## 4 Simulation Results and Analyses
### Results and Discussion  
We first compare the results of our proposed PA-Jaya algorithm in different subpopulation size cases with the asynchronous Jaya and traditional Jaya algorithms. When the total transmit power (\(p_{\text{total}}=1\) W) and the BER (\(\delta=5\) dB) are limited (which means that the model constraints are satisfied), and the maximum number of iterations \(D\) is reached, the results of different algorithms are as shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **SA** & **GA** & **PSO** & **DE** & **ICO** & **Jaya** & **PA-Jaya** \\ \hline Initial temperature & 100 & – & – & – & – & – & – \\ Reannealing interval & 100 & – & – & – & – & – & – \\ Population size & – & 30 & 30 & 30 & 30 & 30 & 30 \\ Scaling factor & – & – & – & 0.3 & – & – & – \\ Crossover factor & – & 0.3 & – & 0.1 & 0.3 & – & – \\ Mutation factor & – & 0.1 & – & – & 0.1 & – & – \\ Initial inertia weight & – & – & 0.9 & – & – & – & – \\ Convergence inertia weight & – & – & 0.4 & – & – & – & – \\ Local acceleration constant & – & 2 & – & – & – & – \\ Global acceleration constant & – & 2 & – & – & – & – \\ Cloning proportion & – & – & – & – & 0.2 & – & – \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Controlled parameters of PA-Jaya and other comparative algorithms. Figure 3: Performance comparison of different Jaya algorithms. In Figure 3, the PA-Jaya algorithm can achieve better results compared with the traditional Jaya algorithm and the asynchronous Jaya algorithm without a parallel structure. Meanwhile, compared with the traditional Jaya algorithm, several other improved Jaya algorithms can get better results, which could be due to the way that asynchronous iteration improves the convergence speed. In addition, comparing the asynchronous Jaya algorithm and the PA-Jaya algorithm with different subpopulation sizes, it can be seen that when the number of subpopulations is 2, the result of PA-Jaya is similar to that of the asynchronous Jaya algorithm. When the number of subpopulations is 3, the result of PA-Jaya is better. However, as the number continues to grow, the result gets worse. On the one hand, this phenomenon shows that the use of a parallel structure can increase the diversity of the whole population to prevent premature local convergence, thereby further improving the performance of the Jaya algorithm. On the other hand, it also shows that when the subpopulation size is too small, the performance of the algorithm is limited. Taking into account the above situation, we set the number of subpopulations to 3 for the simulations hereafter reported in this article. Meanwhile, Figure 4 shows the total transmission rate of the secondary users obtained by those algorithms under the same conditions. Then, when the number of secondary users is 8 and the maximum number of iterations \(D\) is reached, the total transmission rate of the system under different BERs is as shown in Figure 5. Furthermore, the optimal solutions of the total system transmission rate are shown in Table 3, and they are recorded in every 20 generations. While setting the BER of the transmission (\(\delta\)) and the maximum number of iterations (\(D\)) to 5 dB and 200, respectively, the total transmission power of the secondary users changes as shown in Figure 6 with the interference tolerance of different primary users. From Figure 4, it can be seen that, in each iteration, the solution performance of the total system transmission power obtained by our proposed PA-Jaya algorithm is obviously better than that of SA, GA, PSO, DE, ICO, and traditional Jaya algorithms while also achieving faster convergence speed. On the one hand, this is because of the iterative method and parameterless feature of the Jaya algorithm, which make it superior to other algorithms and allow it to converge faster. Then, the asynchronous iteration method we use further accelerates the process.