HHO** & **SSA** & \\ \hline Time(s) & 0.0312 & 0.8908 & 0.5708 & 0.4670 & 202.4345 & 328.2276 & 2.5359 & \\ \(f_{1}\) & 0.1051 & 0.1404 & 0.1395 & 0.1404 & 0.1254 & 0.1019 & 0.1238 & \\ \(f_{2}\) & 0.2833 & 0.3230 & 0.3228 & 0.3224 & 0.2896 & 0.2812 & 0.2558 & \\ R-VIMO & 0 & 0 & 0 & 0 & 16.94\% & 14.72\% & 0 & \\ \hline Time(s) & 0.0805 & 6.9234 & 1.5625 & 0.7388 & 1000.2133 & 923.3016 & 6.3452 & \\ \(f_{1}\) & 0.1154 & 0.1287 & 0.1250 & 0.1315 & 0.1307 & 0.1343 & 0.1170 & \\ \(f_{2}\) & 0.2763 & 0.3079 & 0.3046 & 0.3227 & 0.2525 & 0.3144 & 0.3017 & \\ R-VIMO & 0 & 0 & 0 & 0 & 18.47\% & 22.38\% & 27.47\% & \\ \hline Time(s) & 1.2354 & 159.3826 & 7.0562 & 22.4825 & 1723.6522 & 1523.3016 & 13.0777 & \\ \(f_{1}\) & 0.1145 & 0.1285 & 0.1309 & 0.1288 & 0.1333 & 0.1355 & 0.1172 & \\ \(f_{2}\) & 0.2754 & 0.3008 & 0.3024 & 0.3090 & 0.2575 & 0.2495 & 0.2824 & \\ R-VIMO & 0 & 0 & 0 & 0 & 16.29\% & 15.07\% & 17.37\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Static planning results of SPA*, traditional path planning, and SI-based path planning for different map sizes. Combined with Figure 5, it is observed that the routes obtained by SPA* are better suited to avoid the high-risk area marked in red. At 100 \(\times\) 100, SPA* selects a detour near 90 degrees to avoid the risk zone; in traditional path planning, the algorithm is straight through the risk area; in the SI-based path planning algorithm, ACO and SSA fall into two local optimal solutions, and the path finally crosses the risk area. ACO passes through the medium-risk area, and SSA passes through the high-risk area. At 200 \(\times\) 200, SPA* not only avoids the high-risk area from the middle but also bypasses the medium-risk area of the path.