Analysis of behaviours in swarm systems

Abstract

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.