In nature animal species often exist in groups. We talk of insect swarms, flocks
of birds, packs of lions, herds of wildebeest etc. These are characterised by
individuals interacting by following their own rules, privy only to local information.
Robotic swarms or simulations can be used explore such interactions. Mathematical
formulations can be constructed that encode similar ideas and allow us to explore the
emergent group behaviours. Some behaviours show characteristics reminiscent of the
phenomena of criticality. A bird flock may show near instantaneous collective shifts
in direction: velocity changes that appear to correlated over distances much larger
individual separations.
Here we examine swarm systems inspired by flocks of birds and the role played by
criticality. The first system, Particle Swarm Optimisation (PSO), is shown to behave
optimally when operating close to criticality. The presence of a critical point in the
algorithm’s operation is shown to derive from the swarm’s properties as a random
dynamical system. Empirical results demonstrate that the optimality lies on or near
this point.
A modified PSO algorithm is presented which uses measures of the swarm’s
diversity as a feedback signal to adjust the behaviour of the swarm. This achieves
a statistically balanced mixture of exploration and exploitation behaviours in the
resultant swarm. The problems of stagnation and parameter tuning often encountered
in PSO are automatically avoided.
The second system, Swarm Chemistry, consists of heterogeneous particles
combined with kinetic update rules. It is known that, depending upon the parametric
configuration, numerous structures visually reminiscent of biological forms are found
in this system. The parameter set discovered here results in a cell-division-like
behaviour (in the sense of prokaryotic fission). Extensions to the swarm system
produces a swarm that shows repeated cell division. As such, this model demonstrates
a behaviour of interest to theories regarding the origin of life