## 5 Experiment
### Experimental Results
#### 5.3.3 Robustness  
This section analyzes to what extent the robots are robust to different map sizes when the other components of the environment are held fixed. This is of particular importance because increasing the map size means that the robot travel time will increase and that meeting the deadlines might therefore be more difficult. Starting with the average foraging rate (Figure 9(a)), as in the flexibility experiment, the ACO, hotspot, and blind methods have similar foraging rates in all map sizes. The average foraging rate (Figure 9(a)) of the centralized method, however, is worse than those of the other methods are when the map size is small, medium, and large, although it is better when the map size is very small or very large. This is due to two factors. First, having one collection zone in a very small or very large map when the number of robots is medium can decrease the travel time and hence increase the foraging rate. Second, the foraging rates of the ACO, hotspot, and blind methods in this figure show the average number of  
Figure 9: Scalability results for 40 trials with different setups. The results are ordered from smallest to largest for better representation (**a–f**). resources found in the central collection zone only (F) and not all collection zones (\(\Sigma\)F\({}_{\text{d}}\)). Thus, the small difference between the foraging rates of the centralized method and the other methods can be attributed to the fact that the other methods allocate robots to move resources to the closest collection zone before they die. In regard to the average expiry rate (Figure 10b), the centralized method has the worst results in all map sizes except the 16 \(\times\) 16 map, where it produces the lowest average expiry rate. This behavior will be further investigated when discussing the detailed expiry rates shown in Figure 11. Going back to Figure 10b, in a very small map (4 \(\times\) 4) and a very large map (40 \(\times\) 40) with a medium number of robots, hotspot and blind DTA are better than the ACO method. In a small map (8 \(\times\) 8), however, all three methods perform similarly. In a medium map (16 \(\times\) 16), the ACO and hotspot methods have similar robustness, while the blind method performs worse than the rest. In a large map (20 \(\times\) 20), the ACO and blind methods perform similarly, while the hotspot method is slightly worse. Therefore, it can be concluded that the hotspot method is either more robust than the other methods or is similar to the best method, except in the 20 \(\times\) 20 map. To further investigate the differences among the methods, especially in the case of the 16 \(\times\) 16 and 20 \(\times\) 20 maps, the detailed expiry rate of each trial is presented in Figure 11a-e. The centralized method has the worst expiry rate in all trials with the 4 \(\times\) 4 map (Figure 11a), 8 \(\times\) 8 map (Figure 11b), 20 \(\times\) 20 map (Figure 11d), and 40 \(\times\) 40 map (Figure 11e). In regard to the 16 \(\times\) 16 map (Figure 11c), the centralized method produces very inconsistent results from one trial to another. As seen from the yellow line in Figure 11c, the expiry rate is significantly lower in half of the trials and significantly higher in the other half. This indicates that even though the average expiry rate of the centralized method is low, this result is not guaranteed, and it is not robust in many cases. The ACO, hotspot, and blind methods have similar expiry rates in the 8 \(\times\) 8 map (Figure 11b), 16 \(\times\) 16 map (Figure 11c), and 40 \(\times\) 40 map (Figure 11e). However, in the 4 \(\times\) 4 map (Figure 11a), the ACO method produces a worse expiry rate than the hotspot and blind methods in most trials. This indicates that ACO is not robust to very small maps with a medium number of robots. Moreover, in the 20 \(\times\) 20 map (Figure 11d), the hotspot method produces worse expiry rates than the ACO and blind methods in half of the trials.