## 3 Experiments and Results
### Group Analysis  
In the group analysis phase, adjustments were made to the path costs considering each group's success rate. The success rate, denoted as \(SR_{g}\), is determined by the ratio of ants that successfully reached the exit to the total number of ants within the group. When the colony is composed of a single group, as in Table 3, the success rates at both evaporation rates are comparable (0.849 at \(\rho=0.01\) and 0.848 at \(\rho=0.001\)), indicating consistent performance. The normalized cost considering the success rate allows for a more accurate evaluation. For \(\rho=0.01\) the cost is 1293.53, while at \(\rho=0.001\) the corresponding value is 1311.197. These results suggest that despite minor variations the colony maintains relatively consistent performance in terms of success rates and cost across different evaporation rates. Let us analyze now the results when we have more than one group. In what follows, the index of the group will denote its turn in starting the exploration. Thus, group 1 starts first, then group 2, and so on. When the colony is divided into two groups, as in Table 4, for \(\rho=0.01\) group 1, which is the one that starts first, has the highest success rate of 0.856 and a lower cost of 1270.571. In comparison, the second group, group 2, exhibits a slightly lower success rate of 0.854 and a marginally higher cost of 1281.639. Shifting to \(\rho=0.001\), group 1 maintains a consistently high success rate of 0.860. However, this comes with a higher cost of 1312.964. On the other hand, group 2 shows a notable improvement, achieving the highest success rate in this context at 0.876, accompanied by the lowest cost of 1220.156. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Success Rate**} \\ \hline \(g\) & \(\rho=0.01\) & \(\rho=0.001\) \\ \hline
1 & 0.849 & 0.848 \\
2 & 0.855 & 0.868 \\
5 & 0.862 & 0.8765 \\
**10** & **0.8685** & 0.8665 \\
**20** & 0.8125 & 0.8875 \\
50 & 0.795 & 0.8645 \\ \hline \multicolumn{3}{c}{**Path Cost**} \\ \hline \(g\) & \(\rho=0.01\) & \(\rho=0.001\) \\ \hline
1 & 1293.53 & 1311.20 \\
2 & 1276.09 & 1265.81 \\
5 & 1249.52 & 1251.05 \\
**10** & **1242.63** & 1264.48 \\
**20** & 1339.24 & **1201.36** \\
50 & 1289.45 & 1227.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results obtained based on two evaluation metrics: success rate (on the top) and path cost (on the bottom). \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 \(1\) & 0.849 & 1293.53 & 0.848 & 1311.197 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results obtained with one group \((g=1)\). When the colony is divided into five distinct groups (\(g=5\)), as in Table 5, under \(\rho=0.01\) group 1 shows a remarkable success rate of 0.9125 accompanied by a cost of 1201.690. The subsequent groups (3, 4, and 5) show signs of performance degradation, as evidenced by varying success rates and costs. Transitioning to \(\rho=0.001\), group 1 maintains the best performance across both metrics, with a success rate of 0.9100 and a cost of 1210.888. However, similarly to the \(\rho=0.01\) scenario, groups 2, 3, 4, and 5 exhibit varying degrees of success rates and costs, denoting a slight general degradation in performance as we move across the groups. When the colony is divided into ten groups (\(g=10\)), as in Table 6, under \(\rho=0.01\) group 1 distinguishes itself with an impressive success rate of 0.925, showing a high level of efficiency in reaching the exit. Following closely, group 2 achieves a slightly lower success rate of 0.850 but maintains competitive values for the cost. Group 3 stands out with the lowest cost of 1178.144, emphasizing its cost-effectiveness despite a moderate success rate. Transitioning to \(\rho=0.001\), group 1 continues to lead with the highest success rate of 0.905. Group 2 shows improvement, achieving a success rate of 0.890 with the lowest cost of 1155.843.