文档介绍：58 IEEE TRANSACTIONS ON PUTATION, VOL. 6, NO. 1, FEBRUARY 2002
The Particle Swarm—Explosion, Stability, and
Convergence in a plex Space
Maurice Clerc and James Kennedy
Abstract—The particle swarm is an algorithm for finding op- A. The Particle Swarm
timal regions plex search spaces through the interaction of
individuals in a population of particles. Even though the algorithm, A population of particles is initialized with random positions
which is based on a metaphor of social interaction, has been shown and velocities and a function is evaluated, using the par-
to perform well, researchers have not adequately explained how ticle’s positional coordinates as input values. Positions and ve-
it works. Further, traditional versions of the algorithm have had locities are adjusted and the function evaluated with the new
some undesirable dynamical properties, notably the particles’ ve- coordinates at each time step. When a particle discovers a pat-
locities needed to be limited in order to control their trajectories.
The present paper analyzes a particle’s trajectory as it moves in tern that is better than any it has found previously, it stores the
discrete time (the algebraic view), then progresses to the view of coordinates in a vector . The difference between (the best
it in continuous time (the analytical view). A five-dimensional de- point found by so far) and the individual’s current position
piction is developed, which describes the pletely. These is stochastically added to the current velocity, causing the tra-
analyses lead to a generalized model of the algorithm, containing jectory to oscillate around that point. Further, each particle is
a set of coefficients to control the system’s convergence tendencies.
Some results of the particle swarm optimizer, implementing modi- defined within the context of a topological -
fications derived from the analysis, suggest methods for altering the prising itself and some other particles in the population