# Multi-UAV Cooperative Anti-Submarine Search Based on a Rule-Driven MAC Scheme
## 4 Simulation Experiment and Analysis
### Scenario 2: Multi-UAVs Search Using Association Rules  
The target information setting of scenario 2 is the same as that of scenario 1, and association rules are also used to search under four search algorithms. Figure 6 shows the trajectory diagram of multi-UAVs searching for targets based on association rules. If a UAV first finds an underwater target, the applicable association rules, \(S_{i}\), are applied according to the type of underwater target. Then, the grid where the target is located is used as the center, the surrounding grid is refined, and the search radius is gradually expanded. If a related underwater target is searched, then the current searched target matches rule \(S_{i+1}\), and the UAV searches for the above-water target according to rule \(S_{i+1}\), as well as the connection line of the underwater target and the mid-perpendicular line, and searches for all the underwater targets to complete the search task. The UAV uses two association rules to perform the search task. The RI-MAC algorithm used in this paper has a smaller search trajectory and a better trajectory optimization effect than that of the other three algorithms. Table 5 shows the target-discovery benefits of the four search algorithms under association rules. The Monte Carlo method was used for 500 experiments, and the average number of targets found under different iteration steps is presented. It can be seen from Table 4 that in the 20 th iteration, the gap between the four algorithms is small; as the number of iterations increases, especially after some target information is mastered, in the process of searching for other targets, with additional association rules, the RI-MAC \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Step** & **20** & **40** & **60** & **80** & **100** & **120** & **140** & **160** & **180** \\ \hline RI-MAC & 0.0369 & 0.2161 & 0.7922 & 1.3821 & 1.6164 & 2.3892 & 2.9799 & 3.3142 & 3.8741 \\ MAC & 0.0396 & 0.2170 & 0.7699 & 1.1899 & 1.4871 & 2.1189 & 2.6971 & 3.2457 & 3.7614 \\ ABC & 0.0368 & 0.2156 & 0.7964 & 0.9843 & 1.4532 & 1.9761 & 2.6713 & 3.2241 & 3.6659 \\ PSO & 0.0197 & 0.1335 & 0.6395 & 0.9476 & 1.3984 & 1.7113 & 2.3712 & 2.7366 & 3.3854 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Target-discovery benefit of four search algorithms without association rules. Figure 6: Search track of UAV in Scenario 2: (**a**) RI-MAC, (**b**) MAC, (**c**) ABC, (**d**) PSO. algorithm has more obvious advantages, and relative to the other three algorithms, it finds the target faster. The proposed algorithm locates one more target than MAC, about 1.2 more targets than ABC, and about 1.5 more targets than PSO. With 140 iterations, the proposed algorithm can basically complete the search task, whereas the other three algorithms require more iterations. According to comparative analysis, the algorithm proposed in this paper finds the target faster than the other tested algorithms, with greater benefits, and it is more suitable for solving the nuclear submarine search problem. In Figure 7, the search performance of the four algorithms is further compared. With 180 iterations and with an increasing number of iteration steps, the RI-MAC algorithm used in this paper achieves improved search performance relative to the other three algorithms. In addition, the proposed algorithm requires fewer iteration steps. The highest performance achieved by the RI-MAC, MAC, ABC, and PSO algorithms is 38.6, 36.2, 29.6, and 35.7, respectively. The average performance of the RI-MAC, MAC, ABC, and PSO algorithms is 26.6, 22.2, 22.5, and 19.2, respectively. It is clear that among the tested algorithms, RI-MAC is most suitable for searching for targets with association rules. Table 6 shows the fitness values corresponding to the optimal solutions of the four algorithms in under two scenarios. Each data set contains the mean and standard deviation of the probability of finding the target. It can be seen from the table that the RI-MAC algorithm used in this paper achieves the best results in scenario 1.