PSO Algorithm

A concept for the optimization of nonlinear functions using particle swarm methodology.
Particle swarm optimization is based on artificial life (A-life) and to bird flocking, fish schooling, and swarming theory. It is also related to evolutionary computation, and has ties to both genetic algorithms and evolutionary programming.
The changes to a particle within the swarm are therefore influenced by the experience, or knowledge, of its neighbors. The search behavior of a particle is thus affected by that of other particles within the swarm (PSO is therefore a kind of symbiotic cooperative algorithm).
Particle behavior: to emulate the success of neighboring individuals and their own successes. In simple terms, the particles are “flown” through a multidimensional search space, where the position of each particle is adjusted according to its own experience and that of its neighbors. The position of the particle is changed by adding a velocity to the current position

Global Best PSO

Smaller neighborhoods are defined for each particle
The social component reflects information exchanged within the neighborhood of the particle, reflecting local knowledge of the environment
The velocity equation, the social contribution to particle velocity is proportional to the distance between a particle and the best position found by the neighborhood of particles.

It is important to note that for the basic PSO, particles within a neighborhood have no relationship to each other. Selection of neighborhoods is done based on particle indices.