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performance
1 2
Generation(t)
...
n
parents
Generation(t+1)
1
1
1
.
STEP 1
2
STEP 2
STEP 3
.
.
.
.
.
select n
subgroups
using each
dimension of
performance
in turn
.
shuffle
apply genetic
operators
.
.
n
popsize
popsize
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b
START
initialize
population
gen = 0
front = 1
is
population
classified ?
No
identify
Nondominated
individuals
Yes
reproduction
according to
dummy fitness
gen = gen + 1
Yes
assign
dummy fitness
crossover
sharing in
current front
mutation
front = front + 1
is
gen < maxgen
?
No
STOP
!
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X ` §^e k ie  X ` l k e du$ op l ¢vxzxoxAb
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r k m ž p r \=_|_ r  $ÿ y ÿ b
b o` r|ž p k [‚b E e ` Ÿl \ r k e d¤[ k qAg d &æb I `oh e \ob Rž \ X k h|\=_a` T h|m žcg q \=d O¬q ` l pA_ g ` e¤Q _ah k _a\ f ¢ TôK \ Ÿ k r \ lsg¦e \ T,lsf `oh g _ ž n ?`zh ~Ìp l _ g `z¡S¥£\^m=_ g¦q \ ,]A_ g n gsr k _ g ` e b JLe _ T` .=' '
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E‚b¶[¤b X k ] k gslsg `op{\=_ k l bsF\^d g _a`oh^@
 C:,.;! 46 /,.!<BC > 4 C8'1 L <5.='8
r y ) vovS T _ ž \ ecr  h|\^\=m^\o Q \^]A_a\^n V
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\ &\ f \^h^ k e d XZg \=_ Q ] g \ r|r \ ecr b Rž \ \ e \=_ g m T,lsf `oh g _ ž n
ek d{_ ž \ Q _ah|pcm=_apch|\`z U_ ž \ƒ g _ e \ rar ü k e d r m k ]ª\ob JLe ý g m ž k h|d E‚b \ l \ Ÿ k e d{ü k raž ` e b
`S`oûo\^h^)\^d g _a`oh r @ % < D=6' :;- ,% : &%4 !4 3% %9% ?#%!
B# =D%5!:1C8'½t] k f \ r … ) wxA Q k e ~ k _a\^`c I k lsg ?`oh ecg k  $ÿoÿ bc~Ì`oh f k e E k pc ?n k ece b
wSb R \^`;dc`ohN~ k h|m^pub T n¤p l _ g `o¡A¥£\^m=_ g q \,\ q ` l pA_ g ` e k h£¢ k ]c]ch|` k m ž _a`¤] k _|_a\^h e h|\^m=` foecg _ g ` e ?`oh
h|`o¡cp r _«d g k foe ` rag¦r `o N]ch|`Sm^\ rar k p l _ r b JLe ýLb cb X k _|_a` e k e d cb Iž \ e Z\^d g _a`zh r  B 7 > C:' 5,.C %,./JC8% !" 7 ,D;%%4 5' ! < 73>2\N9:1 !G %%' '3' 7B L,K<$7;7 $t] k f \ r yo… ) yoyA E g¦ecf _a` e !,]F` e ,p lsl " ! ecg _a\^d E gsecf dc`zn T p V
f p r _ -ÿoÿ „Sb
(Ab E k g¦r k ~b)~ g \=_|_ gse \ e b A 5 *-,./!10!233!546 <
! C8?> !tb E l p Ÿ \^h T m k dc\^n g m
X pc¡ lsgsr|ž \^h r  ` r _a` e t~ k rar k m ž p r \=_|_ r  $ÿoÿ yAb
„Sb9[ k qAg d~Ì` e _ k e k Õ~ k h raž k lsl h gsece  Q \ k e ~{`S`oh|\o k e d k h|h|\­_|_ g d Ÿ \ lsl b \ e \=_ g m T,l V
f `oh g _ ž n r å`oh I `on6] l \=€¶DýN\ k l¦VWRg n6\ Q m ž \^dcp lsgsecf b JLe % <5D=6' !:; _ T- %%4!!4V 3% 7;>' &C8'*P"V9<->D0%%!3'a;] k f \ r vov … ) vov yAzü k
o` l¦l k  I k lsg ?`oh ecg k  ,m=_a`o¡ª\=h $ÿoÿ yAb JYO)O)O b
yAb Q b 9¡ k ¢ k ražcg  Q b R k û k ž k ražcg  k e d ¤b R k ûo\ f pcm žcg b K,g m žcg¦ecf k e d OZlsg _ gsr _~Ì`;dc\ lsr ?`oh
~ 9T,r b JLeÑT b O b OZg ¡F\ e )~b Q m ž `S\ e k pc\^h^ k e d +b VóX b Q m ž;Ÿ \^ ?\ l )\=d g _a`oh r @X5
10C 7 4 5.=-9 C AJ!, 7A D¶] k f \ r v(zx ) v( ÿ  T n r _a\^h|d k n9,` lsl k e du
$ÿoÿ yAb Q ]ch g¦ecf \=h VWM \^h l k f b
zÿ b T,e dch § \Y¥ r ¢Am § û k b~{p l _ g m^h g _a\=h g k `o]A_ g n g¦§ k _ g ` e ?`zh+\ ecfogse \^\=h gsecf dc\ r|gsfoe b JLe o` žceÓQ b
\=h|`tc\^d g _a`oh^4
 C8%' =6\<
!5C8 >!ct] k f \ r $ÿ … ) vovo„Sb T m k dc\^n g m X h|\ r|r  $ÿ yzwSb
wxAb M9gsl ?h|\^dc` X k h|\=_a`cb ,.%' C= 9 C8 2 !MO3, = q ` l pcn«\ J k e d J£J bƒbDý`zp f \oDü k p V
r k ece \o y ÿ (Ab
w b o` eÑR bZý g m ž k h|d r ` e ~ k h|û#ýb X k l n«\^h^ p e k h ü g \^] gsecr  k e dÝ~ g ûo\ g¦lslsg k h|dub Q `on6\
p g dc\ lsgse \ r ?`oh \ e \=_ g m T,lsf `oh g _ ž n rŸNg _ žX \ e k l _L¢{ƒ—p e m=_ g ` ecr b JLe cbª[ k qSg d Q m ž k \^h^
\^d g _a`oh^ % < D=6'++ :;+N:D5< &%!@ 3% ?#9!FB# =D%5!:1C8'½
] k f \ r -ÿ%) $ÿ „S \^`oh f \~ k r ` e ! ecg¦q \^h rag _L¢z $ÿ y ÿ bc~Ì`oh f k e E k pc ?n k eceX pc¡ lsgsr|ž \^h r b
wovSb9ýb Q b¬ýN` r \ e ¡F\^h f b 7 5C8,. ! U =D9!(,. !;'-0 5 : 0%! :;%C8 G;%%'½b
XZž [ _ ž \ ragsr " ! ecg¦q \^h r|g _Y¢ `z U~ g m žcgsf k e  T,ece k h|¡F`oh^F~ g m žcgsf k e  $ÿ (;„Sb
w…Ab p [ e _a\^h9ýNpcdc` l ] ž b e k ~Ìp l _ g¦V 9¡S¥£\^m=_ g¦q \ O¬q ` l pA_ g ` e k h£¢ T,lsf `oh g _ ž n k e d J _ rI ` ezq \=h V
f \ e m^\¬_a`_ ž \ X k h|\=_a` Q \=_$b JLe %<5.=' !:;!: 3%+ 4 ,.!4 %>
C:,.Y!cª] k f \ r w ) w (A XZg¦r m k _ k Ÿ k ¢z K \ Ÿ o\^h r \­¢z $ÿoÿ yAb JYO)O)OÝX h|\ r|r b
w b p [ e _a\^hPýNpcdc` l ] ž k e d T,l \­€ k e dch|p T,f k ] g \ob I ` ezq \=h f \ e m^\ X h|`o]F\^h£_ g \ r `o Q `on«\‚~{p l _ g¦V
,¡A¥£\^m=_ g q \ O¬q ` l pA_ g ` e k h£¢ T,lsf `oh g _ ž n r b JLe <5.='- :; 79888 3%@
4 ,.!4 %> C:,.;! t q ` l pcn6\vSD] k f \ r x x ) x (A XZgsr m k _ k Ÿ k ¢z K \ Ÿ o\^h r \­¢z
op l ¢{vxoxzxAb JYO)O)OÑX h|\ rar b
wowSb OZe h gs¯ pc\ +bAýNp r ] gsecg k e d JLf `oh Q bF} ŸNg h^b T pA_a`zn k _a\^d 9p k lsg _ k _ g¦q \,[P\ r m^h g ]A_ g ` e `o U~{\ k V
r pch|\=n«\ e _ r b JLe <5.=' !: _ : ;' %,.C % ; !`9<-* ' ,. %C ;
N9%:D9 =>= 3%9%­ M \ ecg m^\o J _ k l ¢o $ÿoÿoÿ b
w (Ab O h g m Q k e d f h|\ e b~Ìp l _ g m^h g _a\^h g k dc\ r|gsfoe `z]A_ g n gs§ k _ g ` e ¡z¢ f ` k l ]ch|` f h k n«n gsecf b JLe ,` V
¥?¥ k _ T dc\ lsg —\^d g _a`oh^ B#< 4%' \C8%' =6 <65C8?> ! t—m ž k ]A_a\^h«v…A—] k f \ r vovow ) v (zwSb
Iž k ]cn k e ^ k lsl cüD` e dc` e  $ÿoÿ b
wo„Sb cbc[ k qAg d Q m ž k \^h^b *-,./! <#0 233! 42<
!5C8 >!=0 5 : &A 4 /,"&< ?#%!
B =1%5!:DC8'½b XZž [ _ ž \ ragsr  M k e dc\=h|¡ gsl _ ! ecg¦q \^h rag _Y¢z $ÿ y b
wyAb cb¬[ k qAg d Q m ž k \^h^b#~Ìp l _ g ] l \ 9¡S¥£\^m=_ g¦q \ ,]A_ g n g¦§ k _ g ` eŸNg _ žM \=m=_a`oh O¬q k l p k _a\^d \ V
e \=_ g m T,lsf `oh g _ ž n r b JLe ?#9! B# =D%5 :DC8':<+ :;5BT/!G ! ' <5.='# !:
5%' + &%!( 3% %9%@ ?#%! B# =D%5!:1C8'½] k f \ rÿ … ) xoxcb)ü k Ÿ h|\ e m^\
O h l ¡ k pcn $ÿ yzwSb
w ÿ b cb¶[ k qSg d Q m ž k \^h k e 1d z` žce tb h|\= å\ ecr _a\=_|_a\obP~Ìp l _ g `z¡S¥£\^m=_ g¦q \+üD\ k h ecgsecf qAg k \ e \­_ g m
T,lsf `oh g _ ž n r b JLe <5.=' :;K!: %%4!!4 5 ;: 3%F B#%! 3M
%5/ =.%9% 5$BA c] k f \ r w ÿ … ) w ÿ wSAüD` rT,ecf \ l \ r  I k lsg ?`oh ecg k  $ÿ yzwSb T,T,T,J b
(oxAb K b Q h gsecg¦q k r k e d E k l ¢ k e n«`-¢[9\^¡ub#~Ìp l _ g `o¡S¥£\^m=_ g¦q \ ,]A_ g n gs§ k _ g ` e ! ragsecf'K ` e dc`on g¦V
e k _a\^d Q `zh£_ g¦ecfgse \ e \=_ g m T,lsf `oh g _ ž n r b 4 /,.!%> C:,.; !tv ¨ …z® vov %) v yA
ƒ k lsl $ÿoÿ b
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b &æb Q _ k d l \^h^bƒFp e d k n6\ e _ k lsr `o Nn¤p l _ g m^h g _a\^h g k `o]A_ g n gs§ k _ g ` e b JLe & b Q _ k d l \^h^U\^d g _a`oh^
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b &æb Q _ k d l \^h k e Bd cbz[ k pc\^h^b¶~Ìp l _ g m^h g _a\^h g k `z]A_ g n gs§ k _ g ` e¤gse \ ecfogse \^\^h gsecf T _apA_a`oh g k l k e d
r pch q \=¢ob JLe 7 !%,;3,.X<
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JLecr _ g _apA_a\5`o T \^h|` e k pA_ g m r k e d T,r _ah|` e k pA_ g m r  $ÿzÿ vSb
(o…AbP~ k h|
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( b9[ k qAg d T b M k e6M \ l d ž p gs§ \ e $
b *-,./!10!233!546 4 ,.!%>FB# =1%5!:DC8' V ' ' !;'
B#4 /> '3'X 9<BAF 0 ;94H!;'½b XZž [ _ ž \ r|gsr F[9\^] k h£_an«\ e _P`o OZl \^m­_ah g m k l k e d I `zn V
]cpA_a\^h OZecfogse \^\^h g¦ecf b h k dcp k _a\ Q m ž `;` l `o OZecfogse \^\^h g¦ecf b T,g h5ƒt`oh|m^\ JLecr _ g _apA_a\«`o R \=m žAV
e ` l ` f ¢z"&h g¦fzž _ VLX k _|_a\=h r ` eT ƒ  žcg `ct~ k ¢ $ÿoÿoÿ b
(zwSb9[ k qAg d T b M k eM \ l d ž p gs§ \ e k e d k h£¢ buü k n6` e _$b O¬q ` l pA_ g ` e k h£¢ I `on6]cpA_ k _ g ` e k e d
I ` ezq \=h f \ e m^\«_a` k X k h|\­_a`̃—h|` e _$b JLe o` žce ýb$EP` § k U\^d g _a`oh^ " DF 5.=;%%'
!:;+?#%!@= C8C8 D= _ - 3%=o] k f \ r vzv %) vovoyA Q _ k e å`oh|d2! ecg¦q \^h rag _Y¢z
I k lsg å`oh ecg k $ op l ¢ $ÿoÿ yAb Q _ k e ?`oh|d ! ecg¦q \^h rag _L¢ `S`oû r _a`oh|\ob
(6(Ab9[ k qAg d T b M k e‚M \ l d ž p gs§ \ e k e d k h£¢ boü k n6` e _$bt~Ìp l _ g `z¡S¥£\^m=_ g¦q \ O¬q ` l pA_ g ` e k h£¢ T,lsf ` V
h g _ ž n ýN\ r \ k h|m ž T gsr _a`oh£¢ k e d T,e k l ¢ r|gsr b R \=m žcecg m k l ýN\^]F`oh£_ R ý VLÿ y V xo…A;[9\^] k h£_an«\ e _
`o OZl \^m­_ah g m k l k e d I `on6]cpA_a\^h OZecfogse \^\=h gsecf  h k dcp k _a\ Q m ž `S` l `o OZecfogse \=\^h gsecf  T,g hՃF`oh|m^\
JLecr _ g _apA_a\5`o R \=m žce ` l ` f ¢z" &h gsfož _ VóX k _|_a\^h r ` eT ƒ  žcg `c $ÿoÿ yAb
(z„Sb9[ k qAg d T b M k e‚M \ l d ž p gs§ \ e k e d k h£¢ boü k n6` e _$bt~Ìp l _ g `z¡S¥£\^m=_ g¦q \ O¬q ` l pA_ g ` e k h£¢ T,lsf ` V
h g _ ž n R \ r _ Q p g _a\ r b JLe k ecg m^\ I k h|h|` lsl  g¦raž k n k dcd k duª[ k q \ 9]c]F\ ecž \ g n{ k h|h|\=_|_
h£¢ k e _$ k e d k h£¢ buü k n6` e _$¶\^d g _a`oh r  % <5D=6' :; _ B $* 7 > C:' 5,.C
B <Q C: ,!5.=ot] k f \ r …zw ) …zwo„S Q k eT,e _a` ecg `c R \=€ k r  $ÿoÿzÿ b TNI ~b
(oyAb9[¤b Q bL&\ gsl \o O b~ g m žcg \ lsr|r \ e  k e dÝ[¤b O b ` l dc¡F\^h f b \ e \=_ g m k lsf `oh g _ ž ndc\ ragsfoe `o ] k h|\=_a`{`o]A_ g n k l ¡ch|` k d V ¡ k e dn g m=h|` Ÿ k q \ k ¡ r `zh|¡F\^h r b R \^m žcecg m k l ýN\^]F`zh£_ IIO ~ YV Vóÿ (A
OZl \^m­_ah g m k l k e d I `on6]cpA_a\^h OZecfogse \^\=h gsecf [9\^] k h£_an6\ e _$ I \ e _a\^h— ?`oh I `on«]cpA_ k _ g ` e k lSOZl \^m V
_ah|`on k foe \=_ g m r 9 ! ecg¦q \^h rag _Y¢`o JLlslsgse ` gsr k _ !,h|¡ k e k VLIž k n«] k gsfoe t~ k ¢ $ÿzÿ (Ab
( ÿ bcb¶ƒb& žcg dc¡F`oh e \o¶[¤b V &æb pu k e d J b X ` r _ l \=_ žzŸ k g _a\ob T,lsf `oh g _ ž n r ?`oh,_ ž \+n«\­_ ž `Sd'`o gse \ ¯ p k lsg _ g \ r ) k m^`on«] k h k _ g¦q \ r _apcdA¢ob JLe %<5.=' :; _ T B#C %!G ;
%9 =c] f \ r …o… ÿ … ) …o… ÿ „S Q \ _|_ l \o9
 & ražcgsecf _a` e  $ÿoÿ wSb
„xAb X b b & g \ e ûo\ok I b¬üÕpcm k rag p r  k e d k b E k _a\^k n k e b#~Ìp l _ g m=h g _a\^h g k _ k h f \=_6`o]A_ g n gs§ k _ g ` e
`o k e k l ¢S_ g m k l ]ch|`;m^\^dcpch|\ r p ragsecf k f \ e \=_ g m k lsf `oh g _ ž nb B#4 > !G-
:D5C8!G B 3Y
v (zw ¨ vo® v %) vzvowS $ÿoÿ vSb
„ b X b b & gslsr ` e k e d6~bo[‚bz~ k m l \^`;dubªüÕ` ŸÓg n6] l \^n6\ e _ k _ g ` e m^` r _ JLJ ýÝd gsfog _ k l l _a\^hZdc\ ragsfoe
p rag¦ecf5f \ e \=_ g m k l¦f `oh g _ ž n r b JLe /) GF ': AK ,.XB# =1%5!:DC8' 5 7 =6
r Z%) Z yc Iž \ l n r ?`oh|du" !+b E‚bs $ÿoÿ …Ab
' ' 5D=oc] f \ „ovSb9ýb Q b}¶\^¡cp l pck n{~b T b X k m ž \^m=`t k e d~b M \ lsl k r m^`cb T n¤p l _ g¦V `o¡S¥£\^m=_ g¦q \'`o]A_ g n gsr k V
_ g ` e n«\­_ ž `Sdc` l ` f ¢ k ]c] lsg \^d_a`‚_ ž \ r ¢ e _ ž \ r|gsr `o l ` ŸV ]ª` Ÿ \=h`o]ª\=h k _ g ` e k l k n«] lsg t\^h r b JLe
Jóq k e z`oh f \ Iž \^pch g k e d I k h l ` rPT,l ¡F\^h£_a`dc` r ýN\ gsr ƒ gsl¦ž `t¶\^d g _a`oh r 6 % < D=6' 8!:
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v ( ) vo„  I pch g _ g ¡  h §^gsl  T p f p r _ $ÿoÿ yAb
„…Ab \ ecf p g } ž `op k e kdÝ~ g k_ r pc` \ e b \ e \­_ g m T,lsf `zh g _ ž n T ]c]ch|` k m ž ` e ~{p l _ g¦VLI h g _a\^h g k
~ g¦ecg n¤pcn Q ] k ececgsecfR h|\=\ X h|`o¡ l \^nb ,.G; 5,.% ]<
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5C8?> !4$* !:. <'
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Q;ŸNg _ § \^h l k e du K ` q \^n¤¡F\^h $ÿoÿzÿ b
„owSb O m½û k h£_} g _ §^l \^h^1 E k l ¢ k e n«`$¢6[9\^¡u k e d üD`_ ž k h Ržcg \ l \b I `on6] k h g¦r ` e `o Õ~Ìp l _ g `z¡S¥£\^m=_ g¦q \
O¬q ` l pA_ g ` e k h£¢ T,lsf `zh g _ ž n r O n«] g h g m k l ýN\ r p l _ r b 4 ,.!%>B C: ,Y!czy ¨ vz® „… )
$ÿ wA Q pcn6n«\^hNvxoxoxAb
„ (Ab O m½û k h£_Ì} g _ §=l \^h^
 '[pch f \ eR \ g m ž  e d QSž p q h Q b ž _|_ m ž h£¢;¢ b~Ìp l _ g d g n«\ ecr|g ` e l
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