Implement the Accelerated Particle Swarm Optimization algorithm (APSO).
In this variant of Particle Swarm Optimization (PSO) algorithm one dispenses with the particle's velocity and the particle's best position and instead updates the position of the particle according to the following rule,
xi ← (1-β)xi+βg+αv ,where xi is the particle's position, g is the global best, β~0.1-0.7 and α~0.1-0.5 are the parameters of the algorithm, and v is a random vector given as vk=U(-(b-a)k,(b-a)k) where a and b are the "lower-left" and "upper-right" corners of the search volume and U(c,d) is a uniform distribution from c to d.