How to judge the searching precision of Particle Swarm Optimization? As the title mentioned, how can I judge the searching precision of PSO? Is this depending on the velocity of the particles? I would like to give an example to clarify my question: For a 2-D searching, the precision of grid ergodic searching is the searching step. But what the precision should be using PSO searching. From the position update formula of PSO:

$x_i \leftarrow x_i+v_i$

So, we can assume the precision of PSO searching is the maximum of velocity of particles? Is this right?
Generally, we set the maximum of particle velocity is about 10% to 20% of the position scale. But with this setting, we can still obtain a good precision with PSO, which contradicts previous assumption. So the searching precision of PSO is? Or it can be expressed as a function of maximum velocity and other parameters?

It seems that PSO can realize arbitrary precision... Because if there are sufficient particle numbers and iteration times, the PSO can approach to the actual solution.
If by "precision" you mean the error in the result of PSO (i.e., the difference between the value that PSO outputs and the true global optimum), the error can be arbitrarily large.  PSO is a heuristic.  There are no guarantees that it finds the global optimum, or even that it gets close -- and there is no formula in terms of parameters (like velocity) for how large the error will be.  The error depends on the optimization problem you're solving and on the shape of the loss surface.