In this study, we propose the stop and go particle swarm optimization (PSO) algorithm, a new method to dynamically adapt the PSO population size. Stop and go PSO (SG-PSO) takes advantage of the fact that in practical problems there is a limit to the required accuracy of the optimization result. In SG-PSO, particles are stopped when they have approximately reached the required accuracy. Stopped particles do not consume valuable function evaluations. Still, the information contained in the stopped particles' state is not lost, but rather as the swarm evolves, the particles may become active again, behaving as a memory for the swarm. In addition, as an extension to the SG-PSO algorithm we propose the mixed SG-PSO (MSG-PSO) algorithm. In the MSG-PSO algorithm each particle is given a required accuracy, and through the accuracy settings global search and local search can be balanced. Both SG-PSO and MSG-PSO algorithms are straightforward modifications to the standard PSO algorithm. The SG-PSO algorithm shows strong improvements over the standard PSO algorithm on multimodal benchmark functions from the PSO literature while approximately equivalent results are observed on unimodal benchmark functions. The MSG-PSO algorithm outperforms the standard PSO algorithm on both unimodal and multimodal benchmark functions.