Particle Swarm Optimization and Social Interaction Between Agents

Kenneth LeeTJHSST 2008

Overview

Overview of PSO

Background Research

Project Goals

Types of Social Interactions

Project State/Results

Conclusion

Overview Of PSO

Originally designed to model birdsOvertime became more analogous to a swarming animal (bees)Search for Global OptimaInfinite search spaces

Overview Of PSO

“Particles” (vectors)Random PositionRandom VelocityInfluences on Velocity

Cognitive Influence Social Influence

Convergence(?)

Particle Swarm Optimization

for k = 1 to number of particles n doif (fitness(k) < fitness_lbest(k))

lbest(k) = pos(k)endif

end do

for k = 1 to number of particles n dosocial(k)

enddo

for k = 1 to number of particles n dofor I = 1 to number of dimensions d do

R1 = randomNumberR2 = randomNumberV[k][I] = w * (C1 * R1 *

(pos-lbest) + C2 * R2 * (pos-gbest))X[k][I] = pos + V[k][I]

enddoenddo

Determining lbest

Social Interaction

Adjusting Position

Importance of Social Interaction

Influences Velocity V = ??? X’ = X + V

Encourages ExplorationThrough Social Interaction, Particles are able to communicate information and extrapolate data about the objective function.

Social Interactions

Variance of k value (# of neighbors)

Through research k values between 3-5 seem to work best

Topology? Cliques Random Share/Follow

Project State

5 Interactions NIPS SIPS RIPS FIPS DIPS

3 Benchmark Functions

Rastrigin, Six Camel Hump, Sphere

NIPS (Non-Informed Particle Swarm)

0 5 10 15 20 25

0

50

100

150

200

250

RN-3-4--1_0.txt

RN-3-4--1_1.txt

RN-3-4--1_2.txt

RN-3-4--1_3.txt

RN-3-4--1_4.txt

SIPS(Singly-Informed Particle Swarm)

0 20 40 60 80 100 120 140 160

0

50

100

150

200

250

RS-3-4--1_0.txt

RS-3-4--1_1.txt

RS-3-4--1_2.txt

RS-3-4--1_3.txt

RS-3-4--1_4.txt

RIPS(Ring Informed Particle Swarm)

0 100 200 300 400 500 600 700 800

0

50

100

150

200

250

300

350

400

RR-3-4--1_0.txt

RR-3-4--1_1.txt

RR-3-4--1_2.txt

RR-3-4--1_3.txt

RR-3-4--1_4.txt

FIPS(Fully Informed Particle Swarm)

0 5 10 15 20 25 30 35 40 45 50

0

50

100

150

200

250

300

RF-3-4--1_0.txt

RF-3-4--1_1.txt

RF-3-4--1_2.txt

RF-3-4--1_3.txt

RF-3-4--1_4.txt

DIPS(Dynamically Informed Particle Swarm)

0 50 100 150 200 250

0

50

100

150

200

250

300

350

RD-3-4--1_0.txt

RD-3-4--1_1.txt

RD-3-4--1_2.txt

RD-3-4--1_3.txt

RD-3-4--1_4.txt

Conclusions

DIPS seems to perform best

Time onlyDIPS and RIPS have 100% success rateFIPS converges fastest