# 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.

• Welcome to CS.SE! Can you define what you mean by "searching precision"? When you ask what the precision should be, what are you referring to? The precision of what? What do you mean by precision in this context? Can you edit your question to make these points clearer? – D.W. Mar 11 at 17:02
• Cross-posted: mathoverflow.net/q/325109/37212, stackoverflow.com/q/55090656/781723, cs.stackexchange.com/q/105431/755. Please do not post the same question on multiple sites. Each community should have an honest shot at answering without anybody's time being wasted. – D.W. Mar 11 at 17:04
• I think I already presented clearly. The precision here is the difference between the result obtained with PSO and the true value. I dont know if there is other precision in PSO.... – Land Mar 12 at 9:38