## 5 Results
### Experiment B: Borderline Identification  
**Behavi**: In order to assess the correct functioning of the evolved solution, Figure 10 shows the behavior of the robots in a trial with 30 agents. Firstly, Figure 10a, illustrates the swarm spatial distribution and pairwise communication channels. Red balls represent robots belonging to the alpha shape with \(\alpha=15\) (see Section 4) and blue dots represent interior nodes. For the depicted graph, Figure 10c exposes the target LED actions or target alpha shape that the robots should perform in order to correctly identify the swarm borderline. Thus, the robots with horizontal black bars are members of the borderline according to the alpha shape algorithm. Additionally, Figure 10d shows the actual LED actions of the robots, indicating if they are in the frontier or in the interior. Figure 10b displays, in the spatial swarm distribution, the correct frontier classifications (in green) and the errors (in red). The actions of Figure 10b correspond to a snapshot at time instant 480. Observing Figure 10d, the results show outstanding classification accuracy, although sporadically there are some robots whose decision is incorrect (excluding the first 10 time steps, the classification accuracy oscillates between 83%, for instants near time step 80, and 93%, for the last cycles of the trial). Specifically, there are about 2 or 3 robots, depending on the observed time step, whose classification is wrong. It can be observed that there are some agents whose LED actions are remarkably stable (e.g., robots 2, 3 or 10) while the decisions of other robots are much more undefined (e.g., nodes 9, 26 or 28). A common  
Figure 9: (**a**) Spatial graph of the swarm topology, preserving positions and distances. (**b**) Communication state of each robot at each time step. Horizontal black bars correspond to state send and horizontal blank bars denote relay state. (**c**) Message transmitted by the robots at each time instant. The color of the bar at each time step corresponds to a symbol specified in the legend. observable feature is that agents with a robust decision generally have only few neighbors (1 or 2). On the contrary, unstable robots mainly belong to a dense part of the graph, with many neighbors (3, 4 or 5). Thereafter, the errors principally occur when the agents have many neighboring robots, leading to the naive classification of being interior node (which is an incorrect assumption in some cases). Furthermore, another interesting observation is that errors are more likely to appear as false negatives as it can be observed in Figure 11, where the true positive rate (TPR) is slightly inferior than the true negative rate (TNR). At the initial time steps of the simulation, the TPR and the TNR are respectively 1 and 0 because, at the simulation startup, all the agents identify themselves as frontier nodes (see Figure 10d). To observe the behavior in a more visual manner, Figure 12 collects snapshots of a sample trial at different time instants of the simulation. At the initial time step, all robots consider themselves as extremities (red balls). Subsequently, as time elapses, the solution is corrected until the final decision is settled (approximately at time instant 50). The actual alpha shape of the example is shown in purple in Figure 12f. The final classification of this example results in two errors, corresponding to false negatives in both cases. Finally, the behavior of the solution to this experiment can be observed in video format ([[https://youtu.be/tGytXx2](https://youtu.be/tGytXx2) BM2w]([https://youtu.be/tGytXx2](https://youtu.be/tGytXx2) BM2w) accessed on 22 Janunary 2021). Figure 10: (**a**) Spatial graph of the swarm, edges denote the existence of a pairwise communication channel. Red balls represent alpha shape members and blue dots are interior robots. (**b**) Spatial graph of the swarm, red balls denote agent errors (as indicated in (**d**)) and green balls denote correct borderline classifications. (**c**) Target borderline members according to the alpha shape.