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PSOParticle Swarm Optimization

Single_

121

@

126

.com

Xidian Universi ty, Xi

an, China ©

2005

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S S

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(

2

)

(

1

)

i i i x x V

(

1

)

(

2

)

i

1

2

M

M

1

2

---

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(

2

)

(

1

)

i i i x x V

(

1

)

(

2

)

i

1

2

M

M

(swarm intelligence)

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(

2

)

(

1

)

i i i x x V

(

1

)

(

2

)

i

1

2

M

M

Millonas 1994 )

1

2

3

4

5

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

Reynolds Heppner Grenader

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

E.O.Wilson

PSO

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

PSO evolutionary computation , Eberhart kennedy 1995 (Kennedy J Eberhart R

Partic le swarm optimization Proceedings of the IEEE Internati

onal Conference on Neural Networks 1995 1942~1948. )

PSO

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

) NI N Xi x 1 x

2 … xN) Vi v

v

2 … v

N) fitne

ss value) pbest) Xi

gbest) gbest pbest)

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PSO ) pb

est,gbest)i i i

x x V i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

PSO )

pbest,gbest)

(1)

(2)

(1) (2) i 1 2 … M M

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

i i i x x V

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PSO ) pb

est,gbest)i i i

x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

Vipbest gbest

rand() 0 1Xi

c 1 c 2 c 1 c 2 2Vmax

VmaxVmax Vmax >0

PSO

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

1998 shi A modified particle swarm

optimizer (1)

3

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2) (3) pso

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

shi

PSO PSO

shi(linearly decreasing weight, LDW)

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PSO ) pbest,gbest)

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

PSOStep 1: ( m)

Step 2:

Step 3: pbest

pbest;Step 4:

gbestgbest;

Step 5: (2) (3)Step 6 Step 2

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Gk )

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

(2) (3) pbest gbestC1 0

(social -only):

PSO .

PSO

2 () ( )i i i iV V c rand gbest x

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

C2 0(cognition-only)

PSO1

() ( )i i i i

V V c rand pbest x

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

m c 1 c 2Vmax G k

m 20 40100 200

Vmax

);

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

c1 c2

C1 c2 Pbestgbest

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

c 1 c 2 0

0

w

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

c 1 c 2 2 Suganthan c 1 c 22

Clerc (constriction factor) K

1 2()( ) ()( )i i i i i iV K V rand pbest x rand gbest x

1 22

2 , , 4.2 4

K

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PSO ) pbest,gbest)

i i i x x V

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

(1) (2) i 1 2 … M M

PSO

PSOPSO

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

then 1i

x

else 0i

x

1( )

1 exp( )i

i

S V V

sigmoid

2( () ( ))iif rand S V

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PSO ) pbest,gbest)

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

PSO

1 PSO

:(1)

(2)(3)(4)(5)

(6)

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PSO

(1) PSOGA

(2) PSO

GA

(3) GA PSOGA

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PSO ) pbest,gbest)

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

PSO

2 PSO ANN

GA NN

:

PSO PSO

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PSO ) pbest,gbest)

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

ANTSInternational Workshop on Ant Colony Optimizationand Swarm Intelligence

19982006 The Fifth

GECCO( )

Genetic and Evolutionary Computation Conference2006

particle swarm optimization (PSO) , that focuses on continuous optimization problems.

PSO

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PSO ) pbest,gbest)

i i i x x V

1 2() ( ) () ( )i i i i i iV V c rand pbest x c rand gbest x

(2)

(1)

i i i x x V

(1) (2) i 1 2 … M M

PSO

. . .2005.1Kennedy J Eberhart R Particle swarm optimizationProceedings of the IEEE International Conference on NeuralNetworks 1995 1942~1948

. . .2004.5

. . .2004.3

. .

.2005.2 1~3