1. PSO -Introduction Proposed by James Kennedy & Russell Eberhart in 1995
Inspired by social behavior of birds and fishes
Combines self-experience with social experience
Population-based optimization

2. PSO -Introduction
Finds global optimum with a probability of almost one
Suitable for optimizing non-linear non-differentiable and discontinuous functions –Irrespective of shapes of the objective function.
A robust search technique.
Suitable for solving large-sized problems.
Steps extremely simple
-Velocity calculation
- Position updation

3. PSO Concept
Uses a number of particles that constitute a swarm moving around in the search space looking for the best solution.
Each particle in search space adjusts its “flying” according to its own flying experience as well as the flying experience of other particles

4. PSO –how its works
Emulates the behavior of creatures such as a flock of birds or a school of fish.
Basic principle:
Let particle swarm move towards the best position in search space.
Remembering each particle’s best known position (Pbest) and global (swarm’s) best known position (gbest)

5. PSO –how its works Swarm: a set of particles (S)
Particle: a potential solution
Position:
Velocity:
Each particle maintains
Individual best position (PBest)
Swarm maintains its global best (GBest) S
Fitness value
Fitness function

6. Basic algorithm of PSO Initialize the swarm form the solution space
Evaluate the fitness of each particle
Update individual and global bests
Update velocity and position of each particle
Go to step2, and repeat until termination condition

7. PSO Flow Chart

8. PSO-Steps

9. Velocity and Position Updating
Original velocity update equation
w,c1,c2: Constant
random1(), random2(): random variable
Position update 9

10. Velocity and Position Updating

11. Particle’s velocity social cognitive Inertia PBest x(k) x(k+1) v(k+1)

12. Updating the Velocity of a Particle

13. PSO Algorithm

14. Tuning of Parameters for PSO

15. PSO solution update in 2D
GBest
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)
PBest

16. PSO solution update in 2D
Inertia: v(k)=(-2, 2)
GBest
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)
Current solution (4, 2)
Particle’s best solution (9, 1)
Global best solution (5, 10)
PBest

17. PSO solution update in 2D
Inertia: v(k)=(-2,2)
Cognitive:
PBest-x(k)=(9,1)-(4,2)=(5,-1)
Social:
GBest-x(k)=(5,10)-(4,2)=(1,8)
GBest
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)
Current solution (4, 2)
Particle’s best solution (9, 1)
Global best solution (5, 10)
PBest

18. PSO solution update in 2D
GBest
PBest
v(k+1)
Inertia: v(k)=(-2,2)
Cognitive:
PBest-x(k)=(9,1)-(4,2)=(5,-1)
Social:
GBest-x(k)=(5,10)-(4,2)=(1,8)
v(k+1)=(-2,2)+0.8*(5,-1) +0.2*(1,8) = (2.2,2.8)
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)

19. PSO solution update in 2D
GBest
PBest
x(k+1)
Inertia: v(k)=(-2,2)
Cognitive:
PBest-x(k)=(9,1)-(4,2)=(5,-1)
Social:
GBest-x(k)=(5,10)-(4,2)=(1,8)
v(k+1)=(2.2,2.8)
x(k+1)=x(k)+v(k+1)=
(4,2)+(2.2,2.8)=(6.2,4.8)
x(k) - Current solution (4, 2)
PBest - Particle’s best solution (9, 1)
GBest-Global best solution (5, 10)