Sociocognitive Computation With Particle...
Transcript of Sociocognitive Computation With Particle...
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