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The Particle Swarm Optimization Algorithm. Nebojša Trpković [email protected] 10 th Dec 2010. Problem Definition. optimization of continuous nonlinear functions ↓ finding the best solution in problem space. Example. Importance. function optimization artificial neural network training

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The particle swarm optimization algorithm

The Particle Swarm Optimization Algorithm

Nebojša Trpković

[email protected]

10th Dec 2010


Problem definition
Problem Definition

optimization of continuous nonlinear functions

finding the best solution in problem space

Nebojša Trpković [email protected]


Example
Example

Nebojša Trpković [email protected]


Importance
Importance

  • function optimization

  • artificial neural network training

  • fuzzy system control

Nebojša Trpković [email protected]


Existing solutions
Existing Solutions

  • Ant Colony (ACO)

    • discrete

  • Genetic Algorithms (GA)

    • slow convergence

Nebojša Trpković [email protected]


Particle swarm optimization
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 [email protected]


Particle swarm optimization1
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)

Nebojša Trpković [email protected]


Particle swarm optimization2
Particle Swarm Optimization

Benefits:

  • faster convergence

  • less parameters to tune

  • easier searching in very large problem spaces

Nebojša Trpković [email protected]


Particle swarm optimization3
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

Nebojša Trpković [email protected]


Velocity change
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 cognitive social

Nebojša Trpković [email protected]


Position change
Position Change

xi – specific particle

vi – particle’s velocity

xi ← xi + vi

Nebojša Trpković [email protected]


Algorithm
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 [email protected]


Single particle
Single Particle

Nebojša Trpković [email protected]


Parameters selection
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

Nebojša Trpković [email protected]


Avoiding local optimums
Avoiding Local Optimums

  • adding randomization factor to velocity calculation

  • adding random momentum in a specific iterations

Nebojša Trpković [email protected]


Swarm
Swarm

Nebojša Trpković [email protected]


Conclusion
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

Nebojša Trpković [email protected]


References
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

Nebojša Trpković [email protected]


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