## 4 Experimental Verification and Results Analysis
### Simulation of Environment Construction and Parameter Settings  
This experiment used the Windows 10 operating system and the MATLAB R2023b simulation platform to verify the rationality of the task allocation model in this research and the performance of the MSIDBO algorithm in solving multi-agent multi-constraint allocation problems. As shown in Table 2, three task scenarios were assumed and simulated. These scenarios encompassed a wide range of complexities and cross-domain collaborations, spanning from simple tasks involving minimal interaction between agents to highly complex scenarios requiring extensive coordination and communication across multiple domains. By comparing the simulation results of each algorithm across these varying scales of cross-domain collaborative tasks, we were able to comprehensively evaluate the performance of the MSIDBO algorithm in diverse situations. The simulation results of each algorithm on different scales of cross-domain collaborative tasks were compared. Based on the existing agent performance index and experience, the scenario and intelligent algorithm parameters were preconceived as follows:  
1. Basic parameter assumptions: The population size of dung beetles was set to \(n=200\), the number of iterations of the algorithm was set to \(T=300\), and the number of simulations was set to \(F=100\). In the control allocation, the number of radar accumulation pulses was set to \(n_{p}=5\); the probability of radar false alarms was set to \(P_{fa}=1\times 10^{-6}\), which was corresponding number of false alarms \(N_{fa}=\frac{\ln 2}{1\times 10^{-6}}\). 2. Load agent performance index scenario: The average flight speed of the load agent was set as \(\overline{v}=300\) km/h, and a random number in (0, 0.5) was randomly selected as the damage probability of each load agent to each target platform. With an increase in the scale of the task scene and the number of load agents, the regularity of the damage ability distribution of the load agents gradually increased and continued to approach a normal distribution. This is shown in Figure 5; \(N_{cd}\) is the total number of samples, which is obtained by multiplying the number of target agents and the number of load agents. 3. Calculation of threat coefficient of target agent: The threat degree of the target agent was determined by many quantitative and qualitative factors, including quantitative indicators, such as the target's speed, distance, and relative position, and qualitative indicators, such as the target's threat type, defense capability, etc. In order to eliminate the dimension and magnitude differences between various factors, the quantitative factors of the quantitative and qualitative indicators were obtained by combining the analytic hierarchy process and the entropy weight method. Then, the factors that affected the threat degree were normalized to obtain the membership degree of each factor. The characteristic information of the four types of targets is shown in Table 3.  
According to the characteristic information of each target in Table 3, the target membership matrix can be given as follows: \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Mission Scenario** & \multicolumn{2}{c}{\(Mission_{1}\)} & \multicolumn{2}{c}{\(Mission_{2}\)} & \multicolumn{2}{c}{\(Mission_{3}\)} \\ \hline Number of surface agents, \(a\) & & & 2 & & & & 4 & & & 8 & \\ Air relay control agent & & & 4 & & & 8 & & & 16 & \\ number, \(b\) & & & 8 & & & & 16 & & & 24 & \\ Number of target agents & & & & & & & & & & & \\ (of each type) & 1 & 2 & 1 & 4 & 4 & 2 & 3 & 7 & 6 & 3 & 4 & 11 \\ Number of load agents, \(d\) & & & 50 & & & & 100 & & & 200 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Task scenario parameters on different scales. Figure 5: Statistics of damage capability of the load agent. (**a**) Mission I. (**b**) Mission II. (**c**) Mission III.