## 4 Discussion  
The observed trends across the two metrics in the _overall analysis_ are deeply connected to the interplay between the number of groups and the evaporation rate. In terms of success rate, the dynamics shift at different evaporation rates. At a higher rate (\(\rho=0.01\)) the optimal performance is achieved with 10 groups, suggesting that a more consolidated effort among a moderate number of groups is favored for efficient exploration. Conversely,  
Figure 5: Plots obtained with five groups (\(g=5\)) and forty ants per group (\(n_{g}=40\)). Figure 8: Plots obtained with fifty groups (\(g=50\)) and four ants per group (\(n_{g}=4\)). Figure 6: Plots obtained with ten groups (\(g=10\)) and twenty ants per group (\(n_{g}=20\)). Figure 7: Plots obtained with twenty groups (\(g=20\)) and ten ants per group (\(n_{g}=10\)). at a lower evaporation rate (\(\rho=0.001\)) the extended lifespan of pheromones promotes sustained collaboration across 20 groups, leading to improved overall efficiency. The trend in path cost reflects a delicate balance between the collaboration benefits and potential drawbacks of increased group size. At a higher evaporation rate (\(\rho=0.01\)) the optimal path cost is achieved with 10 groups, denoting an optimal level of cooperation. Conversely, at a lower evaporation rate (\(\rho=0.001\)), sustained collaboration across 20 groups becomes beneficial due to the extended period of information retention. The slower evaporation rate facilitates distributed collaboration, enhancing exploration efficiency and reducing overall path costs. In this scenario, the persistence of pheromones enables distributed ant groups to communicate better and share information. In the _group analysis_, operating as a single group, the colony displayed a remarkable level of consistency, showing comparable success rates and costs at different evaporation rates (\(\rho\) values). This consistency suggests that the collective behavior of the colony is inherently robust, adapting seamlessly to varying environmental conditions. Upon division into two groups, a clear dynamic emerged. Group 1 outperformed group 2 when the evaporation rate was higher and vice versa. However, the colony showed an overall consistent performance, hinting at the robustness of its collective decision-making processes. Expanding the analysis to five groups revealed a standout performance by group 1, achieving the highest success rate along with a competitive cost. However, the subsequent groups exhibited signs of performance degradation, highlighting the complexity of managing larger ant colonies with diverse group compositions. Similar trends persisted when the colony was divided into ten groups, with specific groups distinguishing themselves in terms of success rates and costs. Notably, there was a discernible trend of performance degradation progress through the groups. This suggests that as the number of groups increases, the coordination challenges become more pronounced, potentially affecting the overall effectiveness of the colony. Further dividing the colony into twenty and fifty groups exposed a more intricate landscape of performance variations. While certain groups consistently excelled, demonstrating high success rates and cost-effectiveness, others displayed a noticeable decline in performance. Overall, it is noteworthy that the optimization process does not reach its best with the final group of ants in each configuration. In other words, the group achieving the optimal values in terms of success rate or path cost is typically one of the initial groups. Subsequent groups tend to exhibit a decline in performance after one of these early groups attains optimal values in both evaluation metrics. Finally, in the _pheromone distribution analysis_, in general, the plots across all configurations exhibit comparable trends. Initially, there is a noticeable increase in mean pheromone levels, corresponding to active exploration and a significant presence of ants.