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The Particle Swarm Optimization Algorithm

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The Particle Swarm Optimization Algorithm

Nebojša Trpković

trx.lists@gmail.com

10th Dec 2010

optimization of continuous nonlinear functions

↓

finding the best solution in problem space

Nebojša Trpković trx.lists@gmail.com

Nebojša Trpković trx.lists@gmail.com

- function optimization
- artificial neural network training
- fuzzy system control

Nebojša Trpković trx.lists@gmail.com

- Ant Colony (ACO)
- discrete

- Genetic Algorithms (GA)
- slow convergence

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Very simple classification:

- a computational method
- that optimizes a problem
- by iteratively trying to improve a candidate solution
- with regard to a given measure of quality

Nebojša Trpković trx.lists@gmail.com

Facts:

- developed by Russell C. Eberhart and James Kennedy in 1995
- inspired by social behavior of bird flocking or fish schooling
- similar to evolutionary techniques such as Genetic Algorithms (GA)

Nebojša Trpković trx.lists@gmail.com

Benefits:

- faster convergence
- less parameters to tune
↓

- easier searching in very large problem spaces

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Basic principle:

let particle swarm move

towards the best position in search space, remembering each particle’s best known position

and global (swarm’s) best known position

Nebojša Trpković trx.lists@gmail.com

xi – specific particle

pi – particle’s (personal) best known position

g – swarm’s (global) best known position

vi – particle’s velocity

vi ← ωvi + φprp(pi - xi) + φgrg(g - xi)

inertia cognitive social

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xi – specific particle

vi – particle’s velocity

xi ← xi + vi

Nebojša Trpković trx.lists@gmail.com

For each particle

Initialize particle

END

Do

For each particle

Calculate fitness value

If the fitness value is better than the best personal fitness value in history, set current value as a new best personal fitness value

End

Choose the particle with the best fitness value of all the particles, and if that fitness value is better then current global best, set as a global best fitness value

For each particle

Calculate particle velocity according velocity change equation

Update particle position according position change equation

End

While maximum iterations or minimum error criteria is not attained

Nebojša Trpković trx.lists@gmail.com

Nebojša Trpković trx.lists@gmail.com

Different ways to choose parameters:

- proper balance between exploration and exploitation
(avoiding premature convergence to a local optimum yet still ensuring a good rate of convergence to the optimum)

- putting all attention on exploitation
(making possible searches in a vast problem spaces)

- automatization by meta-optimization

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- adding randomization factor to velocity calculation
- adding random momentum in a specific iterations

Nebojša Trpković trx.lists@gmail.com

Nebojša Trpković trx.lists@gmail.com

“This algorithm belongs ideologically to that philosophical school

that allows wisdom to emerge rather than trying to impose it,

that emulates nature rather than trying to control it,

and that seeks to make things simpler rather than more complex.”

James Kennedy, Russell Eberhart

Nebojša Trpković trx.lists@gmail.com

- Wikipedia
http://www.wikipedia.org/

- Swarm Intelligence
http://www.swarmintelligence.org/

- Application of a particle swarm optimization algorithm for determining optimum well location and type, Jerome Onwunalu and Louis J. Durlofsky, 2009
- Particle Swarm Optimization, James Kennedy and Russell Eberhart, 1995
http://www.engr.iupui.edu/~shi/Coference/psopap4.html

- Robot Swarm driven by Particle Swarm Optimization algorithm, thinkfluid
http://www.youtube.com/watch?v=RLIA1EKfSys

Nebojša Trpković trx.lists@gmail.com