ADAPTIVE PARAMETER SELECTION IN COMPREHENSIVE LEARNING PARTICLE SWARM OPTIMIZERAuthors: Mohammad Hasanzadeh,Mohammad Reza Meybodi andMohammad Mehdi Ebadzdeh

Soft Computing Laboratory

OUTLINE

▪ Swarm Intelligence (SI)

▪ Particle Swarm Optimization (PSO)

▪ Comprehensive Learning PSO (CLPSO)

▪ Learning Automata (LA)

▪ Main Idea

▪ Results

▪ Conclusion

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SWARM INTELLIGENCE (SI) 3

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PARTICLE SWARM OPTIMIZATION (PSO)• Introduced by Kennedy and Eberhart in 1995• PSO Imitates animals social behavior• Each particle consists of Position and Velocity vectors • Each particle of PSO share a individual information (pbest)• Population of PSO share a social information (gbest)

• Vt+1 = WVt + C1R1(Pi - Xt) + C2R2(Pg - Xt)

• Xt+1 = Xt + Vt+1

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Social Life

Individual Life

VelocityPosition

VISUALIZING PSO

5C2 r

2 (Pi –

Xt )

• Comprehensive Learning PSO introduced by Liang, Qin andSuganthan in 2006

• Incorporate learning from more previous best particles.

• Vt+1 = WVt + C1R1(Pf(i) - Xt)

• Xt+1 = Xt + Vt+1

• fi = [fi(1), fi(2), …, fi(D) ]

COMPREHENSIVE LEARNING PSO (CLPSO)

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Exemplar Function

LEARNING AUTOMATA (LA)• Introduced by Tsetlin in 1960s and Surveyed by Narendra

and Thathachar 1974• Autonomous decision making components• LA consists of the following components:

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Action Set Probability Vector Learning Algorithm

Learning Automata

Random Environment

Action

Reinforcement Signal

• Parameter Selection• Tuning Refreshing Gap Parameter (m)

• Benchmark structure

• Dimensionality

• Population size

• Exploration

• Exploitation

MAIN IDEA

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CLPSO Population Exemplars

New Exemplar

Lear

n F

rom

Ex

em

pla

rs

Generation mod m

▪ Macroscopic behavior of PSO population

▪ Refreshing gap adjustment by LA

▪ Triple action LA

▪ Reinforcement signal (beta)

▪ 0 if gbest improves

▪ 1 otherwise

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MACROSCOPIC ADAPTIVE PSO (MAPSO)Learning Automaton

CLPSO Population

Learn From Exemplars

Probability Vector

Action Set

PIncrement

PFixed

PDecrement

Increase m

Keep m

Decrease m m

Re

info

rce

me

nt

Sign

al

▪ Microscopic behavior of PSO population

▪ Refreshing gap adjustment by group of LA

▪ Group of Triple action LA

▪ Reinforcement signal (beta)

▪ 0 if pbest improves

▪ 1 otherwise

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MICROSCOPIC ADAPTIVE PSO (MIPSO)

LA Groups

Reinforcement Signal

LA1

CLPSO Population

P1

Inc.

Dec.

Fix.

LAN

Inc.

Dec.

Fix.

m1 m1

PNmN mN

▪ TEC 2006 Benchmark Functions (16)

▪ Unimodal and Simple multimodal (2)

▪ Unrotated multimodal (6)

▪ rotated multimodal (6)

▪ Composition (2)

▪ 10 – Dimensional test

▪ 10 particles

▪ 30000 fitness evaluations

▪ 30 – Dimensional test

▪ 40 particles

▪ 200000 fitness evaluations

▪ Each test runs 30 times

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EXPERIMENTAL SETUP▪ Triple Action LA

▪ Linear Reward – Penalty Algorithm

▪ Alpha = Beta = 0.1

▪ Refreshing gap rang = [1, 20]

1

2

0 00

4 4

2

0 0

2

0

1

0 0 00

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Simple Unrotated Rotated Composition

CPSO-H CLPSO MaPSO MiPSO12

EXPERIMENTAL RESULTS (10D)

2

0 0 00

3

2

1

0 0

1

00

3 3

1

0

0.5

1

1.5

2

2.5

3

3.5

Simple Unrotated Rotated Composition

CPSO-H CLPSO MaPSO MiPSO13

EXPERIMENTAL RESULTS (30D)

3

2

10

6

2

1

1

7

0 2 4 6 8 10 12 14 16 18

10-D

30-D

CPSO-H CLPSO MaPSO MiPSO14

EXPERIMENTAL ANALYSIS (10D, 30D)

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CONCLUSION▪ Adaptive and Agile Parameter Selection

▪ Maintain Solution Diversity

▪ Balancing local and global searches

▪ Escaping from local minima

▪ MaPSO features

▪ Low dimensional problems

▪ Rotated benchmarks

▪ MiPSO features

▪ Higher dimensional problems

▪ Rotated, Unrotated and Composition problems

FOLLOW US

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WE CAN ONLY SEE A SHORT DISTANCE AHEAD, BUT WE CAN SEE PLENTY THERE THAT NEEDS TO BE DONE.

ALAN TURINGThank you for your attention!17