The Particle Swarm Optimization Algorithm Nebojša Trpković trx.lists@gmail.com 10 th Dec 2010.

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The Particle Swarm Optimization Algorithm

Nebojša Trpkovićtrx.lists@gmail.com

10th Dec 2010

Nebojša Trpković trx.lists@gmail.com Slide 2 of 18

Problem Definition

optimization of continuous nonlinear functions

finding the best solution in problem space

Example

Importance

• function optimization

• artificial neural network training

• fuzzy system control

Existing Solutions

• Ant Colony (ACO)– discrete

• Genetic Algorithms (GA)– slow convergence

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

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)

Benefits:

• faster convergence• less parameters to tune

↓• easier searching in very large problem spaces

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

Velocity Change

xi – specific particle

pi – particle’s (personal) best known position

g – swarm’s (global) best known positionvi – particle’s velocity

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

Position Change

xi – specific particle

vi – particle’s velocity

xi ← xi + vi

AlgorithmFor each particle Initialize particleEND

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

Single Particle

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

Avoiding Local Optimums

• adding randomization factor to velocity calculation

• adding random momentum in a specific iterations

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

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, 1995http://www.engr.iupui.edu/~shi/Coference/psopap4.html

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

The Particle Swarm Optimization Algorithm Nebojša Trpković trx.lists@gmail.com 10 th Dec 2010.

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