## 3 Experiments and Results
### Group Analysis
Despite these strengths, there is a slight trend of performance degradation as we progress through the groups, as one can see in both \(\rho\) scenarios. When the colony is divided into \(g=20\) groups, as in Table 7, and \(\rho=0.01\), group 1 emerges as the top performer, with a notable success rate of 0.92 accompanied by a competitive cost of 1171.355. Group 2 closely follows, achieving a success rate of 0.90 and showing competitive values for the cost. Noteworthy is group 6, standing out with the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\rho=0.01\)} & \multicolumn{2}{c}{\(\rho=0.001\)} \\ \hline
**Group** & **Success Rate** & **Cost** & **Success Rate** & **Cost** \\ \hline
1 & **0.925** & 1251.004 & **0.905** & 1227.731 \\
2 & 0.850 & 1288.651 & 0.890 & **1155.843** \\
3 & 0.870 & **1178.144** & 0.880 & 1217.516 \\
4 & 0.895 & 1214.612 & 0.860 & 1287.937 \\
5 & 0.885 & 1180.499 & 0.870 & 1299.610 \\
6 & 0.905 & 1282.315 & 0.880 & 1217.064 \\
7 & 0.830 & 1259.452 & 0.845 & 1306.233 \\
8 & 0.850 & 1198.390 & 0.840 & 1311.303 \\
9 & 0.830 & 1310.130 & 0.855 & 1303.442 \\
10 & 0.845 & 1254.935 & 0.860 & 1331.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results obtained with ten groups (\(g=10\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\rho=0.01\)} & \multicolumn{2}{c}{\(\rho=0.001\)} \\ \hline
**Group** & **Success Rate** & **Cost** & **Success Rate** & **Cost** \\ \hline
1 & **0.856** & **1270.571** & 0.860 & 1312.964 \\
2 & 0.854 & 1281.639 & **0.876** & **1220.156** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results obtained with two groups (\(g=2\)). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\rho=0.01\)} & \multicolumn{2}{c}{\(\rho=0.001\)} \\ \hline
**Group** & **Success Rate** & **Cost** & **Success Rate** & **Cost** \\ \hline
1 & **0.9125** & **1201.690** & **0.9100** & **1210.888** \\
2 & 0.8700 & 1206.368 & 0.8775 & 1235.365 \\
3 & 0.8350 & 1266.726 & 0.8650 & 1301.793 \\
4 & 0.8700 & 1243.534 & 0.8575 & 1268.863 \\
5 & 0.8225 & 1336.451 & 0.8725 & 1240.825 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results obtained with five groups (\(g=5\)). lowest cost of 1115.392, emphasizing its cost-effectiveness. Transitioning to \(\rho=0.001\), group 1 maintains a high success rate of 0.92 with a slightly increased cost of 1226.367. Group 5 exhibits the lowest cost of 1059.165. Conversely, group 4 boasts the highest success rate of 0.96 coupled with a competitive value for the path cost. Additionally, there is a noticeable trend of performance degradation, especially under \(\rho=0.01\). Finally, when the colony is divided into \(g=50\) groups, as in Table 8, under \(\rho=0.01\) group 1 stands out, with a perfect success rate of 1.000 along with a competitive cost of 1162.1375. Subsequent groups closely follow with relatively high success rates and competitive values for cost and exit time. Notably, group 11 excels with the lowest path cost of 985.3046. However, there is a moderate degradation in performance across successive groups. Transitioning to \(\rho=0.001\), group 2 maintains a perfect success rate of 1.000, coupled with a path cost of 1111.2629. Meanwhile, group 6 emerges as the top performer, showing a perfect success rate of 1.000 and the lowest cost of 938.1332. This highlights the group's remarkable ability to efficiently navigate and exit the environment. Overall, for both values of \(\rho\), a diverse range of success rates, costs, and exit times is observed across the groups. Some groups excel in achieving high success rates, while others prioritize minimizing costs or achieving faster exit times, providing valuable insights into optimizing the management of larger ant colonies. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\rho=0.01\)} & \multicolumn{2}{c}{\(\rho=0.001\)} \\ \hline
**Group** & **Success Rate** & **Cost** & **Success Rate** & **Cost** \\ \hline  
\hline \hline \end{tabular}
\end{table}