Particle Swam CA

8/6/2019 Particle Swam CA

http://slidepdf.com/reader/full/particle-swam-ca 1/29

Particle Swarm optimisation2002-04-

24

Maurice.Clerc@WriteM

e.com

Particle Swarm optimisation






24


e.com

The ³inventors´ (2)

JamesKennedy

Kennedy_ [email protected]




24


e.com

Cooperation example






24


e.com

The basic idea II

The particles in the swarm co-o perate. Theyexchange information about what they¶ve discovered

in the places they have visited The co-operation need only be very simple. In basic

PSO (which is pretty good!) it is like this: ± A particle has a neighbourhood associated with it.

± A particle knows the fitnesses of those in its

neighbourhood, and uses the position of the one with bestfitness.

± This position is simply used to adjust the particle¶s velocity




24


e.com

Initialization. Positions

and velocities




24


e.com

The basic idea

Each particle is searching for the optimum

Each particle is moving (can¶t search

otherwise!), and hence has a velocity . Each particle remembers the position it was

in where it had its best result so far (its personal best )

But this would not be much good on its own; particlesneed hel p in fig uring out where to search.




24


e.com

The basic idea II

The particles in the swarm co-o perate. Theyexchange information about what they¶ve discovered

in the places they have visited The co-operation need only be very simple. In basic

PSO (which is pretty good!) it is like this: ± A particle has a neighbourhood associated with it.

± A particle knows the fitnesses of those in its

neighbourhood, and uses the position of the one with bestfitness.

± This position is simply used to adjust the particle¶s velocity




24


e.com

What a particle does

In each timestep, a particle has to move to anew position. It does this by adjusting itsvelocity . ± The adj ustment is essentially this:

± The c urrent velocity PLUS

± A weighted random portion in the direction of its personal best PLUS

± A weighted random portion in the direction of the

neighbourhood best. H aving worked out a new velocity, its position is

sim ply its old position pl us the new velocity.




24


e.com

Neighbourhoods

geographical

social




24


e.com

Neighbourhoods

Global




24


e.com

The circular

neighbourhood

Virtual circle

1

5

7

64

3

8 2Particle 1¶s 3-

neighbourhood




24


e.com

Particles Adjust their positions according to a``Psychosocial compromise¶¶ between what an

individual is comfortable with, and what society reckons

Here I

am!

The best

perf. of my

neighbours

My best

perf.

x p g

pi

v




24


e.com

Pseudocodehttp://www.swarmintelligence.org/tutorials.php

Equation (a)

v[] = c0 *v[]+ c1 * rand() * (pbest[] - present[])+ c2 * rand() * (gbest[] - present[])

(in the original method, c0=1, but manyresearchers now play with this parameter)

Equation (b)present[] = present[] + v[]




24


e.com


For each particleInitialize particle

END

Do

For each particleCalculate fitness valueIf the fitness value is better than its peronal bestset current value as the new pBest

End

Choose the particle with the best fitness value of all as gBestFor each particle

Calculate particle velocity according equation (a)Update particle position according equation (b)

EndWhile maximum iterations or minimum error criteria is not attained




24


e.com


Particles' velocities on each dimensionare clamped to a maximum velocity

Vmax. If the sum of accelerations wouldcause the velocity on that dimension toexceed Vmax, which is a parameterspecified by the user. Then the velocity

on that dimension is limited to Vmax.




24


e.com

The basic algorithm:

again

±

±

°

±±

¯

®

!

t x prand

t x prand

t v

t v

d d g

d d i

d

d

,2

,1

,0

,0

1

N F

N F

E

f or each particle

update

the

velocity

1)1( t vt xt xthen move

f or each component d

At each time step t




24


e.com

Animated illustration

Global

optimum




24


e.com

Parameters

Number of particles

C1 (importance of personal best)

C2 (importance of neighbourhood best)




24


e.com

How to choose

parameters




24


e.com

Parameters

Number of particles

(10²50) are reported as usually

sufficient. C1 (importance of personal best)

C2 (importance of neighbourhood best)

Usually C1+C2 = 4. No good reason other

than empiricism Vmax ± too low, too slow; too high, too

unstable.




24


e.com

Some functions ...

Rosenbrock

Griewank Rastrigin




24


e.com

... and some results

30D function PSO Type 1" Evolutionary

algo.(Angeline 98)

rie ank [±300] 0.003944 0.4033

R astrigin [±5] 82.95618 46.4689

R osenbrock [±10] 50.193877 1610.359

Optimum=0, dimension=30Best result after 40 000 evaluations




24


e.com

Some variants




24


e.com

Adaptive swarm size

There has been enough

improvement

but there has been not enough

improvement

although I'm the worst

I'm the best

I try to kill myself

I try to generate a

new particle




24


e.com

Adaptive coefficients

The better I

am, the more I

f ollow my ownway

The better is my best

neighbour , the more

I tend to go towardshim

Evrand (0«b)( p- x)




24


e.com

Is this Just A Variation on

Evolutionary Algorithms?




24


e.com

An applet

Next « Cellular Automata

Date post:	07-Apr-2018
Category:	Documents
Upload:	nguyen-anh
View:	224 times
Download:	0 times

Particle Swam CA

Documents