i'am trying to find mathematical example for "particla swarm optimization" to understand how it works<in difficult wway i found a question ,don't know how to answer.
the question is
"while optimizing a 2-D problem, given a swarm of three particles located at locations (0,0), (1,1) and (0.5, 0.5). Assume that all random values needed are equal to 0.6. Fitness function f(x,y) = x - 2^y, c1 = c2 = 2, w = 0. Show the particles velocities and locations in the next iteration following the classical PSO equations. Also show the global best and local best locations as well as their fitness before and after the iteration."