Editing Particle swarm optimization (section)

==== Bare Bones PSO ====
Initialization of velocities may require extra inputs. The Bare Bones PSO variant<ref>{{Cite book|last=Kennedy|first=James|title=Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706) |chapter=Bare bones particle swarms |date=2003|pages=80–87|doi=10.1109/SIS.2003.1202251|isbn=0-7803-7914-4|s2cid=37185749}}</ref> has been proposed in 2003 by James Kennedy, and does not need to use velocity at all.

In this variant of PSO one dispences with the velocity of the particles and instead updates the positions of the particles using the following simple rule,
:<math>
\vec x_i = G\left(\frac{\vec p_i+\vec g}{2},||\vec p_i-\vec g||\right) \,,
</math>
where <math>\vec x_i</math>, <math>\vec p_i</math> are the position and the best position of the particle <math>i</math>; <math>\vec g</math> is the global best position; <math>G(\vec x,\sigma)</math> is the [[normal distribution]] with the mean <math>\vec x</math> and standard deviation <math>\sigma</math>; and where <math>||\dots||</math> signifies the norm of a vector.