Particle Swarm Optimization is an algorithm inspired by swarm behavior in nature that was invented by James Kennedy and Russell Eberhart. It is used to find the minimum value of a function by tracking the global best solution and each particle's self best solution. The algorithm works by initializing a random set of solution vectors and updating their positions based on their own experience and the experience of neighboring particles, getting closer to the optimal solution over many iterations similar to the way a flock moves together toward food sources.

1. Introduction to Particles
Swarm Optimization
Presented By Mat S

2. Particle Swarm Optimization
Inventors: 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)

3. 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

4. Particle Swarm Optimization

5. Particle Swarm Optimization
Vi pbest and Vik

6. Particle Swarm Optimization

7. Overview of PSO
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8. Example
Find minimum value in the function:
(x - 15)^2 + (y - 20)^2 = 0
Answer:
x = 15 and y = 20
Now.. Please find minimum value using PSO!

9. Example
1st iterations
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10. Example
Iteration X Y (X-15)^2+(Y-20)^2 Gbest
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2 10 14.9721 50.27981356 25
3 10 23.77597 39.25795364 15.7092

11. Example
0 0 0.7403 1 0 2 0.7404 10 10 2 0.7404 10 10
0 0 0.2934 1 0 2 0.2934 10 10 2 0.2934 10 10
For X

12. Example
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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13. Example
2nd iterations
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14. Example
7th Iterations
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15. Example
30th Iterations
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16. Particle Swarm Optimization
What is P best ?
What is G best ?
Look at the datapbestngbest.xls

17. Demo
Thank You