pso tutorial sis05jimktut

8/3/2019 PSO Tutorial SIS05JimKTut

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Tutorial on Par ticleSw arm Optimization

Jim K ennedy

Russ Eberhart

IEEE Swarm Intelligence Symposium 2005

Pasadena, California USA

June 8, 2005

Jim K ennedy

Bur eau o f Labor Statistics

U. S. Department of Labor

W ashington, [email protected]


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Particle SwarmsPart 1: Sociocognitive Optimization

Artificial IntelligenceAttempted to elicit intelligence from a computing machineby simulating human thought good idea!

Early AI derived in the Dark Ages of psychology, whenstudy of mind was taboo in science. Based on naveintrospectionism.

Computational Intelligence

Perhaps we can apply more scientific concepts of mind. Self-report gives an unsatisfactory account of real cognition Sociocognition: thought as a social act Self-organization of societies, cultures


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Sociocognition

SpanosLevine, Resnick, and HigginsLewins topological space

B=f(P,E)(P,E)=LS

Cognitive DissonanceHypothesis 1: There are two major sources ofcognition, namely, own experience andcommunication from others.

Leon Festinger, 1954/1999, Social Communicationand Cognition(draft)

-Types of cognitive relations-Minimization of dissonance-Fundamental Attribution Error-Exploration/exploitation

Note: vector=point


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Latans Social ImpactTheory

i=f(SIN); i=sNt, t


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Flocks, Herds,and Schools

Heppner & GrenanderCraig Reynolds

Steer toward the centerMatch neighbors velocityAvoid collisions(Seek roost)

Evolutionary Computation

Variation operatorsMutationCrossover

Selection

Population of proposed problem solutions

Emulates natural evolution to breed solutionsto hard problems, write computer programs,build robots, etc.

D.T. Campbell: Blind variation and selective retention


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Particle Swarms

Sociocognitive space

Certainly high-dimensional (i.e., Burgess & Lund)Abstract attitudes, behaviors, cognitionHeterogeneous with respect to evaluation (dissonance)Multiple individuals

Individual has position=mental state:Individual changes:

x ir

vir

Particle Swarms

Individuals learn from their own experience

This formula, iterated over time, causes each individual istrajectory to oscillate around its previous best pointp

iin the

sociocognitive space.

It stochastically adjusts is velocity depending on previoussuccesses, and occasionally updatesp

i the previous best.

+

+

vxx

xpvv

iii

iiiiU

rrr

rr

rr

)(),0( for i=1 to popsize

for j=1 to dimensionv[i][j]=v[i][j]+rand()*(p[i][j]-x[i][j])x[i][j]=x[i][j]+v[i][j]

next jnext i


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2.9

-3

-2

-1

0

1

2

3phi=

3.6

-4

-3

-2

-1

0

1

2

3

4phi=

3 . 9 5

-10

-5

0

5

10phi=

3 . 9 9

-30

-20

-10

0

10

20

30phi=

4

-300

-200

-100

0

100

200

300phi=

0.01

-30

-20

-10

0

10

20

30phi=

0.5

-4

-3

-2

-1

0

1

2

3

4phi=

1.3

-3

-2

-1

0

1

2

3phi=

1.9

-3

-2

-1

0

1

2

3phi=

Oscillating trajectories(nonstochastic)

+

+

vxx

xpvv

iii

iiii

rrr

rr

rr

)(

Particle Swarms

Sociocognitive space can contain many individualsThey influence one another

Evaluateyour present positionCompare it to your previous best and neighborhood bestImitate self and others

(g is neighborhood best)

+

++

vxx

xpxpvv

iii

igiiiiUU

rrr

rr

rrr

r

)())2

,0()()2

,0( 21


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The Drunkards WalkThe particle will explode out of control if it is not limited in some way.

Three methods have been widely used:Vmax

Inertia weight

Constriction coefficient

(note that these last two are equivalent)

))()2

,0()()2

,0( 21( xpxpvv idgdidididid UU ++=

)(),0()(),0(21 xpCxpCvv idgdidididid UU ++=

maxmax

max;max

)()2

,0()()2

,0( 11

VthenVifelse

VthenVif

UU

vv

vv

xpxpvv

idid

idid

idgdidididid

=

++=

Binary Particle Swarms

)exp(1

1)( vvs +=where

logistic functionkeeps it in (0..1)

Kennedy and Eberhart (1997)Kennedy and Spears (1998)

Being looked at closely, expanded

=

=

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