tribes 2006 cooren
TRANSCRIPT
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TRIBESA parameter-free particle swarm
optimization algorithm
Y. COOREN, M. CLERC, P. !ARRY
"th E#$MEeting on A%apti&e, elf-A%apti&e, an%M'lti-Le&el Metahe'ristics
No&em(er )*$)", +*
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Presentation outline
Particle swarm optimization
Why a parameter-ree al!orithm "
TRIBES# the first parameter-free PO algorithm
$E$%&' testin! proce(ure
)umerical results
$onclusions an( perspecti*es
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Particle Swarm+ptimization )$/
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Particle Swarm+ptimization +$/
Stochastic metho(
Biolo!ical inspiration fish schooling an% (ir%floc0ing/
Principle1 2eneration of a swarm of particles in the search space
A fitness is associate% to each particle
Particles mo&e accor%ing to their own e3perience an% that of
the swarm Con&ergence ma%e possi(le (4 the cooperation (etween
particles
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Particle Swarm+ptimization 3/,.trateg4 of %isplacement
5o the (estperformance of
the particle
5o the (estperformance of
the swarm
5o the pointaccessi(le with
the c'rrent&elocit4
C'rrentposition
Newposition
6elocit4
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Particle Swarm+ptimization ,/,.
Algorithm
Particles ran(omly initialize( in the search space
2 stoppin! criteria 0
Acc'rac4
N'm(er of e&al'ations of the
o(7ecti&e f'nction
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Why a parameter-reeal!orithm "
$ommon prolem amon! all metaheuristics
l!orithms *ery (epen(ent o parameters *alues
Time consumin! to in( the optimal *alue o aparameter
The ten(ency is to re(uce the numer o 4ree4parameters
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TRIBES )$/
parameter-ree particle swarm optimizational!orithm
Principles 0
warm %i&i%e% in 8tri(es8 At the (eginning, the swarm is compose% of onl4 one particle
Accor%ing to tri(es9 (eha&iors, particles are a%%e% orremo&e%
Accor%ing to the performances of the particles, theirstrategies of %isplacement are a%apte%
(aptation o the swarm accor(in! to the
perormances o the particles
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Tries +$/tr'ct'ral a%aptations
7einition o a status or each trie1 good, neutralor (a%
7einition o a status or each particle1 goo% orne'tral
Removal of a particle:worstparticle of a goodtri(e
8eneration o a particle1 impro&ement ofperformances of a badtri(e
P M M
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Tries :$/;eha&ioral a%aptations
3 possiilities o *ariations etween 2 iterations1 !mpro&ement of the performance /
?eterioration of the performance -/
9emorization o the 2 last *ariations
$hoice o the strate!y o (isplacement accor(in!to the 2 last *ariations
Gathered statuses Strategy of displacement
(= +) (+ +) local by independent gaussians
(+ =) (- +) disturbed pivot
(- -) (= -) (+ -) (- =) (= =) pivot
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Tries $/Algorithm
structural a(aptations mustnot occur at each iteration
);1 information lin0s n'm(er at
the moment of the lasta%aptation
n1 n'm(er of iterations sincethe last swarm9s a%aptation
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$E$%&' testin! proce(ure1/'.
7eine( (urin! th IEEE $on!ress on E*olutionary$omputation 2&&'
2 tests 0
Error *alues or a i
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$E$%&' testin! proce(ure 2/'.Tests
1rst
test 0 stu(y o the error 7 (imension o the prolem
2' runs
Sin!le stoppin! criterion 9a
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number of successful runs
total number of runs
$E$%&' testin! proce(ure 3/'.Successan(Performancerates
Successrate
Performance rate
MaxEvalmean
. total number of runs
number of successful runs
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$E$%&' testin! proce(ure ,/'.Benchmar>
2' unimo(al or multimo(al unctions
Some characteristics 0
Shite(
Rotate(
+ptimum on oun(s
Interest 0 *oi( particular cases which can ee
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$E$%&' testin! proce(ure '/'.E
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Numerical results (1/5)1rsttest, Unimodal problems
@) @+ @: @ @B
? ),
@es>),,,,,
, , BA".),**" B.**,CE-,A ,
, , ):,BB.A:B)+C C.*"),,AE-,A ).):*C*CE-):
, , +))),.*)++)C A.:AA)":E-,A .ACB)*CE-))
, , +AA,A.)AB"B A.",:CBE-,A :.C**CC"E-,A
, B.*CE-) C,BA*.AC*:A* A.A*)B+BE-,A .++BB"CE-,
Mean , +.+"E-,)B +*CC.CAAC:* C.B:*BA,E-,A )."BBA"CE-,B
t% %e& , ).))E-) )C"":.:"C* +.,CC):E-,A C.+"++C*E-,B
)st
"
th
):th
)Ath
+Bth
Numerical results (2/5)
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Numerical results (2/5)1rsttest, Multimodal problems
@* @" @C @A @), @))
? ),
@es>),,,,,
,.,,:) ,.,)B+C" , +.ACC"" B.A*A"B +."A+):
,.B),CB ,.,B)AC +.CE-) B.A*A"B A.,ACAC" :.B*,A
,.""+B ,.,":"*A ).,+*A) ".ABA**" ),.AB .)BC)*
).),:++* ,.,A), )A.A:*C: A.AABC* )+.A:BC .C")+""
+.)*ABC+ ,.+,)*) +,.:"*": )*.A)+*A +".CBC"C: *.,A",)"
Mean ,.CBCC+ ,.,""" ".+++B+) C.BB**+ )+.))C,,+ .+::AA+
t% %e& ,.B",CC" ,.,:A+ A.)AA):B :.**A++ .**,B"B ,.ABC:)B
)st
"th
):th
)Ath
+Bth
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Numerical results (/5)!onver"ence #rap$s
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Numerical results (%/5)2ndtest, Unimodal problems
@) @+ @: @ @B
N'm(er of sol&e% f'nctions 'ccess rate ),,, +,, *B,, +,, B,,
2-CMA-E B ),,D ).* +B/ ) +B/ ) +B/ ) +B/ ) +B/
E?A B D ), +B/ .* +B/ +.B +:/ .) +B/ .+ +B/
?E B *D + +B/ ).+ +B/ ).B +,/ )". +B/ *. +B/
L-CMA-E B *D )." +B/ ).) +B/ ) +B/ *B.B "/ ) +B/
;L-2LB, ,D ) +B/ )".) +B/ - ).B +B/ ." +B/
PC-PN ,D *." +B/ )+. +B/ - ),." +B/ *. +B/
CoE6O ,D +: +B/ )).: +B/ *. +B/ )*.+ +B/ -
?M-L-PO "*D )+ +B/ B +B/ ). +B/ - ).* +,/
L-a?E "+D ), +B/ .+ +B/ )*/ )B. +/ -
;L-MA : BD )+ +B/ )B. +B/ - +B. +/ -F-PC : B"D ) +B/ ) +B/ - )." +)/ -
TRIBES , 5&C 1@3 2'. 2@' 2'. - 3@61 2'. /# 2'.
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Numerical results (5/5)2ndtest, Multimodal problems
@* @" @ @ @), @))
N'm(er of sol&e% f'nctions 'ccess rate "),, ",, BBB )",,, BB,,, ),,,,
2-CMA-E B *BD ).B +B/ ) +B/ - .B )/ ).+ +:/ ). */
F-PC : BD .* ++/ - - +. +/ ) ++/ -
L-a?E : :"D *.* +/ :*.+ */ - ) +B/ - -
?M-L-PO : :*D ).: +B/ )+* / - +.) +B/ - -
?E ::D ".: +B/ +BB +/ - ),.* ))/ - ) )+/
L-CMA-E ) ::D "." +B/ ).+ +B/ - - - -
;L-2LB, : +BD *.* +B/ )+.: / - ), :/ - -
PC-PN : )*D ) ++/ :: )/ - - - B. )/
;L-MA ) )+D - - - B." )/ - -
E?A + :D - , )/ - - - +. :/
CoE6O , , - - - - - -
TRIBES , ,1C 3@5 2'. &@1/ 2'. 1 1&. /3 2. - -
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$ompetiti*e al!orithm
Parameter-ree
)o waste o time without loss o
perormance Possile impro*ements 0
;etter choice of a%aptation r'les
More acc'rate strategies of %isplacement
G4(ri%ization with an Estimation of ?istri('tionAlgorithm
Better a(aptation o the choices ma(eto the speciicity o the prolem
!onclusions and perspectives
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Than>s or your attention
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Algorithm Name Reference
BLX-GL50
Real-Coded Memetic Algorithm BLX-MA [Molina et al., 2005]
CoEVO [Posik (2005)]
Real-Parameter Optimization with Differential Evolution DE [Rnkknen and Kukkonen, 2005]
DMS-L-PSO [Liang and Suganthan, 2005]
Simple Continuous EDA EDA [Yuan and Gallagher, 2005]
G-CMA-ES [Auger et al., 2005a]
K-PCX [Sinha et al., 2005]
Advanced Local Search Evolutionary Algorithm L-CMA-ES [Auger et al., 2005b]
Self-adaptive Differential Evolution Algorithm L-SaDE [Qin and Suganthan, 2005]
Steady-State Real-Parameter Genetic Algorithm SPC-PNX [Ballester et al., 2005]
Hybrid Real-Coded Genetic Algorithm
with Female and Male Differentiation [Garca-Martnez and Lozano, 2005]
Real Parameter Optimization Using
Mutation Step Co-evolution
Dynamic Multi-Swarm Particle Swarm
Optimizer with Local Search
Restart CMA Evolution Strategy with
Increasing Population Size
Population-Based, Steady-State Procedure
for Real-Parameter Optimization
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X=c1.aleaH
pc
2.alea H
g
c1=
f p
f pf g
c2=
f g
f pf g
Pi*ot strate!y
aleaDp. a point uniormly chosen in the hyper-
sphere o centerpan( ra(ius AAp-!AA
aleaD!. a point uniormly chosen in the hyper-
sphere o center "an( ra(ius AAp-!AA
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7isture( pi*ot strate!y
X=c1.aleaHpc2 .alea Hg
b=N0, f p f g
f p f g
X=1b
.X
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;ocal in(epen(ent !aussians
Xj=g
jalea
normalg
jX
j,gjXj