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We compared, for the clustering process, a probabilistic with a deterministic pick-
up rule. Our CA naturally produced a single cluster which was loosely bound,
resp. compact, in the deterministic, resp. probabilistic case. A comparison of
the density of both largest clusters provided a quantitative measurement of this
fact. Compactness results from the pick-up rule being biased towards depleting
sparse clusters. The underlying process in the deterministic case is just to take a
corpse from one cluster and drop it into another at a rate specified by the ants'
random walk. This rate is improved with probabilistic pick-up. Our pick-up rule
differs from Deneubourg's as it is based on the ants' spatial perception of their
environment rather than on their memory. However, our deposition rule relies
in a certain sense on a very simple memory. In the presence of different types
of corpses, our algorithm sorted the corpses into distinct clusters, one per type.
For probabilistic pick-up, we then considered the dynamics of clustering from a
more analytical point of view. We observed that the number of clusters follows a
power-law with exponent greater than that of the underlying diffusion process,
while the largest cluster density converges exponentially to the maximum value.
It appears that the curves for the number of clusters and the density exhibit
a universal behavior as regards the number
M
of ants. Indeed, rescaling time
by a factor
M
yields the same results. This hints strongly towards asserting
that our clustering process does not stem from some kind of swarm intelligence.
Nevertheless, these results were to be expected, since the ants in our model
have no added-in intelligence. However, it was not completely obvious that some
ants would not undo the job done by others. The important fact is to identify
clearly what level of intelligence produces what result. From that point of view,
our model is a base model over which one could add one or many layers of
intelligence and observe the outcome. Indeed, it would be interesting to exhibit
some kind of intelligence hierarchy.
Concerning performance, the CPU-time of an iteration depends little on
M
.
Thus, it is more advantageous to use more ants. However, there is an optimal
M
,
depending on the other fixed parameters, which produces the best performances.
Furthermore, a CA is naturally parallelizable. Hence, we ran our simulations on
a farm of PCs and thus benefited from a speedup.
We conclude by mentioning some directions for future work. The present pa-
per does not include a systematic study of the probabilistic pick-up parameters
in relation to the clustering process. The influence of the neighborhood on these
probabilities is also of interest. Our CA model does not include a termination
criterion. This should imply some kind of learning, which would allow the ants
to adapt their pick-up probability during the simulation. To add in more in-
telligence, we could also endow our ants with a memory or have them deposit
pheromones along their trail. Hence, the ants would react to their environment
on a larger scale. The idea of combining spatial and temporal perception of the
environment, as is sketched in this work, also seems interesting. Finally, the main
purpose still remains to unearth collaborative effects between artificial ants.
