1

Sociocognitive ComputationWith Particle Swarms

James Kennedy

Cognitivism and Sociocognition

Cognitivism• The individual as information processor• Analyze inputs, make decisions about problem

featuresSociocognition• The individual as a participant in society• Mind as social interaction

2

Social Impact Theory

Nowak, Szamrej, and Latané, 1990

Social influenceConformityNormsSocial learningGroupsCultures

i=f(SIN)

Cognitive Dissonance

•Two cognitions can be either relevant or irrelevant

•If they are relevant, they must be consonant or dissonant

•To say that two cognitions are dissonant is to say that one doesnot follow from the other or that one follows from the converse of the other

•Dissonant cognitions produce an aversive state that the individual will try to reduce by changing one or both of the cognitions

3

The Problem with problems

-Cognitive elements (attitudes, behaviors, & beliefs) are interrelated-People have a drive to minimize dissonance (thinking as optimization)

xxx dx ..., 21=rThe current state

Representation

ppp dp ..., 21=r

The previous best

“Velocity”

vvv dv ,..., 21=r

4

Representation

3-dimensional cognitive space

)(xMr

An evaluation function

Particle Swarms - step one

Individual has position=“mental state”:

Individual changes:

Individual’s memory of previous best:

vxxxpvv

rrr

rrrr

+←−⋅+← )(ϕ

xr

vr

pr

5

2.9

-3

-2

-1

0

1

2

3 p h i=

3 .6

-4-3-2-101234 p h i=

3 .95

-1 0

-5

0

5

1 0 p h i=

3 .99

-3 0

-2 0

-1 0

0

1 0

2 0

3 0 p h i=

4

-300

-200

-100

0

100

200

300 ph i=

0.01

-30

-20

-10

0

10

20

30 phi=

0.5

-4-3-2-101234 phi=

1.3

-3

-2

-1

0

1

2

3 phi=

1.9

-3

-2

-1

0

1

2

3 phi=

Oscillating trajectories (nonstochastic)

Depends on ϕ

vxxxpvv

+←−⋅+← )(ϕ

Explosion!

Random phi leads to explosion

vxxxpUvv

+←−⋅+← )(),0( ϕ

r

6

ConvergenceThe particle will explode out of control if it is not limited in some way.Three methods are widely used:

maxmaxmax;max

))(,0(

VthenVifelseVthenVif

vvvv

xpUvv

idid

idid

idididid

−=−<

=>

−+= ϕr

))(,0( xpUvv idididid −+= ϕαr

)))(,0(( xpUvv idididid −+= ϕχr

Vmax

Inertia weight

Constriction coefficient

ϕϕϕχ

42

22 −−−

=where

Particle Swarms: Individual learning

Individuals learn from their own experience

Stochastically adjusts i’s velocity depending on previous successes, occasionally updating pi --the previous best.

Ideally, better solutions are found during oscillations

⎪⎩

⎪⎨⎧

+←

−+←

vxx

xpUvv

iii

iiiirrr

rrrrr )))(( ,0( ϕχ

7

Individual learning (K=0)

N=3K=0

Dimension=2Iterations=30

Sphere function(Graph is smoothed)

Sociocognitive space can contain many individualsThey influence one another

⎪⎩

⎪⎨⎧

+←

−+−+←

vxx

xpUxpUvv

iii

igiiiirrr

rrrrrrrr )))())(( ,0(,0( 21 ϕϕχ

(g is neighborhood best)

Particle Swarms: Social influence

8

Interacting Particles (K=2)

N=3K=2

Dimension=2Iterations=30

Sphere function(Graph is smoothed)

vxx

xpUxpUvv

iii

igiiiirrr

rrrrrrrr

+←

−+−+← )))())( ,0(,0(( 21 ϕϕχ

Neighborhoods

9

Social Networks

•K=number of neighbors•Clustering: neighbors in common•Mean distance between nodes•etc.

3-dimensional sociocognitive Space

Representation

10

Effects ofNeighbors

The amplitude of search is controlled by the difference between own best and neighborhood best.

pi= 0pg= 0

pi= -2pg= +2

pi= -0.1pg= +0.1

Neighbors in the Problem Space

Though topology correlates with proximity in the problem space, neighbors may be in the same or different regions.

11

Neural networks

Feedforward nets(backprop)

Hopfield nets(Harmony, ECHO, etc.)

Cockshott A. R., Hartman B. E., "Improving thefermentation medium for Echinocandin B production.Part II: Particle swarm optimization", Processbiochemistry, vol. 36, 2001, p. 661-669.

He Z., Wei C., Yang L., Gao X., Yao S., Eberhart R.C., Shi Y., "Extracting Rules from Fuzzy NeuralNetwork by Particle Swarm Optimization", IEEEInternational Conference on EvolutionaryComputation, Anchorage, Alaska, USA, 1998.

Secrest B. R., Traveling Salesman Problem forSurveillance Mission using Particle SwarmOptimization, AFIT/GCE/ENG/01M-03, Air ForceInstitute of Technology, 2001.

Yoshida H., Kawata K., Fukuyama Y., "A ParticleSwarm Optimization for Reactive Power and VoltageControl considering Voltage Security Assessment",IEEE Trans. on Power Systems, vol. 15, 2001, p.1232-1239.

Some Applications

12

Binary Particle Swarms

⎪⎪⎩

⎪⎪⎨

⎧

=

=<

−+−+←

01)()1,0(

))())( ,0(,0( 21

xxv

xpUxpUvv

i

ii

igiiii

elsethensUif

r

rr

rrrrrrrr

rϕϕ

)exp(11)(

vvs

−+=

wherelogistic function keeps it in (0..1)

The same formula, but now v is used as a probability threshold to decide whether x should be tested as a 1 or a 0.

GA vs. Binary PS Kennedy and Spears (1998)

P=number of peaks; N=dimensionGA_c=GA with crossover only; GA_m with mutation only

13

The Particle Swarm Algorithm in pseudo code

Randomly initialize xid and vidLoopFor i = 1 to number of individuals

g = i //arbitrary initial assignmentIf eval(i) ≤ Pbesti then

Pbesti = eval(i)for d=1 to dimensions being optimized

pid = xidnext d

end iffor j = first in neighborhood to last

if Pbestj < Pbestg then g = jnext jfor d=1 to dimensions being optimized

vid = χ * ( vid + rand()*ϕ1*(pid – xid) + rand()*ϕ2*(pgd – xid))next d

next iFor i = 1 to number of individuals //Simultaneous updating

For d = 1 to number of dimensions being optimizedxid = xid + Vid

Next dnext iUntil termination criterion

“Exteriorizing” it

Find the target pattern (dimensionality here is “only” 9)

14

“Swarms”

Ants find the shortest path.

“Swarms”

15

Culture & Immergence

1. 3.2.

4. 5. 6.

7. 8. 9.

+

+ +

+ --

-

+-

+

+ ++-

-

- +

+

---

++

+

“Fuzzy Cognitive Map”(Kosko)

Lbest sociometryNeighbors become similar

(cultures or norms).Multiple optima are found.

Science

Kuhn -- the scientific paradigm as a social activity

• Conferences• Academic departments• Peer review & editorial decision• Tenure• Graduate school passing the torch• Grant committees• Sabbaticals• Journal subscription

16

Adaptive PSInitialization methodsPopulation sizePopulation diameterAbsolute vs. signed velocitiesPopulation topologyBirths, deaths, migrationLimiting domain (XMAX, VMAX)Multiobjective optimization“Subvector” techniques (patches)HybridsDynamic problemsNew formulas

Parameters, Conditions, & Tweaks