Self-adaptive potential-based stopping criteria for Particle Swarm Optimization with forced moves

We study the variant of Particle Swarm Optimization 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 small 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 candidate solutions than the already-found best solution. 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 candidate solutions can be found much faster than setting upper bounds on the iterations and better solutions compared to applying other solutions from the literature.