  We study the variant of Particle Swarm Optimization (PSO) that applies random
velocities in a dimension instead of the regular velocity update equations as
soon as the so-called potential of the swarm falls below a certain bound in
this dimension, arbitrarily set by the user. In this case, the swarm performs a
forced move. In this paper, we are interested in how, by counting the forced
moves, the swarm can decide for itself to stop its movement because it is
improbable to find better solution candidates as it already has found. We
formally prove that when the swarm is close to a (local) optimum, it behaves
like a blind-searching cloud, and that the frequency of forced moves exceeds a
certain, objective function-independent value. Based on this observation, we
define stopping criteria and evaluate them experimentally showing that good
solution candidates can be found much faster than applying other criteria.

Neural and Evolutionary Computing