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Nebojša Trpković [email protected] Slide 2 of 18
Problem Definition
optimization of continuous nonlinear functions
↓
finding the best solution in problem space
Nebojša Trpković [email protected] Slide 4 of 18
Importance
• function optimization
• artificial neural network training
• fuzzy system control
Nebojša Trpković [email protected] Slide 5 of 18
Existing Solutions
• Ant Colony (ACO)– discrete
• Genetic Algorithms (GA)– slow convergence
Nebojša Trpković [email protected] Slide 6 of 18
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] Slide 7 of 18
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] Slide 8 of 18
Particle Swarm Optimization
Benefits:
• faster convergence• less parameters to tune
↓• easier searching in very large problem spaces
Nebojša Trpković [email protected] Slide 9 of 18
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] Slide 10 of 18
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
Nebojša Trpković [email protected] Slide 11 of 18
Position Change
xi – specific particle
vi – particle’s velocity
xi ← xi + vi
Nebojša Trpković [email protected] Slide 12 of 18
AlgorithmFor each particle Initialize particleEND
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] Slide 14 of 18
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] Slide 15 of 18
Avoiding Local Optimums
• adding randomization factor to velocity calculation
• adding random momentum in a specific iterations
Nebojša Trpković [email protected] Slide 17 of 18
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] Slide 18 of 18
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
