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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
=
=