## 3 Simulation Experiments and Analysis
### Experimental Setup  
The CPU used in the experiments of this article is an AMD Ryzen 7 7840 HS CPU at 3.80 GHz with 40 GB of memory. To ensure that the algorithm has good real-time performance and can be applied to practical scenarios, it is specified in this article that the algorithm should run within 120 s and 100 iterations. Based on this, various algorithm parameter settings are determined, as shown in Table 2 (for the SFOA, PK-SFOA, RTPK-SFOA, WPA, GA, and BWO). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & & & \\ \hline \(r_{Gshep}\) & the grazing radius of & \(p\) & the position of the \\  & the sheep & & sheep \\  & the grazing radius of & \(m,n\) & \(m\)th /\(n\)th sheep \\ \(r_{Ggaot}\) & the goats & & \\  & the upper limit of the & & \\ \(upper\)\(bound\) & entire grazing area & \(i,j\) & Row, Column Index \\ \(lower\)\(bound\) & the lower limit of the & & \(d\) & distance \\  & entire grazing area & & \(d_{1}\) & hyperparameter \\ \(T\) & time influence factor & \(d_{2}\) & hyperparameter \\ \(Iteration\) & current number of & \(d_{2}\) & hyperparameter \\  & iteration & & \\ \(MaxIteration\) & maximum number of & & the moving step size \\  & iterations & & of the sheep \\ \(T_{s}\) & hyperparameter & \(\theta\) & prior knowledge set \\ \(v\) & mobility factor & \(\theta\prime\) & secondary prior \\  & & & knowledge set \\ \(C\) & hyperparameter & & sheep numbering \\  & location of an & & index \\ \(X\) & individual & & sheep numbering \\ \(Dim\), \(dim\) & dimensionality of the & & index \\  & problem & & \\ \(Lbest\) & the optimal solution & \(\beta\) & sheep numbering \\  & & & index \\  & & & the number of sheep \\ \(RandomSleep\) & a random sheep & \(t\) & flock breeding \\  & & & iterations \\ \(V\) & comprehensive & & the number of sheep \\  & movement factor & & flocks \\ \(T_{G}\) & hyperparameter & \(Cof\) & the function \\  & & & evaluation cost \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variable descriptions. \(task_{x}\) represents the \(x\)-axis coordinate of the bottom centre point of the task area, \(task_{y}\) represents the \(y\)-axis coordinate of the bottom centre point of the task area, and \(task_{area}\) represents the size of the task area. All task areas require areas searches both on the surface of the water and underwater. The relevant attributes of the unmanned boats are shown in Table A1 (located in Appendix A). \(U_{x}\) represents the \(x\)-coordinate of the starting point of the unmanned boat, \(U_{y}\) represents the \(y\)-coordinate of the starting point of the unmanned boat, \(U_{p}\) represents the maximum cruising speed of the unmanned boat towards the task area, \(U_{v}^{t}\) represents the maximum cruising speed of the unmanned boat during the area search process, \(U_{ProbeCategory}\) represents the type of detection sensor carried by the unmanned boat, \(U_{ProbeCategory}=1\) represents that the boat is carrying a surface detection sensor, \(U_{ProbeCategory}=2\) represents that the boar is carrying an underwater detection sensor, and \(U_{ProbeCategory}=3\) represents that the boat is carrying both types of detection sensors. By running various algorithms, algorithm allocation results (Table A2 (located in Appendix A)) and a schematic diagram of the iteration process are obtained (Figure 2). The fitness values in Figure 2 are capable of assessing the quality of the tested allocation schemes. A higher fitness value indicates that the corresponding allocation scheme enables the USVs to complete tasks in a shorter period with less energy expenditure. In Figure 2, the larger the fitness value at the convergence time of an algorithm, the better the allocation scheme obtained by that algorithm.