## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Network** & **N** & **Method** & **Best** & **Median** & **Mean** & **Worst** & **Std.** & **SR (\%)** & **CPU Time (s)** \\ \hline \multirow{8}{*}{1000} & \multirow{4}{*}{1000} & coACO & \(-\)2259.70 & \(-\)2259.70 & \(-\)2259.70 & \(-\)2259.70 & 0 & 100 & 116.826 \\  & & ACO & \(-\)2259.73 & \(-\)2259.73 & \(-\)2260.94 & \(-\)2262.76 & 1.564 & 60 & 74.335 \\  & & K2 & \(-\)2267.64 & \(-\)2275.90 & \(-\)2276.53 & \(-\)2288.06 & 8.376 & 0 & 0.118 \\  & & B & \(-\)2304.07 & - & - & - & 0 & 0.213 \\ \hline \multirow{8}{*}{3000} & coACO & \(-\)6733.48 & \(-\)6733.48 & \(-\)6733.48 & \(-\)6733.48 & 0 & 100 & 173.060 \\  & ACO & \(-\)6733.48 & \(-\)6733.47 & \(-\)6736.14 & \(-\)6744.19 & 4.376 & 60 & 103.114 \\  & & K2 & \(-\)6739.60 & \(-\)6755.06 & \(-\)6755.95 & \(-\)6797.71 & 16.688 & 0 & 0.142 \\  & & B & \(-\)6873.20 & - & - & - & 0 & 0.276 \\ \hline \multirow{8}{*}{ASIA} & coACO & \(-\)11,193.42 & \(-\)11,193.42 & \(-\)11,193.42 & \(-\)11,193.42 & \(-\)11,193.42 & 1.92 \(\times\) 10\({}^{-12}\) & 100 & 163.858 \\  & ACO & \(-\)11,193.42 & \(-\)11,197.08 & \(-\)11,197.23 & \(-\)11,205.13 & 4.512 & 40 & 100.373 \\  & K2 & \(-\)11,197.08 & \(-\)11,218.39 & \(-\)11,224.51 & \(-\)11,300.65 & 28.867 & 0 & 0.174 \\  & B & \(-\)11,450.81 & - & - & - & 0 & 0.288 \\ \hline \multirow{8}{*}{8000} & coACO & \(-\)17,823.01 & \(-\)17,823.01 & \(-\)17,823.01 & \(-\)17,823.01 & 0 & 100 & 203.835 \\  & ACO & \(-\)17,823.01 & \(-\)17,823.01 & \(-\)17,826.72 & \(-\)17,837.12 & 5.774 & 60 & 127.463 \\  & K2 & \(-\)17,834.80 & \(-\)17,844.42 & \(-\)17,863.88 & \(-\)17,951.13 & 38.805 & 0 & 0.187 \\  & B & \(-\)18,100.86 & - & - & - & 0 & 0.345 \\ \hline \multirow{8}{*}{10,000} & coACO & \(-\)22,290.78 & \(-\)22,290.78 & \(-\)22,290.78 & \(-\)22,290.78 & 3.83 \(\times\) 10\({}^{-12}\) & 100 & 246.144 \\  & ACO & \(-\)22,290.78 & \(-\)22,294.73 & \(-\)22,293.15 & \(-\)22,294.73 & 2.043 & 40 & 153.925 \\  & K2 & \(-\)22,303.21 & \(-\)22,324.18 & \(-\)22,342.28 & \(-\)22,442.17 & 42.487 & 0 & 0.226s \\  & B & \(-\)22,572.73 & - & - & - & - & 0 & 0.459 \\ \hline \multirow{8}{*}{ALARM} & coACO & \(-\)10,818.45 & \(-\)10,852.26 & \(-\)10,852.26 & \(-\)10,950.47 & 41.256 & 100 & 6481.540 \\  & ACO & \(-\)10,957.50 & \(-\)11,002.89 & \(-\)11,012.03 & \(-\)11,138.50 & 52.234 & 100 & 3687.500 \\  & K2 & \(-\)11,443.44 & \(-\)11,694.90 & \(-\)11699.26 & \(-\)11,993.50 & 189.450 & 0 & 3.285 \\  & B & \(-\)3,425,441.5 & - & - & - & - & 0 & 7.913 \\ \hline \multirow{8}{*}{5000} & coACO & \(-\)48,501.03 & \(-\)48,517.21 & \(-\)48,525.78 & \(-\)48579.64 & 28.656 & 100 & 10,800.721 \\  & ACO & \(-\)49,341.99 & \(-\)49,661.63 & \(-\)49,701.69 & \(-\)50,329.43 & 279.589 & 0 & 6921.368 \\ \cline{1-1}  & K2 & \(-\)50,968.63 & \(-\)51,949.21 & \(-\)51,858.65 & \(-\)52,867.42 & 595.86 & 0 & 4.867 \\ \cline{1-1}  & B & \(-\)5,425,441.5 & - & - & - & - & 0 & 25.681 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical results of the BIC score for various methods. Figure 5: Evolution curves of the average BIC score achieved by ACO and coACO on the ASIA dataset with \(\eta=3000\). Figure 8: Evolution curves of the average BIC score achieved by ACO and coACO on the ASIA dataset with \(n=10\),000. Figure 6: Evolution curves of the average BIC score achieved by ACO and coACO on the ASIA dataset with \(n=5000\). Figure 7: Evolution curves of the average BIC score achieved by ACO and coACO on the ASIA dataset with \(n=8000\). Table 3 also shows the summary of the statistical results for various methods tested in the experiment, where \(\mu\pm\sigma\) denotes the mean and the standard deviation over the independent runs and the value inside (_best_) is the corresponding best value. The indicator \(It.\) is the smallest number of iterations when the algorithm finds the optimal network structure.