the particle swarm optimization algorithm

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The Particle Swarm

Optimization Algorithm

Nebojša Trpković trx.lists@gmail.com

10 th Dec 2010

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Problem Definition

optimization of continuous nonlinear functions

↓

finding the best solution in problem space

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Example

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Importance

• function optimization

• artificial neural network training

• fuzzy system control

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Existing Solutions

• Ant Colony (ACO) – discrete

• Genetic Algorithms (GA) – slow convergence

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Particle Swarm Optimization

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

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Particle Swarm Optimization

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)

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Particle Swarm Optimization

Benefits:

• faster convergence

• less parameters to tune

↓

• easier searching in very large problem spaces

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Particle Swarm Optimization

Basic principle:

let particle swarm movetowards the best position in search space,remembering each particle’s best known position

and global (swarm’s) best known position

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Velocity Change

xi – specific particlep i – particle’s (personal) best known position g – swarm’s (global) best known position vi – particle’s velocity

vi ← ω vi + φ prp(p i - xi) + φ grg(g - xi)inertia cognitive social

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Position Change

xi – specific particlevi – particle’s velocity

xi ← xi + vi

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AlgorithmFor each particle

Initialize particleEND

Do

For each particle

Calculate fitness valueIf the fitness value is better than the best personal fitness value in history, set current valueas a new best personal fitness value

End

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

For each particleCalculate particle velocity according velocity change equationUpdate particle position according position change equation

End

While maximum iterations or minimum error criteria is not attained

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Single Particle

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Parameters selection

Different ways to choose parameters:

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

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

• automatization by meta-optimization

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Avoiding Local Optimums

• adding randomization factor to velocity calculation

• adding random momentum in a specific iterations

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Swarm

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Conclusion

“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

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References

• Wikipediahttp://www.wikipedia.org/

• Swarm Intelligencehttp://www.swarmintelligence.org/

• Application of a particle swarm optimization algorithm fordetermining optimum well location and type, Jerome Onwunaluand Louis J. Durlofsky, 2009

• Particle Swarm Optimization, James Kennedy and Russell Eberhart,1995http://www.engr.iupui.edu/~shi/Coference/psopap4.html

• Robot Swarm driven by Particle Swarm Optimizationalgorithm, thinkfluidhttp://www.youtube.com/watch?v=RLIA1EKfSys