A presentation by Rajorshi Mukherjee

CSE 4th Year

Academic Batch : 2011-2015

Introduction

Details

Algorithm

Flowchart

Real Life applications

Conclusion

Bibliography

Contents

Particle Swarm Optimization (P.S.O.) also known as

Swarm Intelligence is an algorithm developed by James Kennedy and Russell Eberhart.

It is a robust stochastic optimization technique based on the movement and intelligence of swarms. PSO applies the concept of social interaction for problem solving.

Introduction

There are a number of particles in this algorithm

which move around in space to search for the best or optimum value. These particles are provided with initial velocities and certain constants and values at the beginning.

Each particle of the system has a certain velocity and learning constants. It then moves in the space, randomly and then adjusts according to the experience collected from other particles.

Introduction contd..

Each particle is swarming for the optimum.

Each particle is moving and hence has a velocity.

Each particle remembers the position it was in where it had best results so far (its personal best).

But this would not be enough, particles would need help in figuring out where to search.

Introductioncontd…

The main motivation of this form of algorithm came

from real life examples.

Swarming is a natural phenomenon.

Swarming helps to get work done better.

Details

In real life we take the example of birds as observed

by Craig Reynolds and proposed in 1995.

He observed three main properties that the birds behaved.

Separation – Each bird is an individual particle and do not collide with other birds.

Alignment – They move in the same general direction.

Cohesion – They do not move away from the flock and try to stick together.

Details contd…

In this method each particle in space keeps track of

their position, and also of their neighbors. This knowledge is used further to know a better position (optimization of solution), this method combines self-experiences and social experiences.

In every iteration each particle keeps track of their personal best attempt, known as pbest.

Details contd…

In every iteration each particle also keeps track of

their neighboring best and global best performance in finding the optimum solution. This is known as gbest.

The main concept of PSO lies in the essence that each particle in the space is accelerated towards the pbestand gbest locations with a random weighted acceleration in each iteration.

Details contd…

Each particle adjusts its travelling speed dynamically

corresponding to the flying experiences of itself and its colleagues.

Each particle modifies its position according to :

Its current position

Its current velocity

The distance between its current position and pbest.

The distance between its current position and gbest.

Details contd…

The PSO algorithm may be written in pseudo code as

follows.

Algorithm Parameters

A: Population of events.

pi: position of agent ai in solution space.

f: Objective function.

vi: Velocity of agents ai.

V(ai) : Neighborhood of agent ai (fixed)

Algorithm

[x*] = PSO()

p=Particle_Initialization();

For i=1 to it_max

For each particle p in P do

fp=f(p);

if fp beter than f(pbest)

pbest = p;

end

end Continued on Next Slide

Algorithm contd…

gbest = best p in P;

For each particle p in P do

vi = vi + c1*rand()*(pbest - p) + c2*rand()*(gbest - p);

p=p+v;

end

end algorithm

Algorithm contd…

Particle update rule

p=p+v

with

v=v+c1*rand()*(pbest-p)+c2*rand()(gbest-p)

where

p: particle position

v: path direction

c1: cognitive learning constant

c2: social learning constant (Continued on Next Slide)

Algorithm contd…

pbest: best position of the particle.

gbest: best position of the swarm

rand: a random variable

Algorithm contd…

Here c1 is the cognitive learning rate and its value

determines the importance of how much necessary it is to learn from own experience.

C2 is the social learning constant. This parameter is places the importance of learning through experience of others.

Vi is the velocity of a particle of the swarm, this value is very important, too high a value will make the system unstable. Too low a value will make the algorithm very slow.

Algorithm contd…

1. First we create a population of agents or particles to

make a swarm, uniformly distributed over a space X.

2. Evaluate the position of each particle according to objective function.

3. If a particle’s current position is better than its initial position, then update it.

4. Determine best particle (according to particle’s previous best position)

Algorithm contd…

5. Update particles position

6. Move particles to new positions.

7. Goto step 2 until stopping criteria are met.

Algorithm contd…

Flowchart of PSO

Nature is the best teacher.

Ant colonies thrive due to this phenomenon.

Birds also use swarm intelligence to survive.

Fishes also exhibit this kind of behavior.

PSO is used in computer science to optimize certain functions.

Real Life applications

These are some functions used for optimization.

Real Life applications contd…

Griewank RastriginRosenbrock

In all we can use particle swarm optimization for

finding optimum solutions to problems.

Constraints to be kept in mind are that velocity should have and optimum value, as too less will be too slow, and if the velocity is too high then the method will become unstable.

Conclusion

A presentation on Swarm Intelligence – from Natural

to Artificial Systems. - Ukradnuté kde sa dalo, a adaptované

A presentation on PSO by Maurice Clerk.

The Particle Swarm Optimization Algorithm by Andry Pinto, Hugo Alves, Inês Domingues, LuísRocha, Susana Cruz

Bibliography