particles swarm optimization

Introduction to Particles Swarm Optimization

Presented By Mat S

Particle Swarm OptimizationInventors: James Kennedy and Russell Eberhart An Algorithm originally developed to imitate the

motion of a Flock of Birds, or insects Assumes Information Exchange (Social Interactions)

among the search agents Basic Idea: Keep track of

– Global Best (G best)– Self Best (P best)

How does it work? Problem:

Find X which minimizes f(X) Particle Swarm:

– Start: Random set of solution vectors– Experiment: Include randomness in the choice of new states.– Remember: Encode the information about good solutions.– Improvise: Use the ‘experience’ information to

initiate search in a new regions

Particle Swarm Optimization

Particle Swarm Optimization

Vi pbest and Vik

Particle Swarm Optimization

Overview of PSO

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Example

Find minimum value in the function:

(x - 15)^2 + (y - 20)^2 = 0Answer:

x = 15 and y = 20

Now.. Please find minimum value using PSO!

Example

1st iterations

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Example

Iteration X Y (X-15)^2+(Y-20)^2 Gbest1 10 10 125 25

2 10 14.9721 50.27981356 25

3 10 23.77597 39.25795364 15.7092

Example

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0 0 0.2934 1 0 2 0.2934 10 10 2 0.2934 10 10

For X

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4.972 6.464 0.7404 1 6.4637 2 0.7404 10 10 2 0.7404 10 10

8.804 11.445 0.2934 1 11.445 2 0.2934 14.97 14.97 2 0.2934 10 10

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Particle Swarm Optimization

What is P best ?What is G best ?

Look at the datapbestngbest.xls

Demo

Thank You