Fitness curves of unsuccessful evolutionary runs

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(c)	(d)
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Figure 1: Graphs showing the fitness of the best groups at each generation of the six unsuccessful evolutionary runs: (a) run5; (b) run6; (c) run7; (d) run8; (e) run9; (f) run10;

Table 1 - results of post-evalution tests

Table 1: Results of post-evaluation tests P showing for all best evolved groups of each run and for each environment the percentage of trials: i) terminated successfully, see column S; ii) in which the agents failed since one or both of them touched the current wrong arms of the revolving door, see column W1; iii) in which the agents failed since one or both of them collided with the arena walls, see column W2; iv) in which the agents failed for reasons other than those mentioned at ii) and iii), see column W3.

Movies of successful group g₂

To download the movie of successful strategy group g₂ right click here, to view it directly on the browser click on the picture below. Figure 2 refers to data recorded during the performance shown in the movie.

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(b)
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Figure 2: Data recorded during post-ealuations of group g2 in the four-trials sequence shown in the movie. Dashed lines and continuous lines refer to the agent placed, at the beginning of the first trial, on the left and on the right arena side respectively. (a) Sound signals emitted by both agents in the intervals S1, S2, and S3. (b) Sound signals emitted by both agents during the whole evaluation. (c) Categorisation outputs emitted by both agents during the whole evaluation. (d) Readings of the floor sensors of both agents during the whole evaluation. On the x axis in (b), (c), and (d) it is shown the time of start and end of each trial.

Table of Contents

Why g₃ and g₄ fail?

Table 2: Results of post-evaluation tests P showing the first, the second (median), and the third quartile (i.e., Q1, Q2, and Q3) of the categorisation outputs emitted by each agent of group g1, g2, g3, and g4, in each environment during the approaching phase (i.e., from the beginning of the second phase of the task to the time of the agent's first collision with the revolving door). For each environment, the descriptive statistics refer to (i) data gathered in successful trials (columns S), if the group success rate turned out to be higher than 80% in that environment; (ii) data gathered in trials in which agents committed W1 error (columns W1), if the group W1 error rate turned out to be higher than 80% in that environment.

Contrary to what observed in successful groups, group g₃ is preferentially in a sound-state. The emission of sound is temporarily stopped by the perception of black ground. When located in E¹¹, both agents stop emitting long enough for the group to switch from the sound-state to the no-sound-state while approaching the revolving door. Consequently, both agents push the revolving door on the correct arms. When located in E⁰¹ and in E¹⁰, the agent that experiences grey never stops emitting sound. The group remains in a sound-state, and both agents push the revolving door on the correct arms. When located in E⁰⁰, the group fails since it lacks the conditions to switch from the sound-state to the no-sound-state. Group g₄ behaves in a very similar way to what observed in successful groups. However, contrary to successful groups, agents of group g₄ do not have any means to switch from sound-state to a no-sound-state states when located in E¹¹. Therefore, anytime both agents experience black ground, the group is unsuccessful. Further data, obtained from tests P, confirmed that the only difference between successful and unsuccessful groups is a sound signalling failure that systematically stops unsuccessful groups from developping the appropriate pushing strategy when located in one specific environment. We recorded the categorisation outputs emitted by each agent of each selected group, in each environment during the approaching phase (i.e., from the beginning of the second phase of the task to the time of the agent's first collision with the revolving door), and we computed first, second (median), and third quartile for each data set. In Table 2, for each environment, the descriptive statistics refer to either data gathered in successful trials (see Table 2, columns S), if the group success rate turned out to be higher than 80% in that environment, or to data gathered in trials in which agents committed W¹ error (see Table 2, columns W¹), if the group W¹ error rate turned out to be higher than 80% in that environment. As expected, in successful groups g₁ and g₂, for three quarter of the approaching phase in E⁰¹ and in E¹⁰, the categorisation outputs of both agents remain set to the signal upper bound, whereas, for three quarter of the approaching phase in E⁰⁰ and in E¹¹, the categorisation outputs of both agents remain set to the signal lower bound. This means, that agents of groups g₁ and g₂ are able to distinguish and correctly categorise E⁰¹ and E¹⁰ from E⁰⁰ and in E¹¹, by differentiating, during the approaching phase, the categorisation outputs associated to each type of environment. Contrary to what observed in groups g₁ and g₂, in unsuccessful groups g₃ and g₄, the statistics concerning the environments in which the groups fail mostly due to W¹ error (i.e., E⁰⁰ for g₃, and E¹¹ for g₄, see Table 2) do not differ from the statistics concerning the environments that require different pushing strategy and in which the groups have a high success rate (i.e., E⁰¹ and E¹⁰ for both groups, see Table 2). This means that, for what concerns the categorisation output, agents of groups g₃ and g₄ mistake E⁰⁰ and E¹¹ respectively, for an E^anti type of environment. However, the causal relationships between categorisation output and pushing strategies in unsuccesful groups are identical to those illustrated for successful groups. Therefore, while approaching the revolving door in E⁰⁰ for group g₃, and in E¹¹ for group g₄, the agents keep the central light on their left since their categorisation outputs are errouneously set to the upper bound. Consequenlty, in these environments, the agents systematically end up collising with the current wrong arms of the revolving door. Given that further analyses of the behavioural strategies proved that agents of groups g₃ and g₃ vary their categorisation output in response to sound, it follows that the maladapted use of categorisation output mentioned above is caused by acoustic interactions that are not sufficient to unambigously and correctly classified all the environments.

Memory test (group g₂)

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Figure 3: Graphs showing the results of seven tests P on group g2 with sound interference. (a) Depiction of the post-evaluation scenario; (b) percentage of success at each test; (b) percentage of W1 error at each test; (c) percentage of W3 error at each test. In all the graphs, white bars refer to E10, light grey bars to E01, dark grey bars to E00, and black bars to E11.

Further post-evaluations tests on group g₂ in which we deliberatly add/remove sound at given intervals while the agents are approaching the revolving door, show that the agents are extremely sensitive to these kind of variations. In particular, we run seventh times tests P each time changing the status of sound while the agents are navigating in the areas shown in Figure 3a. For example, during the 1^st test P, we change the status of sound for the time it takes to the agents to traverse the corresponding area indicated as 1^st zone in Figure 3a. For all the tests, the nature of the change is such that, for trials in E⁰¹ and in E¹⁰, the agents do not perceive sound even if one of them is emitting; for trials in E⁰⁰ and in E¹¹, the agents perceive sound even if none of them is emitting. The results clearly show that in all the tests, the disruptions make the percentage of success drop below 30% (see Figure 3b). The agents commit in all the tests mostly W¹ error (see Figure 3c). That is, even a slight interference on sound far away from the revolving door (e.g., like in the 1^st test, see Figure 3a 1^st zone) makes the agents swap pushing strategy. That is, if sound is played while no agents is emitting (i.e., during trials in E⁰⁰ and in E¹¹), the agents often enter into a no-sound-state and they erroneously push the revolving door in a anticlockwise direction. If the agents are made deaf while one of them is emitting (i.e., during trials in E¹⁰ and in E⁰¹), the agents often enter into a sound-state and they erroneously push the revolving door in a clockwise direction. If the experimenter-induced perception of or deafness to sound appears when the agents are close to the revolving door (e.g., like in the 7^th test, see Figure 3a 7^th zone) than the frequency of W³ error increases. What happens is that the agents can not excert enough forces to completely rotate the revolving door. In this circumstance, W³ error is less frequent when the disruption concerns trials in E⁰⁰ and E¹¹ than when it concerns trials in E¹⁰ and E⁰¹. This analysis has been conducted also on successful group g₁, and it produced very similar results. Thus, we conclude that both successful groups are very sensitive to even small interferences with the agents' signalling system. This suggests that the significance of signalling behaviour is not limited to the time during which the agents are on the coloured zones. That is, to bring fourth their successful strategy, the agents need a certain continuity in signalling behaviour during the time it takes them to move from the coloured zone up to the revolving door. In a way, sound and the absence of sound are two environmentally induced circumstances which remind the agents what to do while aproaching the revolving door.

Evolutionary graphs concerning g₁

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Figure 4: Graphs showing various performance measures, of the best groups from generation 650 to 800, of run1. (a) Final fitness of the best groups at each generation, as observed during evolution. (b) and (c) show data gathered by post-evaluating the above mentioned best groups with test P illustrated at the beginning of Section Results of the paper. In particular the graphs refer to: (b) the percentage of success in each environment; (c) the proportion of time with sound in the arena during the approaching phase (dashed lines), and the average categorisation output during the approaching phase (continuous lines), in each environment.

These graphs show the same phenomena described in in Section 4.1 An Evolutionary analysis of the paper. Also in run₁, the distinctive different strategy with respect to signalling and setting the categorisation output that is associated to environment E⁰⁰, and characterises generation 800 agents but not generation 650 agents, when it appeared it produced groups that on average were more adapted than those that did not showed any strategy differentiation (see Figure 4c). This strategy differentiation is determined by the emergence of mechanisms that regulate the sound and categorisation output in response to environmental stimuli.

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