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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