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Particle swarm optimization (PSO) is a form of swarm intelligence. Imagine a swarm of insects or a school of fish. If one sees a desirable path to go (ie for food, protection, etc.) the rest of the swarm will be able to follow quickly even if they are on the opposite side of the swarm.

This is modeled by particles in multidimensional space that have a position and a velocity. These particles are flying through hyperspace and remember the best position that they have seen. Members of a swarm communicate good positions to each other and adjust their own position and velocity based on these good positions. There are two main ways this communication is done:

  • a swarm best that is known to all
  • local bests are known in neighborhoods of particles
Updating the position and velocity is done through the following formulas at each iteration:
  • x \leftarrow x + v
  • v \leftarrow wv + c_1 r_1 (\hat{x}-x) + c_2 r_2 (\hat{x}_g-x)
    • w is the inertial constant. Good values are usually slightly less than 1.
    • c_1 and c_2 are constants that say how much the particle is directed towards good positions. Good values are usually right around 1.
    • r_1 and r_2 are random values in the range 1.
    • \hat{x} is the best the particle has seen.
    • \hat{x}_g is the global best seen by the swarm. This can be replaced by \hat{x}_l, the local best, if neighborhoods are being used.

Algorithm

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Started a new project today. A Scheme particle swarm optimizer: http://is.gd/5jafg
acfoltzer (Adam Foltzer) Fri, 11 Dec 2009 06:18:50 -0000
Started a new project today. A Scheme particle swarm optimizer: http://is.gd/5jafg
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Inderscience news: Special issue: New trends in particle swarm ...: News from Inderscience Publishers: publishe.. http://bit.ly/5Kmm1Z
Special issue: New trends in particle swarm optimisation: http://url4.eu/uUXJ
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Special issue: New trends in particle swarm optimisation: http://url4.eu/uUXJ

 
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AdaptiveView Computational Intelligence Resources - Contains links to computational intelligence (CI) resources and to an open source Java implementation of Particle Swarm Optimization (PSO).
Meta Description: [ This page contains links to other sites related to PSO, the adaptive modeling of dynamic/complex subsystems (ADM), Computational Intelligence, and Java. We may also make Java source code and alpha versions of our products available here. ]

All about Particle Swarm Optimization - An website about particle swarm optimization and swarm intelligence, including introduction, bibliography, tutorials, links to online papers
Meta Description: [ PSO is a new swarm intelligence technique, inspired by social behavior of bird flocking or fish schooling. ]

Bibliography of Particle swarm optimization - One of the most comprehensive reference lists
Meta Description: [ PSO is a new swarm intelligence technique, inspired by social behavior of bird flocking or fish schooling. ]

Computelligence - computational intelligence virtual world - A virtual world of Computational Intelligence (CI), which provides a platform for CI researchers to exchange information, a warehouse for CI researchers to share resources.

Darwinian Particle Swarm Optimization - An adaptation of the Particle Swarm Optimization algorithm.

EVALife's BBase - A literature search engine on Evolutionary Computation and related topics. This search-engine contains more than 19400 references on Evolutionary Computation and related topics.
Meta Description: [ BBase, is, currently, being, moved, to, a, different, server., Thank, you, ... ]

Particle Swarm Central - Mainly information and links to information about Particle Swarm Optimization.
Meta Description: [ particle swarm optimization ]

Particle Swarm Optimization Resources - Mathematical analysis of Particle Swarm Optimization. Discrete, fuzzy PSO.
Meta Description: [ optimisation par essaim particulaire ]

Particle Swarm Optimization Visualization - A simple Java applet which visually demonstrates a particle swarm searching for a maximum value in a 3-D landscape.

Swarm Intelligence - A new book talking about particle swarm optimization by J. Kennedy, R.C. Eberhart, and Y. Shi.

The PSO Toolbox : Home page - The PSO TOOLBOX is an open source toolbox available as Matlab (.m) files and Java (.class and .java) classes.

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