## 5 Results
### Experiment A: Leader Selection  
**Behavi**: We observed two stages during the evaluation process. Firstly, agents carry out a negotiation phase in order to select a leader. Essentially, all the robots claim the leadership at the beginning of the negotiation process by turning their LEDs on. Thereafter, each robot being the leader eventually turns off its LED in order to yield leadership to other  
Figure 3: Evolution of the fitness function with the generations of SNES in (**a**) the leader selection and (**b**) the border identification tasks. In each generation, the darker curves are the sample mean fitness scores and the upper and lower contours of the shadow areas represent the maximum and minimum fitness values. members of the swarm. The negotiation process can be understood as a winner-take-all competition among agents, so that each potential leader inhibits the others through the communication system. Consequently, the winner of the negotiation, and thus the leader, is the robot whose LED remains turned on. The second phase of the behavior is achieved if an agent is the unique leader of the swarm or, at least, if it does not receive any communication information specifying the opposite. In such a situation, a stable solution is reached and remains still unless a perturbation is introduced in the system. Agents are aware of other robots claiming leadership by means of the communication system. The discussion on the emerged communication is retrieved and elaborated in detail later. Figure 4 shows an example of the emerged behavior, displaying both negotiation and stable leader identification. It shows the LED actions of the agents in a swarm of size 20 as execution time elapses. Black bars indicate that the LED of the corresponding robot in the ordinate axis is turned on. There is no leader fault in this figure as it will be discussed in the robustness analysis below. The results of the figure closely resemble the behavior previously described. The negotiation stage, starting at time step 0 and concluding approximately at simulation cycle 40, exposes the winner-take-all process in which LED actions are constantly being deactivated. Nonetheless, the plot shows an unsuccessful negotiation scenario whereby all the robot LEDs are turned off and no leader is selected around time step 20. In such a case, it can be observed that another negotiation process, of much shorter duration, is initiated with less contestants. Finally, as a result of the second competition, a unique leader is identified and a stable behavior is settled until the simulation ends. The results can be observed in Figure 5 from another perspective, using a different simulation trial. The figure illustrates different frames of a simulation of this experiment. The red balls represent robots whose LED is turned on and the blue balls show agents with deactivated LED. Only instants previous to time step 20 are shown. After this time instant, leader is settled and stable. The last resource to observe the behavior of robots within this task is provided as a video recoding the simulation ([[https://youtu.be/ahBIVf9](https://youtu.be/ahBIVf9) jAbw]([https://youtu.be/ahBIVf9](https://youtu.be/ahBIVf9) jAbw)  
Figure 4: LED actions of the robots in a swarm of size 20 as time elapses in the leader selection experiment. Horizontal black bars denote that the LED is activated. Two phases, namely, negotiation and leader settlement, are observed. **Scalability**: The scalability of the solution is assessed by simulating the experiment with different swarm sizes. Moreover, instead of depicting the results for a single trial, as in the performance evaluation, we collect a total of 50 independent simulations in order to gather a statistically significant number of observations. Figure 6 shows the impact of the swarm size on the leader selection experiment. For each of the 50 episodes, the percentage of the total simulation time in which just a single robot claims leadership is computed and represented in boxplots.