pso(particle swam optimization)

8/14/2019 PSO(Particle Swam Optimization)

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Particle Swarm Optimization (PSO)Particle Swarm Optimization (PSO)

PSO is a robust stochastic optimization technique based on

the movement and intelligence of swarms. PSO applies the concept of social interaction to problem

solving.

It was developed in 1995 by James Kennedy (social-

psychologist) and Russell Eberhart (electrical engineer).

It uses a number of agents (particles) that constitute a

swarm moving around in the search space looking for the

best solution.

Each particle is treated as a point in a N-dimensional spacewhich adjusts its flying according to its own flying

experience as well as the flying experience of other

particles.


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Each particle keeps track of its coordinates in the solutionspace which are associated with the best solution (fitness)

that has achieved so far by that particle. This value is called

personal best , pbest.

Another best value that is tracked by the PSO is the best

value obtained so far by any particle in the neighborhood of

that particle. This value is called gbest.

The basic concept of PSO lies in accelerating each particle

toward its pbest and the gbest locations, with a random

weighted accelaration at each time step as shown in Fig.1



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Fig.1 Concept of modification of a searching point by PSO

sk : current searching point.

sk+1 : modified

searching point.

vk: current velocity.

vk+1 : modified

sk

vk

vpbest

vgbest

sk+1

vk+1

sk

vk

vpbest

vgbest

sk+1

vk+1


x

y


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Particle Swarm Optimization (PSO)Particle Swarm Optimization (PSO) Each particle tries to modify its position using the following

information: the current positions, the current velocities, the distance between the current position and pbest, the distance between the current position and the gbest.The modification of the particles position can be mathematically

modeled according the following equation :

Vik+1

=w

Vik

+c1 rand1() x (pbesti-sik

) + c2 rand2() x (gbest-sik

) .. (1)where, vi

k : velocity of agent i at iteration k,

w: weighting function,

cj : weighting factor,

rand : uniformly distributed random number

between 0 and 1, sik : current position of agent i at

iteration k, pbesti : pbest of agent i,


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Thefollowing weighting function is usually utilized in (1)

w= wMax-[(wMax-wMin) x iter]/maxIter (2)

where wMax= initial weight,

wMin = final weight,

maxIter = maximum iteration number,

iter = current iteration number.

sik+1

= sik

+ Vik+1

(3)



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Comments on the Inertial weight factor:Comments on the Inertial weight factor:

A large inertia weight (A large inertia weight (ww) facilitates a global search while) facilitates a global search whilea small inertia weight facilitates a local search.a small inertia weight facilitates a local search.

By linearly decreasing the inertia weight from a relativelyBy linearly decreasing the inertia weight from a relativelylarge value to a small value through the course of thelarge value to a small value through the course of the

PSO run gives the best PSO performance comparedPSO run gives the best PSO performance comparedwith fixed inertia weight settings.with fixed inertia weight settings.

Larger w ----------- greater global search abilityLarger w ----------- greater global search ability

Smaller w ------------ greater local search ability.Smaller w ------------ greater local search ability.

Particle Swarm OptimizationParticle Swarm Optimization

(PSO)(PSO)


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Flow chart depicting the General PSO Algorithm:

Start

Initialize particles with random position

and velocity vectors.

For each particles position (p)

evaluate fitness

If fitness(p) better than

fitness(pbest) then pbest= pLoop

untilall

particles

exhaust

Set best of pBests as gBest

Update particles velocity (eq. 1) and

position (eq. 3)

Loopun

tilmaxiter

Stop: giving gBest, optimal solution.


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Comparison with other evolutionaryComparison with other evolutionary

computation techniques.computation techniques. Unlike in genetic algorithms, evolutionary programming andevolutionary strategies, in PSO, there is no selection operation.

All particles in PSO are kept as members of the population through

the course of the run

PSO is the only algorithm that does not implement the survival of

the fittest.

No crossover operation in PSO.

eq 1(b) resembles mutation in EP. In EP balance between the global and local search can be adjusted

through the strategy parameter while in PSO the balance is

achieved through the inertial weight factor (w) of eq. 1(a)


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Variants of PSOVariants of PSO

Discrete PSO can handle discrete binaryvariables

MINLP PSO can handle both discrete binary and

continuous variables.

Hybrid PSO. Utilizes basic mechanism of PSO

and the natural selection mechanism, which is usually

utilized by EC methods such as GAs.


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Application ofPSOALGORITHMto Optimize a

Meander-line Polarizer for LICP conversion

Intialization parameters used for PSO:

wMax=0.41

wMin=0.4

(Note:The inertial weight ,w is linearly decreased from wMaxto wMinaccording the Eq. (2), w is chosen virtually constant in this case for better

local search near the Suns Optimized parameters.)

c1=c2=1.49

maxIter=2000

The above parameters are used in conjuction with eqs.

(1) & (2)

Swarm size/Population size used for solution search : 25


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Frequency band of interest: 3.5 to 6.5 (GHz)

(evaluated at 12 frequency points)

Desired VSWR


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Mean best & Best fitness over50 runs


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VSWR


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Axial Ratio (dB)


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4 Layers for CP

Spacer

(inches)

loi

dielectric(inches)

l i

Line Width

(inches)

w1 w2

Height

(inches)

h

Period

(inches)

b

Pitch

(inches)

a

Layer

----8.4705018E-

03

1.5984001E-

02

2.2501351E-

020.25205650.72833820.34493604

0.54281283.4676325E-

03

9.4296653E-

03

5.3999661E-

030.47074200.87043980.37984693

0.42118453.4676325E-

03

9.4296653E-

03

5.3999661E-

030.47074200.87043980.37984692

0.54281288.4705018E-

03

1.5984001E-

02

2.2501351E-

020.25205650.72833820.34493601

Dielectric

Sheet

Metal

Layer

Spacer

55.2i = 15.1i0 =Dielectric constants:

Optimized dimensions for 4-layer

Meander Line Polarizer


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Frequency bands of interest:

Band1: 3.7 to 4.2 (GHz)

Band2: 5.9 to 6.4 (GHz)

(evaluated at 2 frequency points: 3.95 (GHz), 6.15 (GHz))

Desired VSWR


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VSWR


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Axial Ratio (dB)


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4 Layers for CP

Spacer

(inches)

loi

dielectric(inches)

l i

Line Width

(inches)

w1 w2

Height

(inches)

h

Period

(inches)

b

Pitch

(inches)

a

Layer

----4.1147252E-

03

2.7704202E-

02

4.0456183E-

020.24801430.80816690.25289134

0.45338233.9593712E-

03

4.4981677E-

02

5.0358579E-

020.34337220.95296580.54257243

0.44821953.9593712E-

03

4.4981677E-

02

5.0358579E-

020.34337220.95296580.54257242

0.45338234.1147252E-

03

2.7704202E-

02

4.0456183E-

020.24801430.80816690.25289131

Dielectric

Sheet

Metal

Layer

Spacer





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Meander-line Polarizer forLP rotation

Intialization parameters used for PSO:

wMax=0.41

wMin=0.4

(Note:The inertial weight ,w is linearly decreased from wMaxto wMinaccording the Eq. (2), w is chosen virtually constant in this case for better

local search near the Suns Optimized parameters.)

c1=c2=1.3

maxIter=1000

The above parameters are used in conjuction with eqs.

(1) & (2)

Swarm size/Population size used for solution search : 25


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Frequency band of interest: 3.5 to 6.5 (GHz)

(evaluated at 12 frequency points)

Desired VSWR


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VSWR


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Axial Ratio (dB)


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Phase Difference


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8 Layers for LP

Spacer

(inches)

loi

dielectric(inches)

l i

Line Width

(inches)

w1 w2

Height

(inches)

h

Period

(inches)

b

Pitch

(inches)

a

Layer

----2.1623570E-

02

3.0709708E-

02

2.8606838E-

020.21480451.0206000.36318784, 8

0.45507974.0660784E-

02

3.4942929E-

02

4.1542474E-

020.43749990.82257650.38481703, 7

0.39594684.0660784E-

02

3.4942929E-

02

4.1542474E-

020.43749990.82257650.38481702, 6

0.45507972.1623570E-

02

3.0709708E-

02

2.8606838E-

020.21480451.0206000.36318781, 5

Dielectric

Sheet

Metal

Layer

Spacer





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Frequency bands of interest:

Band1: 3.7 to 4.2 (GHz)

Band2: 5.9 to 6.4 (GHz)

(evaluated at 2 frequency points: 3.95 (GHz), 6.15 (GHz))

Desired VSWR


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VSWR


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Axial Ratio (dB)


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8 Layers for LP

Spacer

(inches)

loi

dielectric(inches)

l i

Line Width

(inches)

w1 w2

Height

(inches)

h

Period

(inches)

b

Pitch

(inches)

a

Layer

----2.2299249E-

02

3.2010745E-

02

3.3202391E-

020.27475691.0555960.31508694, 8

0.35447253.1127717E-

020.1126298

6.0811251E-

020.35656081.1645760.40858013, 7

0.31593893.1127717E-

020.1126298

6.0811251E-

020.35656081.1645760.40858012, 6

0.35447252.2299249E-

02

3.2010745E-

02

3.3202391E-

020.27475691.0555960.31508691, 5

Dielectric

Sheet

Metal

Layer

Spacer





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END

pso(particle swam optimization)

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