## 5 Simulation Experiments
### Sensitivity Analysis of Parameters  
The performance of the proposed TLISOA is highly dependent on the parameter settings within the algorithm, specifically \(f_{c}\), \(u\), and \(\
u\). Different parameter configurations can lead to significantly different optimization results, affecting both the solution quality and computational efficiency. In the context of multi-UAV task allocation, optimization algorithms must operate efficiently under complex task constraints and multi-objective requirements to achieve rational task distribution and optimal resource utilization. Incorrect parameter settings may cause the algorithm to become trapped in local optima during the search process or incur unnecessary computational costs, thereby reducing the practical effectiveness of the algorithm. Given that TLISOA incorporates certain improvements to the spiral coefficient \(\
u\), it is necessary to conduct a sensitivity analysis on the remaining \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Description** \\ \hline Processor & Intel® Core(TM) i5-8300H CPU @ 2.30 GHz 2.30 GHz \\  & (Intel, Santa Clara, CA, USA) \\ RAM & 8 GB \\ OS & Windows 11 (64-bit) \\ Python version & Python 3.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation environment. list the optimal task allocation schemes designed by these algorithms for the two experimental scenarios. Tables 6 and 7 present the algorithmic performance comparison between TLISOA and the other five algorithms under the two experimental scenarios in terms of optimal, mean, median, worst, standard deviation, and average convergence time. Box plots of the results from 20 independent runs of each of the six algorithms are provided in Figures 8 and 9, respectively. Figures 6 and 7 reveal a notable discrepancy in the iteration speeds among the six algorithms, all of which gradually converge toward the optimal value throughout the iteration process. Notably, TLISOA exhibits a swifter iteration pace. This can be attributed to its larger spiral coefficient during the early stages, facilitating rapid optimization progress. Additionally, the combined effect of population initialization via Tent chaotic mapping and Levy flight enables TLISOA to swiftly converge to the global optimal solution without succumbing to local optima. Compared to the other algorithms, TLISOA demonstrates superior fitness values within the same number of iterations, underscoring its enhanced global search capability and faster convergence rate. Consequently, TLISOA yields optimization results more aligned with the multi-UAV task allocation requirements. Tables 6 and 7, and Figures 8 and 9, show the excellent performance of TLISOA compared to the other five algorithms in two different experimental scenarios. Although the standard deviation of TLISOA slightly lags behind that of PSO-AWOA, TLISOA's optimality finding ability is more significantly improved compared to the other five algorithms in terms of the optimal, mean, median, and worst values. In addition, TLISOA has a shorter average convergence time, which suggests that it has the ability to find a better allocation scheme in a shorter time. In conclusion, the proposed algorithm has significant advantages in handling MCMUAVCTAP. Figure 6: Algorithms’ fitness curve in experimental scenario 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**TLSOA vs.** & **Optimum** & **Average** & **Median Value** & **Worst Value** & **Standard** & **Average** \\  & **Value** & **Value** & & **Deviation** & **Convergence Time/s** \\ \hline SOA & 2.44\% & 11.55\% & 15.11\% & 13.46\% & 42.22\% & 12.24\% \\ CAM-GA & 8.05\% & 16.86\% & 17.10\% & 26.09\% & 55.17\% & 13.06\% \\ A-QCDPSO & 9.35\% & 18.00\% & 19.55\% & 23.15\% & 49.02\% & 0.00\% \\ PSO-AWOA & 10.61\% & 10.89\% & 12.16\% & 10.20\% & \(-\)30.00\% & 11.07\% \\ CESMA & 4.76\% & 9.72\% & 10.61\% & 5.37\% & 33.33\% & 15.73\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison of algorithms for scenario 1. Figure 7: Algorithms’ fitness curve in experimental scenario 2.