## 5 Numerical Experiments
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistics** & **SSO** & **PSO** & **PSSO** & **GA** \\ \hline Max (Best) & **0.9999759790** & 0.9998579620 & 0.9998130200 & 0.9956341980 \\ Gen\({}_{\text{convergent}}\) & 628 & 576 & **468** & 999 \\ Min (Worse) & **0.9998471140** & 0.9960312840 & 0.9967661500 & 0.0915097220 \\ Average & **0.9999484850** & 0.9989969110 & 0.9990356900 & 0.4793065570 \\ STD & **0.0000255121** & 0.0007723344 & 0.0006460497 & 0.3281670328 \\ \hline \hline \end{tabular} The best solution marked in bold.  
\end{table} 
Table 6: The statistics of system reliability for benchmark 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistics** & **SSO** & **PSO** & **PSSO** & **GA** \\ \hline Min (Best) & **0.169000** & 0.173000 & 0.176000 & 0.290000 \\ Gen\({}_{\text{convergent}}\) & 884 & 545 & **222** & 999 \\ Max (Worse) & **0.224000** & 0.263000 & 0.235000 & 0.360000 \\ Average & **0.193840** & 0.209380 & 0.209820 & 0.327020 \\ STD & 0.014315 & 0.015369 & **0.013011** & 0.018947 \\ \hline \hline \end{tabular} The best solution marked in bold.  
\end{table} 
Table 7: The statistics of running time (units used: seconds) for benchmark 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistics** & **SSO** & **PSO** & **PSSO** & **GA** \\ \hline Max (Best) & **0.999886930** & 0.999567032 & 0.999680340 & 0.999073625 \\ Gen\({}_{\text{convergent}}\) & **100** & 376 & 489 & 999 \\ Min (Worse) & **0.9999592066** & 0.994620740 & 0.993449271 & 0.055013273 \\ Average & **0.999814268** & 0.998070072 & 0.997827517 & 0.427838158 \\ STD & **0.000064727** & 0.001102467 & 0.001329463 & 0.304351767 \\ \hline \hline \end{tabular} The best solution marked in bold.  
\end{table} 
Table 8: The statistics of system reliability for benchmark 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistics** & **SSO** & **PSO** & **PSSO** & **GA** \\ \hline Min (Best) & **0.169000** & 0.173000 & 0.176000 & 0.290000 \\ Gen\({}_{\text{convergent}}\) & 884 & 545 & **222** & 999 \\ Max (Worse) & **0.224000** & 0.263000 & 0.235000 & 0.360000 \\ Average & **0.193840** & 0.209380 & 0.209820 & 0.327020 \\ STD & 0.014315 & 0.015369 & **0.013011** & 0.018947 \\ \hline \hline \end{tabular} The best solution marked in bold.  
\end{table} 
Table 8: The statistics of system reliability for benchmark 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistics** & **SSO** & **PSO** & **PSSO** & **GA** \\ \hline Max (Best) & **0.999886930** & 0.999567032 & 0.999680340 & 0.999073625 \\ Gen\({}_{\text{convergent}}\) & **100** & 376 & 489 & 999 \\ Min (Worse) & **0.9999592066** & 0.994620740 & 0.993449271 & 0.055013273 \\ Average & **0.999814268** & 0.998070072 & 0.997827517 & 0.427838158 \\ STD & **0.000064727** & 0.001102467 & 0.001329463 & 0.304351767 \\ \hline \hline \end{tabular} The best solution marked in bold.  
\end{table} 
Table 9: The statistics of running time (units used: seconds) for benchmark 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistics** & **SSO** & **PSO** & **PSSO** & **GA** \\ \hline Min (Best) & **0.172000** & 0.187000 & 0.182000 & 0.298000 \\ Gen\({}_{\text{convergent}}\) & 954 & **319** & 450 & 999 \\ Max (Worse) & **0.219000** & 0.225000 & 0.225000 & 0.345000 \\ Average & **0.193260** & 0.203340 & 0.202720 & 0.320140 \\ STD & 0.010240 & **0.010277** & 0.010500 & 0.012249 \\ \hline \hline \end{tabular} The best solution marked in bold.  
\end{table} 
Table 9: The statistics of running time (units used: seconds) for benchmark 3. For the benchmark 1, the experimental results are analyzed as below and shown in Tables 4 and 5. 1. The adopted SSO has the best performance including Max, Min, Average, and STD of system reliability, i.e., **0.931235373**, **0.867673755**, **0.920391358**, and **0.011218917**. 2. The adopted SSO has the best performance including Min, Max, and Average of running time, i.e., **0.17100**, **0.26200**, and **0.19778**. 3. The PSSO has the best performance in STD of running time, i.e., **0.02151**. 4.