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^ Zhang, Wen-Jun; Xie, Xiao-Feng (2003). A. (2016). (2011). It solves a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity.

for each particle i = 1, ., S do Initialize the particle's position with a uniformly distributed random vector: xi U(blo, bup) Initialize the particle's best known position to its initial position: pi xi if f(pi) < f(g) then update the swarm's best known position: g pi Initialize the particle's velocity: vi U(-bup-blo, bup-blo) while a termination criterion is not met do: for each particle i = 1, ., S do for each dimension d = 1, ., n do Pick random numbers: rp, rg U(0,1) Update the particle's velocity: vi,d vi,d p rp (pi,d-xi,d) g rg (gd-xi,d) Update the particle's position: xi xi vi if f(xi) < f(pi) then Update the particle's best known position: pi xi if f(pi) < f(g) then Update the swarm's best known position: g pi . pp.603607. Algorithm. Another school of thought is that PSO should be simplified as much as possible without impairing its performance; a general concept often referred to as Occam's razor. doi:10.1109/TEVC.2004.831258. Simulation of PSO convergence in a two-dimensional space (Matlab). doi:10.1007/978-3-319-44427-77. (2006). (2007).

"Corrections to "A Robust Stochastic Genetic Algorithm (StGA) for Global Numerical Optimization". However, metaheuristics such as PSO do not guarantee an optimal solution is ever found. 241-248 ^ Spears, W. One approach is to modify the algorithm so that it is not any more sensitive to the system of coordinates. Note that some of these methods have a higher computational complexity (are in O(n^2) where n is the number of dimensions) that make the algorithm very slow for large scale optimization.. doi:10.1016/S0020-0190(02)00447-7. Each particle's movement is influenced by its local best known position, but is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. 4bc16de163