# Multi-Strategy-Improvement-Based Slime Mould Algorithm
## 4 Experimentation and Application
### Collaborative Multi-UAV Path Planning  
Collaborative multi-UAV path planning has important applications in several fields. In search and rescue, multiple drones can work together to cover large areas, quickly locate survivors, and avoid obstacles while avoiding repeated searches by sharing information in real time [26]. In agricultural monitoring, drones can efficiently collect farmland data, optimize paths to cover the entire area, and avoid collisions, improving monitoring efficiency [27]. In logistics distribution, multiple UAVs collaborate to perform package delivery tasks, dynamically adjusting paths to cope with obstacles and traffic changes in urban environments to ensure delivery accuracy and timeliness. The main methods for collaborative multi-UAV path planning include centralized planning, distributed planning, and population intelligence algorithms [28; 29]. Centralized planning assigns tasks and paths to all UAVs by a central controller, which is suitable for small teams but has high computational complexity; distributed planning relies on the autonomous decision making of each UAV, which is suitable for large teams but requires \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **MSSMA** & **SMA** & **WOA** & **KO** & **BWO** & **IVY** \\ \hline (W \(\mid\) T \(\mid\) L) & (43 \(\mid\) 7 \(\mid\) 0) & (14 \(\mid\) 31 \(\mid\) 5) & (7 \(\mid\) 32 \(\mid\) 11) & (13 \(\mid\) 35 \(\mid\) 2) & (7 \(\mid\) 40 \(\mid\) 3) & (14 \(\mid\) 16 \(\mid\) 20) \\ Ave & 1.86 & 2.88 & 3.22 & 3.94 & 4.58 & 4.52 \\ Rank & 1 & 2 & 3 & 4 & 6 & 5 \\ \(p\)-value & - & 0.0159 & 9.7 \(\times\) 10\({}^{-6}\) & 0.0013 & 0.0242 & 0.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The experimental results of six algorithms on Friedman and Wilcoxon signed-rank test. an efficient communication mechanism; swarm intelligence algorithms such as Particle Swarm Optimization (PSO) and Ant Colony Algorithms (ACOs) solve the multi-objective optimization problem by simulating natural behaviors but may face the convergence challenges of slow speed. The difficulties in cooperative multi-UAV path planning are mainly focused on environmental complexity, dynamic obstacles, and communication constraints [30]. Complex 3D environments require path planning algorithms that can efficiently handle obstacles and terrain changes; dynamic obstacles, such as moving vehicles or other UAVs, require real-time path adjustments to avoid collisions; and communication constraints can affect the efficiency of UAV collaboration, especially in large teams or long-distance missions. In addition, multi-objective optimization (e.g., of path length, energy consumption, and mission completion time) adds to the complexity of the problem. The flight paths of UAVs are affected by many factors, and in this paper, we construct path planning evaluation functions in terms of path length, deflection angle size, and flight threat conditions. Usually, when the UAV maintains a fixed speed during flight, \(f_{L}\) can be equivalently expressed as a fixed proportion of the flight path length, as shown in Equation (23) [31]. \[f_{L}=\sum_{i=1}^{n}l_{i} \tag{23}\]  
Here, \(l_{i}\) is the distance from the ith path point \(Li\) to the next path point \(Li+1\). The flight altitude of the UAV is limited by the function \(f_{H}\) as shown in Equation (24):  
\[f_{H}=\sum_{i=1}^{n}h_{i} \tag{24}\]  
Here, the altitude penalty function \(h_{i}\) is shown in Equation (25). \[hi=\left\{ \begin{aligned} &(z_{i}-H_{max})&&,z_{i}>H_{ max}\\ & 0&&,\ H_{min}\leq z_{i}\leq H_{max}\\ &(H_{min}-z_{i})&&,z_{i}<H_{min}\end{aligned} \right. \tag{25}\]  
Here, \(z_{i}\) is the flight altitude of the ith path point, and \(H_{max}\) and \(H_{min}\) are the maximum and minimum flight altitudes of the UAV, respectively. To further test the performance of the algorithm, a battlefield environment with radar, missiles, and other threats is simulated as follows [32]. Here, the threat probability from radar to UAV can be approximated as follows:  
\[P(d_{R})=\left\{