# Bio-Inspired Traffic Pattern Generation for Multi-AMR Systems
## 4 Case Studies
### Evaluation in the Event-Based Simulator  
Although the event-based simulator was primarily used for optimization, its computational efficiency also makes it valuable for rapid evaluation of different movement strategies. We leveraged this capability to perform detailed performance comparisons across multiple metrics. For each scenario, key operational aspects were evaluated through simulations running for 10,000 iterations (ticks of simulated time) with 10 repetitions to ensure statistical significance. The evaluation tracked the number of conflicts (collisions requiring recovery), tasks completed, percentage of tasks completed within their due time, average delay per task, and total path length traveled by all the AMRs. In the rooms scenario (Table 3), our approach performed significantly better across all the metrics compared to unweighted pathfinding. Conflicts decreased by 41.9% (7.50 vs. 12.90), whereas task completion improved by 10.7% (9.12 vs. 8.24). On-time task completion increased substantially from 63.4% to 85.0%. The average delay per task dropped by 68.9% (2.34 vs. 7.52), with only a minimal increase in path length (90.98 vs. 88.44). \begin{table}
\begin{tabular}{l c c} \hline \hline
**Metric** & **Unweighted** & **Ours** \\ \hline Conflicts (per AMR/1000 iter.) & 12.90 \(\pm\) 0.48 & 7.50 \(\pm\) 0.44 \\ Tasks Completed (per AMR/1000 iter.) & 8.24 \(\pm\) 0.18 & 9.12 \(\pm\) 0.20 \\ Tasks in Time (\%) & 63.39 \(\pm\) 2.33 & 84.99 \(\pm\) 2.38 \\ Delay (per task) & 7.52 \(\pm\) 0.69 & 2.34 \(\pm\) 0.35 \\ Path Length (per task) & 88.44 \(\pm\) 0.90 & 90.98 \(\pm\) 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Rooms’ results. Figure 9: The (**a**) expert and (**b**) algorithmic solutions for industrial scenario B. In industrial scenario A (Table 4), our method showed statistically significant improvements over both the unweighted and expert approaches. Conflicts were significantly reduced to 3.55 \(\pm\) 0.25 compared to the unweighted (6.85 \(\pm\) 0.35, \(p\)\(<\) 0.05) and expert (3.85 \(\pm\) 0.40, \(p\)\(<\) 0.05) solutions. The task completion rate was highest at 22.70 \(\pm\) 0.25, significantly higher than the expert (20.05 \(\pm\) 0.35) and unweighted (22.05 \(\pm\) 0.35) solutions. On-time task completion reached 76.6%, with the lowest average delay being 0.47 units. This was achieved with only a modest increase in path length compared to unweighted routing (39.62 vs. 37.84). The more complex industrial scenario B (Table 5) demonstrated statistically significant improvements across the key metrics. Conflicts decreased significantly by 20.3% compared to the expert solution (14.64 \(\pm\) 0.40 vs. 18.38 \(\pm\) 0.96) and by 30.8% compared to unweighted (21.16 \(\pm\) 0.60). Task completion showed significant improvement to 14.36 \(\pm\) 0.22 tasks versus the expert (12.98 \(\pm\) 0.44) and unweighted (12.42 \(\pm\) 0.28) solutions. On-time delivery reached 85.72%, significantly higher than the expert (77.15%) and unweighted (68.39%) solutions. Average delay was reduced to 2.54 units while maintaining path lengths comparable to the expert solution. Across all the evaluated scenarios, our bio-inspired optimization approach consistently demonstrated substantial reductions in conflicts and delays while enhancing task completion rates and punctuality. As shown in Figure 10, the system achieves a steady improvement in punctuality--a critical metric for industrial applications--throughout the 200,000 iteration optimization process. The minimal increases in path lengths indicate that the algorithm effectively balances the trade-offs between minimizing traversal distances and enhancing overall system performance.