## 4 Simulation Results  
In the simulations, we assume \(T=40\) ms, \(T_{h}=4\) ms and \(T_{r}=400\) ms. Eight target channels are considered with the mean vacant time durations of 10 ms, 60 ms, 25 ms, 170 ms, 83 ms, 5 ms, 54 ms, and 155 ms, respectively. The parameters for PSO are as follows. Thirty habitats in a swarm are used. \(\xi_{1}=\xi_{2}=2\). \(V_{\max}=4\). Figure 4 illustrates the convergence property of the algorithm. It can be observed that as the number of iterations increases, better solutions are obtained. Note that we only plot results when time duration during which a channel remains vacant follows Uniform and Exponential distributions. Similar trends have been observed with the other three distributions. For simplicity, we omitted these results. Tables 3 and 4 show the performance of the proposed algorithm compared with the other two target channel visiting methods: the random target channel visiting and the optimal target channel visiting. Two cases are considered respectively: (Case A) Nine target channels with the mean vacant time durations of 170 ms, 30 ms, 210 ms, 300 ms, 52 ms, 5 ms, 130 ms, 59 ms, 111 ms, respectively, and (Case B) Eight target channels with the mean vacant time durations of 10 ms, 60 ms, 25 ms, 170 ms, 83 ms, 5 ms, 54 ms, and 155 ms, respectively. The optimal target channel visiting order is obtained by exhaustive search. It can be seen that the proposed method performs far better than the random channel visiting scheme. The solutions obtained by the proposed algorithm are very close to the optimal solutions. The small standard deviation values also indicate that the proposed scheme is quite stable. \begin{table}
\begin{tabular}{p{14.2 pt} p{142.3 pt}} \hline \hline
**Steps** & **Procedures** \\ \hline
1 & **Swarm initialization.** Set \(k=0\), and randomly generate \(x_{id}^{k}\) and \(y_{id}^{k}\), where \(x_{id}^{k}\in\{0,1\}\), \(y_{id}^{k}\in[-V_{\max}\,,+V_{\max}\,,]\), and \(1\leq i\leq S\). Apply “position correction” procedure to all particles in the swarm. \\
2 & **Fitness evaluation.** Compute the fitness value of each particle according to (2). Set \(\mathbf{p}_{i}^{k}=[p_{i1}^{k},p_{i2}^{k},...,p_{iD}^{k}]\) and \(\mathbf{p}_{g}^{k}=[p_{g1}^{k},p_{g2}^{k},...,p_{gD}^{k}]\), where \(g\) is the index of the particle which has the highest fitness value. \\
3 & **Velocity updating.** Set \(k=k+1\), and update the velocity of the particle according to (6). If \(y_{id}^{k}>V_{\max}\), set \(y_{id}^{k}=V_{\max}\) ; if \(y_{id}^{k}<-V_{\max}\), set \(y_{id}^{k}=-V_{\max}\). \\
4 & **Position updating.** Update the position of the particle according to (7). Apply “position correction” procedure to all particles in the swarm. \\
5 & **Fitness evaluation.** Compute the fitness value of each particle according to (2). For particle \(i\), if it’s fitness value is greater than the fitness value of \(\mathbf{p}_{i}^{k-1}\), then set \(\mathbf{p}_{i}^{k}=\mathbf{x}_{i}^{k}\) ; if it’s fitness value is greater than the fitness value of \(\mathbf{p}_{g}^{k-1}\), then set \(\mathbf{p}_{g}^{k}=\mathbf{x}_{i}^{k}\). \\
6 & **Stop criteria evaluation.** If \(k\) equals to the predefined maximum iteration, the algorithm is terminated; otherwise, go to step 3. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proposed algorithm for target channel visiting order. Figure 4: Convergence property of the algorithm averaged over 100 independent experiments. (**a**) Performance of the best particle of the swarm (time duration during which a channel remains vacant follows Uniform distribution). (**b**) Average performance of the whole swarm (time duration during which a channel remains vacant follows Uniform distribution). (**c**) Performance of the best particle of the swarm (time duration during which a channel remains vacant follows Exponential distribution). (**d**) Average performance of the whole swarm (time duration during which a channel remains vacant follows Exponential distribution).