## 4 Experimental Verification and Results Analysis
### Comparative Analysis of Simulation Results  
To evaluate the performance of the improved dung beetle optimization algorithm in the cross-domain cooperative task allocation model proposed in this study, several classical metaheuristic algorithms were utilized as benchmarks. These algorithms included particle swarm optimization (PSO) [34], sparrow search algorithm (SSA) [35], and gray wolf optimizer (GWO) [36]. By comparing the results obtained from these algorithms with the improved dung beetle optimization algorithm, the effectiveness and efficiency of the proposed approach could be assessed. Additionally, the original dung beetle optimizer (DBO) and its many newer and original improved forms (for example, Original MODBO, MSADBO [32], and IDBO [33]) were used as comparison algorithms to verify the superiority of MSIDBO. The parameters of these methods are shown in Table 4 below. In Table 4, \(p_{1a}\) and \(p_{1b}\) denote the upper limit and starting proportion of the rolling dung beetles; \(\Omega_{\text{max}}\), \(\Omega_{\text{min}}\), and \(\varepsilon\) represent the maximum and minimum values of the variable inertia weight coefficient of the MSADBO algorithm and the coefficient of variation of Gaussian disturbance, respectively; \(p_{1}\), \(p_{2}\), \(p_{3}\), \(p_{4}\), and \(s\) are the proportions of rolling balls, newborns, young, and thieves in the population and the constant coefficient of thieves in the DBO algorithm, respectively; \(w\), \(c_{1}\), \(c_{2}\), and \(k_{V_{\text{max}}}\) are the inertia weight coefficient of the PSO algorithm, the acceleration coefficient of personal cognition, the acceleration coefficient of social cognition, and the limit speed proportion coefficient; and \(p_{main}\) is the main population proportion coefficient of the SSA. In a task allocation simulation calculation, the performance of each algorithm was greatly affected by the initial random search; the objective function value changed sharply, the performance of each algorithm fluctuated with an increase in the number of iterations, and a regularity conclusion could not be determined. In order to visually display the performance of each algorithm, the average value of 100 Monte Carlo simulation results was used, and the change curve for the mean value of the fitness of each algorithm in solving the task allocation model with an increase in the number of iterations was plotted, as shown in Figures 7 and 8. The convergence index \(E=\frac{Fitness(t)}{Fitness(1)}\) and fitness function \(Fitness(t)\) were used to describe the convergence effect of the algorithm, as shown in Figures 9 and 10. In order to evaluate and verify the significant differences between different target allocation schemes to enhance the reliability of the results, the average running time and global optimal solution of each algorithm are given in Table 5; the LSD significance test was conducted, and statistical analysis box plots of the results were drawn. The letters above each algorithm denote the LSD significance test results, and the different letters of the two algorithms indicate significant differences, as shown in Figures 11 and 12. Figure 8: Comparison of average fitness of algorithms for control allocation. Figure 10: Convergence index change in control allocation. Figure 9: Convergence index change in target allocation.