## 5 Experiment
### Experimental Results
#### 5.3.2 Scalability  
This section analyzes to what extent the algorithm is scalable with swarms that range from tens to thousands. This is of particular importance because increasing the number of robots produces more inter-robot collisions, which affects the scalability of the algorithms. Thus, adding more robots does not necessarily improve performance, and the algorithm's behavior in such setups needs to be further investigated. Starting from the total foraging rate of all zones, i.e., \(\sum_{\forall\text{d}}(\text{F}_{\text{d}})\) (see Figure (a)a), it can be seen that having a very small or very large number of robots in a medium-sized map is not a good choice and negatively affects the foraging rate. From the figure, the best result is obtained when the number of robots is intermediate (136) with a 16 \(\times\) 16 map. This confirms the conclusion in the literature, where it was emphasized that increasing the number of robots can negatively affect the foraging rate and that it is better to set the number of robots in proportion to the map size. One interesting observation from Figure (a)a is that the foraging rate is affected more by the zone's setup than by the allocation method used. In particular, all multiple-collection-zone methods (ACO, hotspot, and blind) have similar foraging rates that are better than that of the centralized method, which has only one collection zone. Only in the case when the number of robots is very small (24 robots) does the centralized method produce slightly better results than the other methods. This is because having a very small number of robots reduces the collision and hence improves the foraging rate. Therefore, when increasing the number of robots around one central collection zone (i.e., 112, 136, 144, and 592 robots) in  
Figure 8: Average scalability of the different methods in terms of the (**a**) foraging and (**b**) expiry rates. Figure 8a, the foraging rate is significantly affected in the centralized method, to the point that the results are less than half of what the other methods are able to collect. In regard to the average expiry rate (Figure 8b), each algorithm behaves differently from one test to another. Thus, the detailed results of each trial will be investigated next. However, in general, it can be noted that the centralized method is highly inconsistent, as it significantly reduces the average expiry rate when the number of robots is small while significantly increasing it when the number of robots is large. This indicates that having one collection zone is not a good choice, especially when we are targeting sensitive search and rescue missions. Going deeper into the detailed results of the expiry rate (Figure 9a-e), it can be clearly seen that the centralized method is inconsistent. Its expiry rate starts from a very low level (a zero expiry rate) when the number of robots is 24 (Figure 9a) and rises as the number of robots increases (Figure 9b-d) until it becomes significantly higher than those of the other methods, with an 80% expiry rate when the number of robots is 592 (Figure 9e). In regard to the ACO method, inconsistent behavior can also be observed, similar to that of the centralized method but not as obvious. When the number of robots is very small to medium (Figure 9a-c), the ACO method produces a similar expiry rate to those of the hotspot and blind methods in more than two-thirds of the trials while producing lower expiry rates in one-third of the trials. When the number of robots is large to very large (Figure 9d,e), however, the ACO method behaves in exactly the opposite fashion, producing expiry rates similar to those of the hotspot and blind methods in more than two-thirds of the trials while producing higher expiry rates in one-third of the trials. This means that its results are not consistent, and the expiry rate is greatly affected by the number of robots.