Tribes 2006 Cooren

7/25/2019 Tribes 2006 Cooren

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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

Tribes 2006 Cooren

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