## 3 Simulation Experiments and Analysis
### Experimental Setup
\begin{table}
\begin{tabular}{c c c} \hline \hline
**SFOA** & **PK-SFOA** & **RTPK-SFOA** \\ \hline Population Size: 200 & Population Size: 200 & Number of Goats: 20 \\ Population Size: 200 & Number of Goats: 20 & Number of Sheep: 180 \\ Number of Goats: 20 & Number of Sheep: 180 & The Size of \(\theta\): 20 \\ Number of Sheep: 180 & The Size of \(\theta\): 20 & The Size of \(\theta\): 80 \\ Goat Step Size: 2 & Goat Step Size: 2 & Goat Step Size: 2 \\ Sheep Step Size: 1 & Sheep Step Size: 1 & Sheep Step Size: 1 \\  & \(d_{1}\): 2 & \(d_{1}\): 2 \\  & \(d_{2}\): 2 & \(d_{2}\): 2 \\ \hline WPA & GA & BWO \\ \hline Population Size: 400 & & \\ Number of Scout Wolves: 209 & & \\ Number of Fierce Wolves: 190 & Population Size: 1000 & Population Size: 1000 \\ Number of Alpha Wolves: 1 & Cross Probability: 0.44 & Reproduction Rate: 0.6 \\ Capture Radius: 4 & Mutation probability: 0.01 & Cannibalism Rate: 0.44 \\ Roaming Step Size: 2 & Mutation Rate: 0.4 \\ Assault Step Size: 1 & & \\ Siegep Step Size: 1 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Algorithm parameter settings. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(task_{x}\)**(_m_)** & \(task_{y}\)**(_m_)** & \(task_{area}\)**(_m\({}^{2}\)_)** \\ \hline Task 1 & 1000 & 2000 & 20,000,000 \\ Task 2 & 2500 & 2000 & 20,000,000 \\ Task 3 & 4000 & 2000 & 20,000,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Task scenario attributes. According to Figure 2, compared to the SFOA [9], due to the presence of prior knowledge, the PK-SFOA can better escape from local optima and achieve better convergence. Compared to the PK-SFOA, the RTPK-SFOA introduces an updating mechanism based on prior knowledge, which enhances its ability to escape local optima and guide the population towards the optimal solution. Moreover, the RTPK-SFOA outperforms other algorithms, such as the GA [7], BWO [11], and WPA [10], in terms of the optimization effect. Due to the random nature of intelligent algorithms, this paper runs the various algorithms 30 times against the background of experimental scenario 1 and statistically analyses the final results, as shown in Figure 3. In Figure 3, the mean values represent the average fitness levels of the algorithms after 30 runs, which represent the average performance of the algorithms. The best and worst values are the best (upper limit) and worst (lower limit) fitness values produced by the algorithms after 30 runs, respectively, and the Std values are the standard deviations of the fitness levels of the algorithms after 30 repeated runs; the smaller a value is, the more stable the corresponding algorithm is. As shown in Figure 3, the PK-SFOA with a priori knowledge significantly improves the mean fitness, best fitness and worst fitness values over those of the SFOA [9]. This is because the a priori knowledge helps to prevent the algorithm from falling into a local optimum. However, since the a priori knowledge is not updated, underexplored regions may be located near the a priori knowledge set, which may result in the algorithm failing to find the optimal solution if the optimal solution occurs in that region. Compared with the PK-SFOA, the RTPK-SFOA updates the a priori knowledge set to better explore the previously underexplored regions. As a result, the RTPK-SFOA obtains better mean fitness and worst fitness values than those of the PK-SFOA. Figure 3a,b show that the RTPK-SFOA has a greater mean fitness and a lower standard deviation value than those of the SFOA, PK-SFOA, GA [7], BWO [11] and WPA [10]. This indicates that the RTPK-SFOA is more stable and able to obtain better allocation schemes in a shorter period. Due to the presence of both prior and candidate prior knowledge sets in the RTPK-SFOA, the algorithm effectively reduces the probability of falling into a local optimum. As a result, compared to all other algorithms, the RTPK-SFOA has a higher mean (indicating better performance) and a smaller standard deviation (indicating greater stability).