## 5 Simulation Experiment
### Experimental Result  
In this part, the data will be simulated and analyzed from many aspects and the experimental results will be displayed in the form of curves, bar charts and tables. Figure 5a,b is graphs showing the simulation results of the CEAGA, HGA, MBPSO and ISA under different task numbers and sensor nodes. As depicted in Figure 5a, with a task count of 30 and 16 sensors, the optimal outcomes achieved by the CEAGA and the other 3 algorithms after 1000 generations are as follows: 12.9437, 11.9723, 12.0466, and 11.8698, respectively. It can be seen from the figure that the convergence speed of ISA is slow, and the performance of the algorithm is poor. Meanwhile, MBPSO converges prematurely at the 50 th generation, leading to local optimization. The application of the HGA relies on fixed crossover and mutation probabilities, and the selection of these parameters significantly impacts the quality of the solution. When the algorithm runs to 350 generations, the CEAGA has reached convergence and found the best solution. The CEAGA uses improved Sine chaotic stochastic optimization technology to generate population, thus enriching population diversity and helping to find feasible solutions close to the optimal solution. In addition, the CEAGA also uses elitist selection to avoid local optimization and improve the convergence speed of the algorithm. The crossover probability and mutation probability of the CEAGA are dynamically calculated by adaptive strategy, which can avoid the influence on the quality of solution. Therefore, the CEAGA can obtain higher network revenue in operation. In Figure 5b, when the number of tasks is 45 and the number of sensors is 24, the best results of the CEAGA and the other three algorithms are 19.3968, 17.4022, 17.6138 and 17.1563, respectively. From the figure, it is evident that the HGA and MBPSO exhibit rapid convergence, leading to local optimization. The curve fluctuation of ISA is small, and the network income is the worst. While the CEAGA converges to generation 550, its network benefits are far greater than the other three algorithms. The reason is consistent with the above analysis. Chaos operator, elite operator and adaptive operator are used in the CEAGA to optimize the GA, so that the performance of the CEAGA is much higher than the other three algorithms. Similar conclusions can be drawn from Figure 5c,d. Through the analysis of Figure 5a-d, it can be clearly understood that the CEAGA can better solve the task allocation problem of IUWSNs, and not only has higher network income, but also has faster convergence speed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm Name** & **Generations** & \begin{tabular}{c} **Number of Iterations** \\ **at Each Temperature** \\ \end{tabular} & \
\begin{tabular}{c} **The Initial** \\ **Temperature** \\ \end{tabular} &
\begin{tabular}{c} **Temperature Attenuation** \\ **Coefficient** \\ \end{tabular} \\ \hline ISA & 1000 & 100 & 1000 & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental parameter setting of the SA. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm Name** & **Generations** & **Population Number** & **Crossover Probability** & **Mutation Probability** \\ \hline HGA & 1000 & 100 & 0.8 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental parameter setting of the GA. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm Name** & **Generations** & **Population Number** & **Learning Factor** & **Inertia Weight** & **Speed Limit** \\ \hline MBPSO & 1000 & 100 & 0.8 & 0.01 & [\(-\)0.5, 0.5] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental parameter setting of the PSO. Figure 6a-d, respectively, show the comparison of network revenue optimization trends of the CEAGA, HGA, MBPSO and ISA algorithms under different sensor node numbers and different task numbers: Figure 6a-d show the final results of the four algorithms running in 1000 generations.