The Particle Swarm
Optimization Algorithm
Nebojša Trpković
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10th Dec 2010
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
Nebojša Trpković
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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 move
towards 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 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
Nebojša Trpković
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cognitive
social
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Position Change
xi – specific particle
vi – particle’s velocity
xi ← xi + vi
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Algorithm
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
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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 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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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
• 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
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