presentation on ga
TRANSCRIPT
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NATURAL EVOLUTION AS APROCESS OPTIMISATION
Dr. R. BALU,Professor,Department of Aeronautical Engineering,Noorul Islam College of Engineering,Kumaracoil, K K District, TamilNau, !"#$%&
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Optimised Man!Optimised Man!
Tracey’s personal photograph collection
Mr. Tracey Cool,
Rolls Royce
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WR21 GAS TURBINEWR21 GAS TURBINE
ASSEMBLYASSEMBLY
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WR21 ENGINE HARDWARE
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Marie Gas T!r"ie # WR21
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WR21 Schematic
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Spiral RecuperatorSpiral Recuperator
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W$a% &ro'er%ies Ma(e a Goo)W$a% &ro'er%ies Ma(e a Goo)
Hea% E*c$a+erHea% E*c$a+er EffectivenessEffectiveness maximisedmaximised
– How efficient the heat exchane! isHow efficient the heat exchane! is
Vo"#meVo"#me minimisedminimised
– Sma""e! $ "ihte! % chea&e!Sma""e! $ "ihte! % chea&e!
P!ess#!e '!o& (!actionP!ess#!e '!o& (!action minimisedminimised
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What Parameters Can Vary?What Parameters Can Vary?
&ar%i+ s$ee% %$ic(ess&ar%i+ s$ee% %$ic(ess
-i %y'e-i %y'e -i %$ic(ess-i %$ic(ess
-i )esi%y-i )esi%y
Layer $ei+$%Layer $ei+$% Layer arra+ee%Layer arra+ee%
N!"er o/ layersN!"er o/ layers
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Co'oe%s o/ a Hea%Co'oe%s o/ a Hea%
E*c$a+er E*c$a+er
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Variable ParametersVariable Parameters
“Heat Transfer and Fluid Flow Service Handbook” Sheet YM! ""!
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0aria"le &arae%ers0aria"le &arae%ers
• Hot layer heiht hh
• Cold layer heiht hc
• Hot layer in thic"ness th
• Cold layer in thic"ness tc
• Hot layer in density dh
• Cold layer in density dc
• #$mber o layers #
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Lii%s o 0aria"le &arae%ers
$$
$c%$
%c
)$)c
N
# 2
# 2 .2 # .3
.2 # .3
14 #1 # 12 #114 #1 # 12 #1
4 # 24 layer 'airs
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-i%ess
/:771#ε90ra%9
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#ontribution to “chro$oso$e”#ontribution to “chro$oso$e”
%ariable%ariable
hhhh hhcc tthh ttcc ddhh NN
ddcc
Whole systemWhole system
Binary StringBinary String
11 characters11 characters 11 characters11 characters
9 characters9 characters
9 characters9 characters
11 characters11 characters
11 characters11 characters
8 characters8 characters
70 character string70 character string
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What o$r ) man * has achie+ed ?What o$r ) man * has achie+ed ?
, enetic alorithm de+eloped -ointly by Rolls Royce and Rensselaer , enetic alorithm de+eloped -ointly by Rolls Royce and RensselaerPolytechnic .nstit$te prod$ced a hih/perormance marine enine desinPolytechnic .nstit$te prod$ced a hih/perormance marine enine desinthat 0asthat 0as
o$r times better than a h$man/desined coni$rationo$r times better than a h$man/desined coni$ration
M$ch better than a coni$ration desined by an e'pert system byM$ch better than a coni$ration desined by an e'pert system bys$ccess$lly na+iatin a sol$tion space containin more than 1345s$ccess$lly na+iatin a sol$tion space containin more than 1345possibilities6possibilities6
the enetic alorithm disco+ered this sol$tion on a typical enineerinthe enetic alorithm disco+ered this sol$tion on a typical enineerindes"top 0or"station ater e+al$atin abo$t 7 possibilities in a typicaldes"top 0or"station ater e+al$atin abo$t 7 possibilities in a typical
time rame o a daytime rame o a day
Con+entional methods or desinin s$ch t$rbines can ta"eCon+entional methods or desinin s$ch t$rbines can ta"e
$p to i+e years and$p to i+e years and
cost o+er 82 billion9cost o+er 82 billion9
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Gee%ic Al+ori%$ &arae%ersGee%ic Al+ori%$ &arae%ers
3#c$arac%er "iary s%ri+ /or eac$ +ee3#c$arac%er "iary s%ri+ /or eac$ +ee co%ais i/ora%io o eac$ o/ %$e 3co%ais i/ora%io o eac$ o/ %$e 3
5aria"les5aria"les
4 "iary s%ri+s i eac$ 'o'!la%io4 "iary s%ri+s i eac$ 'o'!la%io 1 +eera%ios1 +eera%ios
!%a%io ra%e o/ .1!%a%io ra%e o/ .1
eli%is e'loye)eli%is e'loye) ==/i%%es%> s%ri+ is re'ea%e) i %$e e*%/i%%es%> s%ri+ is re'ea%e) i %$e e*%
+eera%io+eera%io
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#o6 O :heoretical Possibilities#o6 O :heoretical Possibilities
5 character ;inary strin < typical or5 character ;inary strin < typical or
practical %, problems =practical %, problems =
22 5252 > 1> 1 ?5?5 possibilitiespossibilities #o6 o #anoseconds in one billion years >#o6 o #anoseconds in one billion years >
11 @@ ' 37 ' 4A > 1' 37 ' 4A > 1 1?1?
An unimaginable huge task !! An unimaginable huge task !!
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Ii%ial a) 1%$ Geera%ioIi%ial a) 1%$ Geera%io
67
6
65
64
6@
1
627 67 657 1
Vol$me Ratio
& ! ! e c t i + e
n e s s
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Variable Parameters OptimisedVariable Parameters Optimised
Ho% layer $ei+$%Ho% layer $ei+$% # ?.@ # ?.@
Col) layer $ei+$%Col) layer $ei+$% # .3 # .3
Ho% layer /i %$ic(essHo% layer /i %$ic(ess # .24 # .24
Col) layer /i %$ic(essCol) layer /i %$ic(ess # .24 # .24
Ho% layer /i )esi%yHo% layer /i )esi%y # @@4 # @@4 #1#1
Col) layer /i )esi%yCol) layer /i )esi%y # 1?4 # 1?4 #1#1
N!"er o/ layersN!"er o/ layers # 2# 2
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#at$re*s Startin Point !!#at$re*s Startin Point !!
< Mr :racey Cool*s B6< Mr :racey Cool*s B6
%randather !! =%randather !! =
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NATURES &TIMISATIN
A +ol) /is$ $ic$ cae /ro C$ia, 'rice) a% @4, Is )is'laye))!ri+ %$e -is$loo( 2 e*$i"i%io i Fa(ar%a I)oesia, Si+a'ore a) Malaysia are 'ar%ici'a%i+ i %$e se5e )ay e*$i"i%io‑
%o /i) %$e +ol) /is$ i%$ %$e ices% colo!r a) s$a'e.
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-ISH MILLIN YEARS AG
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NATURES CREATINSNATURES CREATINS
PO,R ;&,R ,#D .:SPO,R ;&,R ,#D .:S
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PO,R ;&,R ,#D .:SPO,R ;&,R ,#D .:S
SEEROE#D.#%SSEEROE#D.#%S
POLAR BEARS HUDDLE TOGETHER TO ESACPE RO BE"#G HU#TED OR SA$E THESEL$ES RO ASCUDD"#G S#O%STOR
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WHAT IS COVEREDWHAT IS COVERED ??
&TIMISTATIN&TIMISTATIN CLASSICAL GRADIENT BASED METHDSCLASSICAL GRADIENT BASED METHDS NATURAL E0LUTINNATURAL E0LUTIN
NATURE T CM&UTER MA&&ING THENATURE T CM&UTER MA&&ING THEGENETIC ALGRITHMGENETIC ALGRITHM
BASIC INGREDIENTS - GABASIC INGREDIENTS - GA WHY D GAs WR THE SCHEMATAWHY D GAs WR THE SCHEMATA
THEREMTHEREM GA#13 GA DRI0ER S-TWAREGA#13 GA DRI0ER S-TWARE EAM&LES - A&&LICATINEAM&LES - A&&LICATIN GA STRATEGIES # HW T MAE THEM WRGA STRATEGIES # HW T MAE THEM WR
BETTERBETTER CNCLUSINSCNCLUSINS
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THE RMAN GDDESS &STHE RMAN GDDESS &S
)I(E O( SATURN)I(E O( SATURN** THE +O' O( TIMETHE +O' O( TIME
MOTHER O(MOTHER O(,UPITER,UPITER
** THE +O' O(THE +O' O(PO)ER PO)ER
A Fitting patroness of A Fitting patroness of science of science ofoptimisationoptimisation
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Optimisation
-- '(for Englis) Dictionar*
“ To make the best or most effective use of
a situation or an opportunity “
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&TIMISATIN&TIMISATIN
.n a broader sense and in the conte't o.n a broader sense and in the conte't oenineerin desinF it can be deined as aenineerin desinF it can be deined as aprocess o indin or identiyin the best romprocess o indin or identiyin the best romamon a collection o alternati+esF 0itho$tamon a collection o alternati+esF 0itho$te'plicitly e+al$atin or en$meratin all o them6e'plicitly e+al$atin or en$meratin all o them6
.n essenceF it ma"es a.n essenceF it ma"es a desired quantitydesired quantity
maximum or an undesired quantity minimummaximum or an undesired quantity minimum,, 0hen this G$antity is a comple' $nction o many0hen this G$antity is a comple' $nction o many
independent parameters or +ariables6independent parameters or +ariables6
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Optimisation Methods
Local TechniquesGlobal Techniques
Si'le*
J!asi Ne%o
Gra)ie% Me%$o)s Ra)o Wal(
Si!la%e) Aeali+
Genetic Algorithms
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OP M!A O" # A" $%AMPL$
P M!A O" # A" $%AMPL$
Optimisation is at work at all times in our life, knowingly
or unknowingly
Adjusting the focusing knob of an optical instrument( camera, binocular )
Objective function ------- Good mage
!ariables"ocal length the lenses
#ime of $%posure
&ighting in the environment
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SME MRE EAM&LESSME MRE EAM&LES
%$er E*a'les;%$er E*a'les;
S$a'e /or %$e co//ee 'o% $a)leS$a'e /or %$e co//ee 'o% $a)le A a%ios ea'os s%oc(#'ileA a%ios ea'os s%oc(#'ile Mi* o/ i+re)ie%s /or s%re+%$ o/ cocre%eMi* o/ i+re)ie%s /or s%re+%$ o/ cocre%e &rocess /or re/ii+ 'e%role!&rocess /or re/ii+ 'e%role!
S$a'e o/ a /lyi+ o"Kec% /or ii! )ra+S$a'e o/ a /lyi+ o"Kec% /or ii! )ra+ Wei+$% o/ T$eral Is!la%io /or aWei+$% o/ T$eral Is!la%io /or a
Re#e%ry 0e$icleRe#e%ry 0e$icle
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'iffe!entia" Ca"c#"#s'iffe!entia" Ca"c#"#s(#nction of Sin"e Va!ia-"e(#nction of Sin"e Va!ia-"e
. $ f /x0. $ f /x0
y
&
y ' (
y ' )
y ' (
ma&
min
y* )
y* (
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More Co'le* -!c%iosMore Co'le* -!c%ios
M&'' () *SS+ )&',(&)"
Direc%i5i%y &a%%er o/ A A%ea
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W$ere are e
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.
* a$ at the %alley
* have found the
peak
I am also at the valley
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-!c%io o/ Se5eral 0aria"les-!c%io o/ Se5eral 0aria"les
y ' f ( %, %, %*, ++++%i,+++++% ) ' f ( X )
% ' (%
, %
, %*
, ++++%i
,+++++%
)
Gradient ( "irst Order .erivatives )
f( % ) ' ( /f 0 / %, /f 0 / % , /f 0 / %*, /f 0 / %i, /f 0 / % )# ' grad ( f )
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-!c%io o/ Se5eral 0aria"les-!c%io o/ Se5eral 0aria"les
Hessian Mat!ix / Second O!de!Hessian Mat!ix / Second O!de!
'e!ivatives 0'e!ivatives 0 ▼▼11 f/ x 0 $f/ x 0 $
/ 2/ 211 f 32 xf 32 x44115 25 211 f 32 xf 32 x44xx115 666 25 666 211 f 32 xf 32 x44xxNN 00
/ 2/ 211 f 32 xf 32 x44xx115 25 211 f 32 xf 32 x11115 666 25 666 211 f 32 xf 32 x44xxNN 00
/66666666666666677766770/66666666666666677766770
/666666666666666666770/666666666666666666770
/ 2/ 211 f 32 xf 32 xNNxx445 25 211 f 32 xf 32 xNNxx115 6667725 66677211 f 32 xf 32 xNN11 00
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CNDITINS -R MAIMA ANDCNDITINS -R MAIMA AND
MINIMAMINIMA
f (f (&
) =) = grad ( f (grad ( f ( &
& ) ) = 0) ) = 0
22 f (f (&
) is psiti!" # d"$%it" fr) is psiti!" # d"$%it" fr
&i%i&'&&i%i&'&
is %"gati!" # d"$%it" fris %"gati!" # d"$%it" fr&ai&'&&ai&'&
"r i%dicat"s i%*"cti%"r i%dicat"s i%*"cti%
pi%tpi%t
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N!erical E5al!a%io "y -ii%eDi//ereces
(i!st O!de! 'e!ivatives
Sim&"e (o!wa!d o! 8ac9wa!d'iffe!ences
Re:#i!es 1 f#nction Eva"#ations fo!each de!ivative
Tota"". 1N f#nction Eva"#ations fo!a"" de!ivatives
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"umerical $valuation by +inite"umerical $valuation by +inite
,ifferences,ifferences
Seco) r)er Deri5a%i5esSeco) r)er Deri5a%i5es
22/ : */ : *ii22 ee)s /!c%io E5al!a%iosee)s /!c%io E5al!a%ios
22/ : */ : *ii ** ee)s /!c%io E5al!a%iosee)s /!c%io E5al!a%ios
To%ally 2NTo%ally 2N22 1 /!c%io E5al!a%ios /or all 1 /!c%io E5al!a%ios /or all
%ers o/ Hessia Ma%ri*%ers o/ Hessia Ma%ri*
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GRADIENT SEARCH DIRECTINGRADIENT SEARCH DIRECTIN
A% 'oi% O* O ay searc$ )irec%io )A% 'oi% O* O ay searc$ )irec%io )7%97%9 isis
a )esce% )irec%io i/ a )esce% )irec%io i/ /7*9./7*9. ))7%97%9 P .P .
T$e )esce% )irec%io #/7*9 +i5es %$eT$e )esce% )irec%io #/7*9 +i5es %$e
a*i! ao!% o/ )esce%. Hece i%a*i! ao!% o/ )esce%. Hece i%
is calle) as %$e s%ee'es% )esce%is calle) as %$e s%ee'es% )esce%
)irec%io.)irec%io.
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GENERAL &TMISATINGENERAL &TMISATIN
&RBLEM WITH CNSTRAINTS&RBLEM WITH CNSTRAINTS
Miiise / 7 * 9 s!"Kec% %o
+ K 7 * 9 Q , K 6 1, 2, , .. ...F Ie!ali%y Cos%rai%s
$ ( 7 * 9 6 , ( 6 1, 2, , ... E!ali%y Cos%ri%s
*i7L9 P *i P *i
7U9 I 6 1, 2, ,..N
A sol!%io is /easi"le i/ a) oly i/ all %$e a"o5e are sa%is/ie).
Ay o%$er sol!%io is i/easi"le. T$!s a i/easi"le 'oi% ca
e5er "e a o'%i! 'oi%.
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;UHN*TUC;ER;UHN*TUC;ERCON'ITIONSCON'ITIONS
La+ra+ia M!l%i'lier Tec$i!e is !se) %o co5er% %$e cos%raie)o'%iisa%io 'ro"le i%o a !cos%raie) 'ro"le "y o)i/yi+%$e o"Kec%i5e /!c%io %o icl!)e %$e cos%rai%s
/ 7 * 9 ! K + K7*9 # 5( ▼$(7*9 6
i%$
+ K 7 * 9 Q , K 6 1, 2, , .. ...F Ie!ali%y Cos%rai%s
$ ( 7 * 9 6 , ( 6 1, 2, , ... E!ali%y Cos%ri%s
! K + K7*9 6 K 6 1, 2, , F ly /or E. cos%rai%s
! K Q K 6 1, 2, , ..F
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S:,%&S .# HEM,# &VOE:.O#
S%oe A+e # 2 MillioYears %o E+y'%ia Dyas%y &aleoli%$ic 14 Years # H!%i+, +a%$eri+.
No Tec$ical &ro+ress e*ce'% 'er$a's Ca5e&ai%i+s
Mesoli%$ic @ Years # S%oe#Wor(i+ Ma%erial :Tools Be+ii+ o/ Tec$olo+ical a)5acee% Neoli%$ic # Broe A+e Io5a%ios a) Crea%i5i%y
S%oe:Woo):Me%als &yrai)s ere "!il% Hellesi%ic # Gree( Ci5ilisa%io # 1 s% Ce%!ry BC
Mi))le A+es Roa Ci5ilisa%io I)!s%rial Re5ol!%io Mo)er Co'!%er : S'ace Era 1?4s ar)
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DARWINIAN H+,OTHESISDARWINIAN H+,OTHESIS
Charles Dar0in )Charles Dar0in ) On the Origin of Species byOn the Origin of Species by
means of Natural Selectionmeans of Natural Selection ) < 147@ =) < 147@ =
Primary Dri+in Mechanism o &+ol$tion isPrimary Dri+in Mechanism o &+ol$tion is
Na%!ral Selec%ioNa%!ral Selec%io .ndi+id$als ;etter ,dapted to en+ironment 0ill.ndi+id$als ;etter ,dapted to en+ironment 0ill
lea+e behind F on an a+eraeF more o sprinslea+e behind F on an a+eraeF more o sprins
than their less adapt collea$es6than their less adapt collea$es6S$r+i+al o the ittestS$r+i+al o the ittest
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G$$#1 "O23A#O #2A4"$2
T$e i/ora%io )e%erii+ %$e+ro%$ a) )e5elo'e% o/ i)i5i)!also/ a s'ecies is eco)e) i %$eir +ees.
I se*!al s'ecies, $e %o i)i5i)!als"ree), co'lee%ary 'or%ios o/ %$eir
+ee%ic a%erial 7c$roosoes9 are'asse) o %o %$eir o// s'ri+ ra)oly6
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TW ESSENTIAL INGREDIENTSTW ESSENTIAL INGREDIENTS
• .#H&R.:,#C& ( O sprins m$st retain at least some o the
eat$res that made their parents itter than
a+erae6 Other0ise e+ol$tion is reset at e+eryeneration
• V,R.,;..: ( ,t any i+en time indi+id$als 0ith +aryin
itness m$st co/e'ist in the pop$lation6Other0ise nat$ral selection has nothin tooperate $pon6
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A &&ULATIN - RABBITS
+O% P-$.! O" /$M
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!OM$ -A00 ! A-$ +A! $- A", !MA- $-
/$. A-$ L$!! L1$L. O 0$ $A $" 0.
/$ +O%
MO-$ O+ !23/ !MA- $- O"$! $", O
!2-44$ O" A" A4$-AG$
/$. $", O 0-$$, AMO"G
/$M!L$4$! A", AL!O AMO"G
L$!!5!MA- $- O"$!
-A00T !TO-.
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-A00 ! O-.
A00 ! O-.
IT RES-.TS IN A /OOD I1 O /OOD RA33IT4SIT RES-.TS IN A /OOD I1 O /OOD RA33IT4S/ENETIC ATERIA./ENETIC ATERIA.
O CO-RSE5 EVEN D-3 AND S.OWER ONESO CO-RSE5 EVEN D-3 AND S.OWER ONESS-RVIVES-RVIVE
3ECA-SE O .-C65 AND THE+ A.SO ATE AND3ECA-SE O .-C65 AND THE+ A.SO ATE AND3REED3REED
THE O7S,RIN/S WI..5 ON AN AVERA/E5 3ETHE O7S,RIN/S WI..5 ON AN AVERA/E5 3ESARTER AND ASTER THAN THEIR ,ARENTS INSARTER AND ASTER THAN THEIR ,ARENTS INORI/INA. ,O,-.ATION 3ECA-SE ON.+ THEORI/INA. ,O,-.ATION 3ECA-SE ON.+ THEITTEST S-RVIVE WITH ORE ,RO3A3I.IT+ ITTEST S-RVIVE WITH ORE ,RO3A3I.IT+
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NATURES &RINCI&LENATURES &RINCI&LE
;&S: .#D.V.DE,S R&P.C,:& ,#D;&S: .#D.V.DE,S R&P.C,:& ,#D%&: PROP,%,:&D .# :H&%&: PROP,%,:&D .# :H&
POPE,:.O# MOR& ,#D MOR&POPE,:.O# MOR& ,#D MOR&
,V&R,%& .#D.V.DE,S S:, O# ,V&R,%& .#D.V.DE,S S:, O#
WORS: .#D.V.DE,S WH.:H&R ,W,WORS: .#D.V.DE,S WH.:H&R ,W, ,#D D.& , #,:ER, D&,:H ,#D D.& , #,:ER, D&,:H
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MM31"G "AT2-ALMM31"G "AT2-AL
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MM31"G "AT2-ALMM31"G "AT2-AL
$4OL2TO"$4OL2TO"
"A 2-$ P-O3$!!
A 2-$ P-O3$!!
+ene!ation+ene!ation < n
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MATHEMAT!S MATHEMAT!S
Geera%io Geera%io
Selec% /easi"le se%s o/ i)e'e)e% 5aria"les ii%ial 'o'!la%ioSelec% /easi"le se%s o/ i)e'e)e% 5aria"les ii%ial 'o'!la%io
T$ese are co)e) as +ees 7s%ri+s o/ "iary : real !"ers9T$ese are co)e) as +ees 7s%ri+s o/ "iary : real !"ers9
Ra( %$e "y %$e o"Kec%i5e /!c%io a) selec% %$e "es% /eRa( %$e "y %$e o"Kec%i5e /!c%io a) selec% %$e "es% /e
Allo %$e %o "ree) "y crossi+ %$eir +ees a% ra)o 'osi%iosAllo %$e %o "ree) "y crossi+ %$eir +ees a% ra)o 'osi%ios
To i%ro)!ce 5aria"ili%y !%a%e %$e s%ri+s ra)olyTo i%ro)!ce 5aria"ili%y !%a%e %$e s%ri+s ra)oly
Ne*% Geera%io 7 i%era%io 9Ne*% Geera%io 7 i%era%io 9
MM31"G "A 2-AL
M31"G "A 2-AL
$4OL2 O"
4OL2 O"
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NATURE T CM&UTER MA&&INGNATURE T CM&UTER MA&&ING
#,:ER,:ER& CM&UTERCM&UTER",4,2AL O+ T/$ !P$3$!
POP2LTO"
POP2LATO"
+T"$!! TO $"4-O"M$"T
3/-OMO!OM$
!$L$3TO"
3-O!!!)O4$-
M2TATO"
$4OL2TO"
&SSIBLE SLUTINS
SET - SLUTINS
BFECTI0E -UNCTIN
CDING -R INDE&ENDENT0ARIABLES
SEARCH &ERATRS T MIMICGENETIC BREEDING
&TIMAL SLUTIN
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%, H.S:OR%, H.S:OR
1@7 Modelin ;ioloical &+ol$tion1@7 Modelin ;ioloical &+ol$tion &+en in the ormati+e years o &lectronic Comp$ter&+en in the ormati+e years o &lectronic Comp$ter
Re+ol$tionRe+ol$tion
1@2 %&P ;OIF %J redmanF WW ;eldman //1@2 %&P ;OIF %J redmanF WW ;eldman //&+ol$tionary ,lorithms or Optimisation and&+ol$tionary ,lorithms or Optimisation and
Machine earninMachine earnin
1@71@7 .no.no Rec$e"er+Rec$e"er+ , Ui5ersi%y o/ Berli,, Ui5ersi%y o/ Berli,
i%ro)!ces e5ol!%io s%ra%e+ies, a e%$o) $ei%ro)!ces e5ol!%io s%ra%e+ies, a e%$o) $e!se) %o o'%iie real 5al!e) 'arae%ers /or!se) %o o'%iie real 5al!e) 'arae%ers /or
)e5ices. 7 air /oils 9)e5ices. 7 air /oils 9
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GA /!TO-.GA /!TO-.
Gee%ic al+ori%$s ere i5e%e) "y =Gee%ic al+ori%$s ere i5e%e) "y =Fo$Fo$Holla)Holla)> i %$e 1?Vs a) ere la%er )e5elo'e) "y> i %$e 1?Vs a) ere la%er )e5elo'e) "yHolla) a) $is s%!)e%s a) collea+!es a% %$eHolla) a) $is s%!)e%s a) collea+!es a% %$eUi5ersi%y o/ Mic$i+a i %$e 1?Vs a) 1?3s.Ui5ersi%y o/ Mic$i+a i %$e 1?Vs a) 1?3s.
Holla)s 1?34 "oo( =A)a'%a%io i Na%!ral a)Holla)s 1?34 "oo( =A)a'%a%io i Na%!ral a)Ar%i/icial Sys%es> 'rese%e) %$e +ee%icAr%i/icial Sys%es> 'rese%e) %$e +ee%ical+ori%$s as a a"s%rac%io o/ "iolo+ical e5ol!%ioal+ori%$s as a a"s%rac%io o/ "iolo+ical e5ol!%io
a) +a5e a %$eore%ical /raeor( /or a)a'%a%ioa) +a5e a %$eore%ical /raeor( /or a)a'%a%io!)er %$e +ee%ic al+ori%$s.!)er %$e +ee%ic al+ori%$s.
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GA /! O-.
A /! O-.
1@4*s sa0 many a )real/0orld* applications d$e to1@4*s sa0 many a )real/0orld* applications d$e to.nternet re+ol$tion and increase in po0er o Pc*s.nternet re+ol$tion and increase in po0er o Pc*s Pattern RecoonitionPattern Recoonition
lo0 Control De+iceslo0 Control De+ices
Str$ct$ral OptimisationStr$ct$ral Optimisation Micro/chips DesinMicro/chips Desin ,erospace ,pplications ,erospace ,pplications Micro/;ioloyMicro/;ioloy
1@@*s sa0 commercial and b$siness applications1@@*s sa0 commercial and b$siness applications Stoc" Mar"et PredictionsStoc" Mar"et Predictions Sched$lin and PlanninSched$lin and Plannin
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&INEERS - GA&INEERS - GA
FHN HLLAND 7 1?34 9FHN HLLAND 7 1?34 9 ( Di+i%al Biolo+yDi+i%al Biolo+y
( N!erical Gee%icsN!erical Gee%ics
DA0ID GLDBERG 7 1?@4 9DA0ID GLDBERG 7 1?@4 9 MICHAELWIC 7 1??V 9MICHAELWIC 7 1??V 9
FHN CA 7 1???9FHN CA 7 1???9
Bar"ara Mis(er 7 29Bar"ara Mis(er 7 29 ALYANMY DEB 7 IIT AN&UR 9ALYANMY DEB 7 IIT AN&UR 9
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STARTING SHA&E
&TIMISED SHA&E
DEINITION O THE /ENETICDEINITION O THE /ENETIC
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DEINITION O THE /ENETICDEINITION O THE /ENETIC
A./ORITHA./ORITH
,RO8 9OHN CO::A ( STANORD ),RO8 9OHN CO::A ( STANORD )
Th"Th" genetic algorithmgenetic algorithm is a pr;a;a
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0A!3
"G-$,$" ! O+
GA
8 G$"$ 3 -$-$!$" A O" O+
",$P$",$" 4A-A0L$!
8 M$ /O, O 3-$A $ " AL
POP2LA O"
8
$4AL2A O" +2"3 O" O -A $
/$ + "$!! 9 O0:$3 4$
+2"3 O" ;
8
G$" 3 OP$-A O-! O $4OL4$ /$
POP2LA O" O "$% G$"$-A O"
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T$e Gee%ic Al+ori%$ A''roac$
De/ie lii%s o/ 5aria"le 'arae%ers
Geera%e a ra)o 'o'!la%io o/
)esi+sAssess =/i%ess> o/ )esi+s
Ma%e selec%io
Crosso5er
M!%a%io
Reassess /i%ess o/ e 'o'!la%io
3/-OMO!OMAL3/-OMO!OMAL -$P-$!$"TATO"-$P-$!$"TATO"
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3/-OMO!OMAL3/-OMO!OMAL -$P-$!$"TATO"-$P-$!$"TATO"
-*+./Y ST/*+0 T1 /23/2S2+T /2.4-*+./Y ST/*+0 T1 /23/2S2+T /2.4%.452S 1F .+ *+6232+62+T%.452S 1F .+ *+6232+62+T%./*.-42 7%./*.-42 7
M*+*M5M %.452 1F 7 , 7M*+*M5M %.452 1F 7 , 744 M.7*M5M %.452 1F 7 , 7M.7*M5M %.452 1F 7 , 755 .##5/.#Y /285*/26 , 9d’ deci$al.##5/.#Y /285*/26 , 9d’ deci$al
places places
61M.*+ 42+0TH61M.*+ 42+0TH
''dd
:7:7
55 ,7,7
44;;
F*+6 9+’ S5#H TH.TF*+6 9+’ S5#H TH.T
!! :+,;:+,; < '< 'dd :7:755 ,7,744; < !; < ! + +
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3/-OMO!OMAL
/-OMO!OMAL -$P-$!$" A O"
$P-$!$" A O"
• THE BINARY STRINGTHE BINARY STRING
• (b(bn-1n-1bbn-2n-2bbn-3n-3……..b……..b22,b,b11,b,b00) is equal !) is equal ! "b"bii 22ii i # 0,i # 0,1, 2,…..N-11, 2,…..N-1
• $e %is be &''$e %is be &''
• T%e eal nube & # &T%e eal nube & # &$$ * &+* &+ (&(& -&-&$$) ( 2) ( 2 NN -1-1 ))
•Sin ( 000000…………….0000 ) /!es!ns !Sin ( 000000…………….0000 ) /!es!ns !&&$$
• Sin ( 1111111…………..11111) /!es!nsSin ( 1111111…………..11111) /!es!ns!! &&
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CHROOSOA. RE,RESENTATIONCHROOSOA. RE,RESENTATION
EACH O THE IN,ENDENT VARIA3.E 1 () WI.. 3EEACH O THE IN,ENDENT VARIA3.E 1 () WI.. 3ETRANSORED INTO 3INAR+ STRIN/TRANSORED INTO 3INAR+ STRIN/
O .EN/TH (&O .EN/TH (& (i)(i) ) as a;!"8) as a;!"8
IN THE CO3INED STRIN/5 THE IRST &IN THE CO3INED STRIN/5 THE IRST &BB 3ITS WI..3ITS WI..
RE,RESENT VARIA3.E RE,RESENT VARIA3.E B55B55 THE NE1T &THE NE1T &22 3ITS 3ITS 22 ANDANDSO ON8 THE TOTA. STRIN/ .EN/TH WI.. 3ESO ON8 THE TOTA. STRIN/ .EN/TH WI.. 3E &&ii
B00B0BBB00B0BB0B0B0B0BB0BB0BBB000B0B0BB000B0B0 0B0BB00B000B00B0BB00B000B0
B 2 FB 2 F
TOTA. STRIN/ .EN/TH =TOTA. STRIN/ .EN/TH = && =B525GGG886 =B525GGG886
/ENERATION O INITIA./ENERATION O INITIA.
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/ENERATION O INITIA./ENERATION O INITIA.
,O,-.ATION,O,-.ATION
K /ENERATE RANDO N-3ERS 3ETWEEN 0/ENERATE RANDO N-3ERS 3ETWEEN 0a%d B8 I IT .IES 3ETWEEN 0 a%d 08F TA6E THEa%d B8 I IT .IES 3ETWEEN 0 a%d 08F TA6E THE3IT AS 04 AND I IT .IES 3ETWN 08F a%d B803IT AS 04 AND I IT .IES 3ETWN 08F a%d B80TA6E THE 3IT AS B4TA6E THE 3IT AS B4
K /ENERATE RANDO N-3ERS AND/ENERATE RANDO N-3ERS ANDCREATE THE IRST SET O INDE,ENDENTCREATE THE IRST SET O INDE,ENDENTVARIA3.ES WITHIN THEIR A..OWA3.E RAN/EVARIA3.ES WITHIN THEIR A..OWA3.E RAN/E
K SII.AR.+ /ENRATE N,O,SI:E4 SETS8 THISSII.AR.+ /ENRATE N,O,SI:E4 SETS8 THISCONSTIT-TES THE INITIA. ,O,-.ATION ORCONSTIT-TES THE INITIA. ,O,-.ATION OR
THE ,RO3.E8THE ,RO3.E8K N,O,SI:E CAN 3E T+,ICA..+ AS .OW AS B0N,O,SI:E CAN 3E T+,ICA..+ AS .OW AS B0
AND AS HI/H AS B00AND AS HI/H AS B00
DECDING AND -ITNESS
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DECDING AND -ITNESSE0ALUATIN
DECDE THE BINARY STRING TREAL 0ALUES - 0ARIABLES *7i9i61,2,.( , -R EACH SET -
THE &&ULATIN0i 7 *1i, *2i, *i, .*(i9 i 6 1,2,.N&&SIE
E5al!a%e %$e "Kec%i5e /!c%io /or eac$ o/ 57i9
/7i9 6 o"K757i99 I 6 1,2,..N&&SIE
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.:#&SS &V,E,:.O#.:#&SS &V,E,:.O#
• -i) To%al BFECTI0E -UNCTIN - 6 / 7i9i61,2,.N&&SIE
• Calc!la%e %$e 'ro"a"ili%y o/ selec%ioaccor)i+ %o i%s o /i%ess
• '7i9 6 /7i9 : -
• -i) %$e c!!la%i5e 'ro"a"ili%y 7i9 6 '7K9 K 61,2,,,I
S C O O S
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S&&C:.O# M&:HODSS&&C:.O# M&:HODS
• &.:.S: S&&C:.O#• .:#&SS PROPOR:.O#,:& S&&C:.O#
• RULETTE WHEEL SELECTIN
• SC,.#% S&&C&:.O#• :OER#,M: S&&C:.O#
• R,#L S&&C:.O#
• %&R,:.O#, S&&C:.O#
• S:&,D S:,:& S&&C:.O#
• H.&R,RCH., S&&C:.O#
SELECTIN RULETTE
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SELECTIN RULETTEWHEEL
GENERATE A RANDM NUMBER O r O I/ r X 719 c$oose 0719
I/ o% c$oose 07i9 s!c$ %$a%
7i#19 X r X 7i 9
I% is li(ely %$a% sae c$roosoe ay "e
selec%e) ore %$a oce "!% %$a% ill $a5e a$i+$ O /i%ess ra%io O 7 a "i+ c$!( i %$ero!le%%e $eel 9. T$is is cosis%e% i%$Na%!res o'era%ios.
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Ma%e Selec%io Ro!le%%eMa%e Selec%io Ro!le%%e
11
34
5
1
3
27
<
24<
<
11
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&RBABILISTIC SELECTIN BASED&RBABILISTIC SELECTIN BASED
N -ITNESSN -ITNESS
Be%%er i)i5i)!als are 're/erre)Be%%er i)i5i)!als are 're/erre) Bes% is o% alays 'ic(e)Bes% is o% alays 'ic(e)
Wors% is o% ecessarily e*cl!)e)Wors% is o% ecessarily e*cl!)e) No%$i+ is +!ara%ee)No%$i+ is +!ara%ee) Mi*%!re o/ +ree)y e*'loi%a%io a)Mi*%!re o/ +ree)y e*'loi%a%io a)
a)5e%!ro!s e*'lora%ioa)5e%!ro!s e*'lora%io
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CROSS - OVER• 4enerate a ranom integer in t)e range 5 $,"6
6.m$ 7 Let it /e 1 pos 1
• Let t)e /inar* representation of t)e pair selecte/e
– -8$9 : 8 /$,/",/;,6../pos, /pos
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CRSS#0ER &ERATIN
• Cross 5er 'era%io is )oe %o %$eri+$% o/ "i% "'os a) %$e e s%ri+s are
o
• 0719 6 7 "1,"2,",.."'os, c'os1, ..c.9
• 0729 6 7 c1,c2,c,..c'os, "'os1,.". 9
-TATION O,ERATION-TATION O,ERATION
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-TATION O,ERATION-TATION O,ERATION
KDONE ON A 3IT 3+ 3IT 3ASISDONE ON A 3IT 3+ 3IT 3ASIS
KDECIDE ON A -TATIONDECIDE ON A -TATION
,RO3A3I.IT+77 ,&,RO3A3I.IT+77 ,&
3"?ar"3"?ar"
T
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ME:,:.O#
Geera%e a ra)o !"er O r O
I/ O r O X & !%a%e %$a% "i% 7 %o 1 or 1 %o 9
No %$e O e O 'o'!la%io is rea)y /or e*%
e5al!a%io o/ /i%essT$e a"o5e o'era%ios are )oe i a cyclic
aer ay %ies 7 ay +eera%ios 9
T$e !l%ia%e 'o'!la%io is e*'ec%e) %o
co%ai %$e "es% c$roosoe7 o'%i! sol!%io 9.
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S&ECIAL GA &ERATRS
ELITISM ## GD INDI0IDUALS ARE&RESER0ED DURING ANY GENERATIN
NICHE &L - O BEST O INDI0IDUALS
MICR#GA &ERATES N SELECTEDINDI0IDUALS
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Co'arisoCo'ariso
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Co'arisoCo'ariso
Na%!re .5s. Co'!%er GANa%!re .5s. Co'!%er GA
Na%!reNa%!re o% 5ery e//icie%o% 5ery e//icie%
• a% leas% a 2 year ai% "e%ee +eera%iosa% leas% a 2 year ai% "e%ee +eera%ios
•o% all a%i+ co"ia%ios 'ossi"leo% all a%i+ co"ia%ios 'ossi"le
Co'!%er Gee%ic al+ori%$Co'!%er Gee%ic al+ori%$ e//icie% a) /as%e//icie% a) /as%
• o'%iisa%io co'le%e i a a%%er o/ i!%eso'%iisa%io co'le%e i a a%%er o/ i!%es• a%i+ co"ia%ios +o5ere) oly "ya%i+ co"ia%ios +o5ere) oly "y
=/i%ess>=/i%ess>
INIISATIONINIISATION
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INIISATIONINIISATION
/A TEND TO A1IISE A /IVEN/A TEND TO A1IISE A /IVEN-NCTION-NCTION
TO INIISE AN O39ECTIVETO INIISE AN O39ECTIVE
-NCTION DEINE IT AS-NCTION DEINE IT ASNE/ATIVE O ORI/INA.NE/ATIVE O ORI/INA.
&i% f() = &a J 7f()K&i% f() = &a J 7f()K
W" ca% a
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HANDLING NEGATI0E -UNCTIN0ALUES
+A ASSUMES THAT O8,ECTIVE(UNCTION IS AL)A=S POSITIVE
TO ACCOUNT (OR NE+ATIVEVALUES )E A'' A CONSTANT < C <
max /f/x00 $ max > f/x0?C@
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HANDLING CNSTRAINTS WITHIN GA
-RAMEWR
+i7*9 Q i61,2,.
$K7*9 6 K61,2,,.
Re)e/ie /7*9 as
/7*9 6 /7*9 r Z +i7*9 [ $ere
Or is 'eal%y coe//icie% a) is %$e 'eal%y
/!c%io Soe cos%rai%s ay "e 5iola%e) )e'e)i+
o O r O
E&LRATIN AND
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E&LITATIN
RANDM SEARCH E&LRES THE SEARCHS&ACE # IGNRES E&LITATIN -&TENTIAL REGINS - &SSIBLESLUTINS
HILL CLIMBING DES NT E&LRE THESEARCH S&ACE BUT E&LITS THE BESTSLUTIN -R IM&R0EMENT
GENETIC ALGRITHMS STRIE AREMARABLE BALANCE BETWEENE&LRATIN AND E&LITATIN
.6%.+T.02S 1F 0..6%.+T.02S 1F 0.
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.6%.+T.02S 1F 0..6%.+T.02S 1F 0.
BASED ON SI!"E !#IN$I!"ES O%BASED ON SI!"E !#IN$I!"ES O%NA&'#A" E(O"'&ION ) NO *#EA&NA&'#A" E(O"'&ION ) NO *#EA&
A&+A&I$SA&+A&I$S DOES NO& #E,'I#E $OS&" E(A"'A&IONDOES NO& #E,'I#E $OS&" E(A"'A&ION
O% %I#S& O# SE$OND DE#I(A&I(ES O%O% %I#S& O# SE$OND DE#I(A&I(ES O%
OB.E$&I(E %'N$&IONOB.E$&I(E %'N$&ION A"WAS &END &O %IND &+E *"OBA"A"WAS &END &O %IND &+E *"OBA"
INI' O# A/I' DOES NO& *E&INI' O# A/I' DOES NO& *E&
BO**ED DOWN IN "O$A" +I""S ANDBO**ED DOWN IN "O$A" +I""S AND
(A""ES(A""ES
AD0ANTAGES - GAAD0ANTAGES - GA
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AD0ANTAGES - GAAD0ANTAGES - GA
VER= USE(UL (OR PRO8LEMSVER= USE(UL (OR PRO8LEMS)ITH TOTALL= UN;NO)N)ITH TOTALL= UN;NO)NCHARACTERISICS O( O8,CTIVECHARACTERISICS O( O8,CTIVE
(UNCTION HAVIN+ LAR+E(UNCTION HAVIN+ LAR+ENUM8ER O( PARMETERSNUM8ER O( PARMETERS NOT A((ECTE' 8= LOCALNOT A((ECTE' 8= LOCAL
'ISCONTINUITIES'ISCONTINUITIES CAN HAN'LE NOIS= AN'CAN HAN'LE NOIS= AN'
MULTIMO'AL (UNCTION SPACEMULTIMO'AL (UNCTION SPACE
DISAD0ANTAGES - GADISAD0ANTAGES - GA
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DISAD0ANTAGES - GADISAD0ANTAGES - GA
NOT 8ASE' ON SOUN'NOT 8ASE' ON SOUN'THEOETICAL CONSI'ERATIONSTHEOETICAL CONSI'ERATIONSECEPT THAT ON SCHEMATAECEPT THAT ON SCHEMATA
TEMPLATESTEMPLATES
'I((ICULT= IN (IN'IN+ EACT'I((ICULT= IN (IN'IN+ EACT+LO8AL MAIMA OR MINIMA+LO8AL MAIMA OR MINIMA
LAR+E NUM8ER O( (UNCTIONLAR+E NUM8ER O( (UNCTIONEVALUATIONSEVALUATIONS
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,!A,4A" AG$! O+
GA
8
0$"G ! O3A/! 3 " "A 2-$<
3O"4$-G"3$ ! -A /$- !LO=
8
P-O0L$M !P$3+3 !$ "G O+
4A-O2! P-O0A0L $! 9 3-O!!)
O4$- M2 A O" $ 3 ; /O2G/
!OM $MP-3AL -2L$! A-$
1"O="
8
,$AL POP2LA O" !>$ ! "O
$A!. O 3/OO!$
HO% GA OPERATES &HO% GA OPERATES &
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"'a(ine an ar') of
parac*utists droppin( ontot*e landscape of apro+le',s searc* space-.it* eac* one +ein( (i/enorders to nd t*e *i(*estpea01 S'all &'tati%s
ena+le eac* indi/idual toe2plore its i''ediatenei(*+or*ood- .*iles"
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/ENETIC A./ORITH/ENETIC A./ORITH
/"%"rati/"%"rati% 0% 0
/"%"rati%/"%"rati%BB
I%di!id'a
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CHRMSME 7GENME9 - THECHRMSME 7GENME9 - THE
GLBAL &TIMUMGLBAL &TIMUM
&TIMUM SLUTIN
1 1 1
T=E +EARC= +PACE
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T=E +EARC= +PACE
• Alp)a/et si>e K :", Lengt) L :;
• +i>e of searc) space? K L : "L : "; :%
1 000
2 0013 010
4 011
5 1006 101
7 110
8 111
GENERATIN #
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GENERATIN #
Geera%io 1 11
2 1 1
11 V
1 2
To%al
Wors%
A5era+e
Bes%
DARWINIAN -ITNESS
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&R&RTINATE SELECTIN
Geera%io Ma%i+ 'ool
1 11 .24 11
2 1 1 .@ 11 V
11 V .4 11 V
1 2 .13 1 2
To%al 12 13
Wors% 1 2
A5era+e . .4
Bes% V V
PRO;,;..S:.C S&&C:.O# ;,S&D O#PRO;,;..S:.C S&&C:.O# ;,S&D O#
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.:#&SS.:#&SS
MUTATIN &ERATIN
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MUTATIN &ERATIN &are% c$ose 'ro"a"ilis%ically "ase) o
/i%ess
M!%a%io 'oi% c$ose a% ra)o
e o//s'ri+
Parent1
Parent
//
Osprin
11
A-TER MUTATIN &ERATIN
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A-TER MUTATIN &ERATIN
Geera%io Ma%i+ 'ool Geera%io 11 11 3 627 11 3
2 1 1 64 11
3 11 67 11 A 1 2 615 1 2 /// 11 3
:otal 12 15
Worst 1 2
,+erae 36 A67
;est
CRSS0ER &ERATINCRSS0ER &ERATIN
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CRSS0ER &ERATINCRSS0ER &ERATIN
2 parents chosen probabilistically2 parents chosen probabilistically
based on fitnessbased on fitness
arent !arent ! arent 2arent 2
"!!"!! !!"!!"
CRSS0ER 7CNTINUED9CRSS0ER 7CNTINUED9
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I%ers%i%ial 'oi% 'ic(e) a% ra)oI%ers%i%ial 'oi% 'ic(e) a% ra)o
2 reai)ers2 reai)ers
2 o//s'ri+ 'ro)!ce) "y crosso5er 2 o//s'ri+ 'ro)!ce) "y crosso5er
RemainderRemainder11 Remainder
Remainder22
/ / 1/ / 1 / / / /
Osprin 1Osprin 1 Osprin 2Osprin 2
111111 11
rament 1rament 1 rament 2rament 21/1/ 11/11/
A(TER CROSSOVER OPERATIONA(TER CROSSOVER OPERATION
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+ene!ation B Matin &oo" +ene!ation 4
4 B44 71D B44 1 444
1 BB4 4 7BF 44B G 1 B4B 1
44B G 7DB 44B G
B4B 1 74 B4B 1
Tota" 41 4
)o!st 4 1
Ave!ae 7BB 7D
8est G G
A-TER RE&RDUCTIN &ERATIN
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UC
*eneration 0 ating ool *eneration 1
1 11 3 627
2 1 1 64
3 11 67 11 /// 11
A 1 2 615
:otal 12 15
Worst 1 2 ,+erae 36 A67
;est
GENERATIN 1GENERATIN 1
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GENERATIN 1GENERATIN 1
Geera%io Geera%io
Ma%i+Ma%i+'ool'ool Geera%io 1
Geera%io 1
11 1111 33 627627 1111 33 22 111111 55
22 11 11 6464 1111 22 11 22
33 1111 6767 1111 ////// 1111
AA 11 22 615615 11 22 ////// 1111 33
:otal:otal 1212 1515 1414
WorstWorst 11 22 22
,+erae ,+erae 3636 A67A67 A67A67
;est;est 55
&RBABILISTIC STE&S
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&RBABILISTIC STE&S
T$e ii%ial 'o'!la%io is %y'icallyra)o
&ro"a"ilis%ic selec%io "ase) o /i%ess
# Bes% is o% alays 'ic(e)# Wors% is o% ecessarily e*cl!)e)
Ra)o 'ic(i+ o/ !%a%io a)crosso5er 'oi%s
/%e, %$ere is 'ro"a"ilis%ic sceario as'ar% o/ %$e /i%ess eas!re
GENETIC ALGORITHMSGENETIC ALGORITHMS
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GENETIC ALGORITHMSGENETIC ALGORITHMS
T$eT$e genetic algorithmgenetic algorithm is a 'ro"a"ilis%ic searc$is a 'ro"a"ilis%ic searc$al+ori%$ %$a% i%era%i5ely %ras/ors a se%al+ori%$ %$a% i%era%i5ely %ras/ors a se%7calle) a7calle) a population population9 o/ a%$ea%ical o"Kec%s9 o/ a%$ea%ical o"Kec%s7%y'ically /i*e)#le+%$7%y'ically /i*e)#le+%$ "iary"iary c$arac%erc$arac%er
s%ri+ss%ri+s9, eac$ i%$ a associa%e)9, eac$ i%$ a associa%e) /i%ess/i%ess5al!e,5al!e, i%o a e 'o'!la%io o/ o//s'ri+i%o a e 'o'!la%io o/ o//s'ri+o"Kec%s !si+ %$eo"Kec%s !si+ %$e Dariia 'rici'le o/Dariia 'rici'le o/a%!ral selec%ioa%!ral selec%io a) !si+ o'era%ios %$a%a) !si+ o'era%ios %$a%
are 'a%%ere) a/%er a%!rally occ!rri+are 'a%%ere) a/%er a%!rally occ!rri++ee%ic o'era%ios+ee%ic o'era%ios,, s!c$ ass!c$ as crosso5er crosso5er 7se*!al reco"ia%io9 a)7se*!al reco"ia%io9 a) !%a%io.!%a%io.
-.S*# ST23S *+ 3/1-42M S14%*+0-.S*# ST23S *+ 3/1-42M S14%*+0
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-Y 02+2T*# .401/*THM-Y 02+2T*# .401/*THM
#H/1M1S1M.4 /23/2S2+T.T*1+ 1F#H/1M1S1M.4 /23/2S2+T.T*1+ 1F3./.M2T2/S3./.M2T2/S
*+*T*.4 31354.T*1+ 02+2/.T*1+*+*T*.4 31354.T*1+ 02+2/.T*1+ /232.T *+ . #Y#42/232.T *+ . #Y#42
/.+=+*+0 -Y F*T+2SS/.+=+*+0 -Y F*T+2SS M.T2 S242#T*1+M.T2 S242#T*1+ #/1SS,1%2/ #/1SS,1%2/ M5T.T*1+M5T.T*1+
+2> 31354.T*1+ +2> 31354.T*1+ T*44 “-2ST 62S*0+” ? 13T*M.4T*44 “-2ST 62S*0+” ? 13T*M.4
S145T*1+ *S 1-T.*+26@S145T*1+ *S 1-T.*+26@
T i < Ch T i < Ch
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Tpica< Chr&s&"Tpica< Chr&s&"
A , < ti A , < ti
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A ,p'
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Ra%i%g ; it%"ssRa%i%g ; it%"ss
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Crosso5erCrosso5er
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Crosso5er Crosso5er
M#tationM#tation
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M#tationM#tation
Bes% Desi+Bes% Desi+
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Bes% Desi+Bes% Desi+
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;,S.C NE&S:.O#S
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N
HOW DER.#% %, / CC& OP&R,:.O#SF WH.CH ,R& R,#DOM .##,:ER&F :H& ;&S: SOE:.O# < ;&S:CHROMOSOM&= .# &,CH %&R,:.O#
,W,S SHOWS , :DC :OMOV& :OW,RDS .#CR&,S.#% .:#&SS< OP:.MEM SOE:.O# = ?
HOW DO&S %, MOV& :OW,RDOP:.MEM W.:HOE: &V,E,:.#% ,POSS.;& SOE:.O#S ?
GENETIC ALGRITHM DRI0ERGENETIC ALGRITHM DRI0ER
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GA13GA13
#EVE$%E# B& M.C'(%$$ C%()E$$#EVE$%E# B& M.C'(%$$ C%()E$$
*)+VE(,+T& 'E(%,'CE E)*)+VE(,+T& 'E(%,'CE E)
#ET#ETVE(,+%) !. (E$E',E# +) 2""!VE(,+%) !. (E$E',E# +) 2""!
C%#E# +) /%(T(')C%#E# +) /%(T(')
*,E( ,EC+/+E# ,*B(%*T+)E*,E( ,EC+/+E# ,*B(%*T+)E /*)C/*)C
GA7?@ GA ,-4$-
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COD&D&COD&
CROSOVR&V,OE:.#PE:.#.:.,
ME:,:&#&W%
#.CH&POSS.;
R,#3R&S:,R:
S&&C: S&&C:#SHE&
%,M.CRO
OE:PE:
+2"3
M,.#
P,R,MS
a6inp
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.S:.#% O SE;ROE:.#&
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c:::::::::::::::::::::::::::::::::::c S"#GLE $AR"ABLE OPT""SAT"O# PROBLE 2;2?2c:::::::::::::::::::::::::::::::::::: su+routine func@-func/al i'plicit real; @a*-o sa/e
include ,para's1f, di'ension parent@npar'a2-ind'a2 di'ension iparent@nc*r'a2-ind'a2c di'ension parent9@ind'a2-npar'a2-iparent9@ind'a2-nc*r'a2 co''on ? (a9 ? npara'-nc*ro'e co''on ? (a7 ? parent-iparent 25Fparent@5- func/alF@2;2?2 return endc:::::::::::::::::::::::::::::::::::::::::
.S:.#% O SE;ROE:.#&
%, CO#V&R%C&%, CO#V&R%C&
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%, CO#V&R%C&%, CO#V&R%C&
H.MM&;&,E E#C:.O#H.MM&;&,E E#C:.O#[ ] [ ]!!
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( ) [ ] [ ]!
!
!
!
!
!
A −++−+= x x x x x f
::::::::::::::::::::::::::::::::::::::::::c T%O $AR"ABLE OPT""SAT"O# PROBLEc::::::::::::::::::::::::::::::::::::::::: su+routine func@-func/al i'plicit real; @a*-o
sa/e include ,para's1f, di'ension parent@npar'a2-ind'a2 di'ension iparent@nc*r'a2-ind'a2c di'ension parent9@ind'a2-npar'a2-iparent9@ind'a2-nc*r'a2 co''on ? (a9 ? npara'-nc*ro'e
co''on ? (a7 ? parent-iparent 25Fparent@5-
29Fparent@9- func/alF@25;;9
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INI- OCC-RS AT 1B= a%d 12=2 a%d f(B52)
H"ELBLAU U#CT"O# "#""SAT"O#::::::::::::::::: Generation 5 :::::::::::::
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: Binar) Code Para'5 Para'9 itness 5 44455554445544544444445454 41=4 519=8 555187=4>
9 55454554454544554554454445 >158 91594 1=879= A/era(e $aluesI 917 518 >1=5> A/era(e unction $alue of GenerationF >1=5> a2i'u' unction $alue F 1=879= #u'+er of Crosso/ers F 9= Elitist Reproduction on "ndi/idual 9
::::::::::::::::: Generation 54 :::::::::::: : Binar) Code Para'5 Para'9 itness 5 54454554445544544554455445 917> 51=44 >1477 9 55454554455544544554455445 >15 51=44 8=14>7> A/era(e $aluesI 71=85 51=44 7>1=58> A/era(e unction $alue of GenerationF 7>1=58>
a2i'u' unction $alue F >1477 #u'+er of Crosso/ers F 98 Elitist Reproduction on "ndi/idual 5
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::::::::::::::::: Generation =4 ::::::::::::::: : Binar) Code Para'5 Para'9 itness
5 54454554445444454445455455 9179 4185 5=1>= 9 54454554445444554445455555 9179 5177 41797 A/era(e $aluesI 9179 5174 1574 A/era(e unction $alue of GenerationF 1574 a2i'u' unction $alue F 41797 #u'+er of Crosso/ers F 74
JJJJJJJ Restart 'icropopulation at (eneration =4 JJJJJJJ
::::::::::::::::: Generation 544 :::::::::::
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::::::::::::::::: Generation 544 ::::::::::: : Binar) Code Para'5 Para'9 itness 5 54454555445444554445545545 91=9 51>9 415=97 9 55454555445545554545545545 >1947 >1= >871==5 A/era(e $aluesI 71= 7194 9751=> A/era(e unction $alue of GenerationF 9751=> a2i'u' unction $alue F 415=97 #u'+er of Crosso/ers F 9> Elitist Reproduction on "ndi/idual 5::::::::::::::::: Generation 944 ::::::::::: : Binar) Code Para'5 Para'9 itness 5 54454555544554554455454545 9185 9144= 414=5> 9 55545454454545445544545555 >1= 91 95418=98 A/era(e $aluesI 718 91=49 54=1777
A/era(e unction $alue of GenerationF 54=1777 a2i'u' unction $alue F 414=5> #u'+er of Crosso/ers F 9> Elitist Reproduction on "ndi/idual 9JJJJJJJ Restart 'icropopulation at (eneration 9 JJJ
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::::::::::::::::: Generation 744 :::::::::::: : Binar) Code Para'5 Para'9 itness
5 54454555544554554455555545 9185 91474 414>97 9 45555545445555445555445554 91>>8 714= 91779 A/era(e $aluesI 914> 91=89 5>1>99 A/era(e unction $alue of GenerationF 5>1>99 a2i'u' unction $alue F 414>97 #u'+er of Crosso/ers F 9
Elitist Reproduction on "ndi/idual 9::::::::::::::::: Generation >44 :::::::::::: : Binar) Code Para'5 Para'9 itness
5 54455454444444554454554545 800Q B8Q 41447= 9 55455454544445555454554545 >198 >1 ==819975 A/era(e $aluesI 7187 7179 915577
A/era(e unction $alue of GenerationF 915577 a2i'u' unction $alue F 41447= #u'+er of Crosso/ers F 74 Elitist Reproduction on "ndi/idual 9
CO#$ERGE#CE O GA OR H"ELBLEAU U#CT"O#
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,O,-.ATION OVEENT IN 1B712 ,.ANE
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EAMPLE (UNCTIONS
+ 9&7 < & ; B 75C ( &7 sin9 D Π &7; ( & sin 9 @ Π & ; variables &7 < &
-ange of &7 )E5@ to 757 -ange of & D57 to C5F -equired Precision D decimals -ange of &7 must be divided into 7C57 & 7@@@@ points -ange of & must be divide into 75? & 7@@@@ points " for &7 is 7F as 7F 7C7@@ " for & is 7C as 7C 7?@@@ Total string length required is 7F ( 7C B EE 3ross over Probability Pc B @5C Mutation Probability Pm B @5@7 "POP!>$ B @
S,MP&S .S:.#% OE#C
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E#CC SE;ROE:.#& E#C < -F$nc+al =C .MP.C.: R&,Q4
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3HEESHA4S .E/ENDAR+ 3ED O ARROWS
THIS -NCTION HAS RO-/H.+ 0 ,EA6S AND VA..E+S
S,MP& CHROMOSOM&S,MP& CHROMOSOM&
,#D .:#&SS,#D .:#&SS
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,#D .:#&SS ,#D .:#&SS
1111111111111111111111111111
D&CODO.#%D&CODO.#% '1 1672A2 '2 7657733'1 1672A2 '2 7657733
itness < '1F '2 = 26272Aitness < '1F '2 = 26272A
25 29
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.:#&SS V,E&S.:#&SS V,E&S
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TOTA. ITNESS = "!a
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S&&C:.O# PRO;,;..:S&&C:.O# PRO;,;..:
CEME,:.V& PRO;,;..:CEME,:.V& PRO;,;..:
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ROE&::& WH&& S&&C:.O#ROE&::& WH&& S&&C:.O#
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POP2LA O" -A"1$, +O-
OP2LA O" -A"1$, +O-
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!$L$3 O"
$L$3 O"
CROSS OV&R OP&R,:.O#CROSS OV&R OP&R,:.O#
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"f @ r K 419= select t*e c*ro'oso'e for cross o/er operation
POP2LA O" A+ $-OP2LA O" A+ $-
3-O!!O4$-
-O!!O4$-
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ME:,:.O# OP&R,:.O#ME:,:.O# OP&R,:.O#
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POPE,:.O# ,:&R ME:,:.O#POPE,:.O# ,:&R ME:,:.O#
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,:&R 1 %&R,:.O#SB6 ,:&R 1 %&R,:.O#SB6
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A0ERAGE AND BEST -UNCTINA0ERAGE AND BEST -UNCTIN
0ALUES0ALUES
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0ALUES0ALUES
CN0ERGENCE -CN0ERGENCE -
&ARAMETERS&ARAMETERS
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&ARAMETERS&ARAMETERS
ANTENNA DESIGNANTENNA DESIGN
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ANTENNA DESIGNANTENNA DESIGN
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T$e 'ro"le 7Al%s$!ler a) Li)e 1??@9 is %oT$e 'ro"le 7Al%s$!ler a) Li)e 1??@9 is %o)e%erie %$e)e%erie %$e x"y"# x"y"# coor)ia%es o/ %$e #coor)ia%es o/ %$e #
)iesioal 'osi%io o/ %$e e)s 7)iesioal 'osi%io o/ %$e e)s 7 X1 X1,, Y1Y1,, Z1Z1,,
X2 X2 ,, Y2 Y2 ,, Z2 Z2 ,$ ,,$ , X7 X7 ,, Y7 Y7 ,, Z7 Z7 9 o/ 3 s%rai+$% ires so9 o/ 3 s%rai+$% ires so
%$a% %$e res!l%i+ 3#ire a%ea sa%is/ies%$a% %$e res!l%i+ 3#ire a%ea sa%is/ies
cer%ai 'er/orace re!iree%scer%ai 'er/orace re!iree%s
T$e /irs% ire s%ar%s a% /ee) 'oi% 7, , 9 i %$eT$e /irs% ire s%ar%s a% /ee) 'oi% 7, , 9 i %$e
i))le o/ %$e +ro!) 'laei))le o/ %$e +ro!) 'lae T$e a%ea !s% /i% isi)e %$e .4T$e a%ea !s% /i% isi)e %$e .4
λ
c!"ec!"e
ANTENNA GENMEANTENNA GENME
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4BD*-it ch!omosome /enome04BD*-it ch!omosome /enome0
EachEach x-y-z x-y-z coo!dinate is !e&!esentedcoo!dinate is !e&!esented
-. D -its /*-it !an#"a!it. fo! data-. D -its /*-it !an#"a!it. fo! data
&"#s a sin -it0&"#s a sin -it0
Tota" ch!omosome is Tota" ch!omosome is ×
×
D $ 4BDD $ 4BD
-its-its
00!! &&!! 11!! 0022 &&22 1122 66
?BB4B?BB4B *44B4*44B4 ?BBBB?BBBB ?BB4B?BB4B *B444*B444 ?BB4B?BB4B 66
ANTENNA -ITNESSANTENNA -ITNESS
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A%ea is /or +ro!)#%o#sa%elli%eA%ea is /or +ro!)#%o#sa%elli%eco!ica%ios /or cars a) $a)se%sco!ica%ios /or cars a) $a)se%s
We )esire ear#!i/or +ai 'a%%er 1We )esire ear#!i/or +ai 'a%%er 1°
a"o5e %$e $orioa"o5e %$e $orio -i%ess is eas!re) "ase) o %$e-i%ess is eas!re) "ase) o %$ea%ea]s ra)ia%io 'a%%er. T$ea%ea]s ra)ia%io 'a%%er. T$era)ia%io 'a%%er is si!la%e) "yra)ia%io 'a%%er is si!la%e) "y
Na%ioal Elec%roa+e%ics Co)e 7NEC9Na%ioal Elec%roa+e%ics Co)e 7NEC9
ANTENNA -ITNESSANTENNA -ITNESS
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-i%ess is s! o/ %$e s!ares o/ %$e-i%ess is s! o/ %$e s!ares o/ %$e)i//erece "e%ee %$e a5era+e +ai)i//erece "e%ee %$e a5era+e +ai
a) %$e a%ea]s +aia) %$e a%ea]s +ai
S! is %a(e /or a+lesS! is %a(e /or a+les Θ "e%ee #?"e%ee #?° a) ?a) ?
°
a) all ai!%$ a+lesa) all ai!%$ a+les /ro/ro
°
%o 1@%o 1@°
T$e saller %$e 5al!e o/ /i%ess, %$eT$e saller %$e 5al!e o/ /i%ess, %$e"e%%er "e%%er
GRA&H - ANTENNA -ITNESSGRA&H - ANTENNA -ITNESS
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U. +. PATENT @,$#,#
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A
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2;
C
C
P
HS&C:.O# C/C
t
d
&ARAMETERS RANGES&ARAMETERS RANGES
AND CNSTRAINTSAND CNSTRAINTS
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CNSTANT &ARAMETERSCNSTANT &ARAMETERS LAD & UNITSLAD & UNITS HAL- S&AN B UNITSHAL- S&AN B UNITS
THICNESS .1 UNITSTHICNESS .1 UNITS MAIMUM ALLWABLEMAIMUM ALLWABLE
STRESS 1, UNITSSTRESS 1, UNITS
ELASTIC MDULUS * 1ELASTIC MDULUS * 1 33UNITSUNITS
DENSITY . UNITSDENSITY . UNITS
INDE&ENDENT 0ARIABLESINDE&ENDENT 0ARIABLES
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'IAMETER O( PIPE < d
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THE 8EAM SHOUL' NOT (AIL INTHE 8EAM SHOUL' NOT (AIL IN8UC;LIN+8UC;LIN+
JJ88 K JK J..
=ie"d St!ess sho#"d -e "ess than=ie"d St!ess sho#"d -e "ess thana""owa-"e st!essa""owa-"e st!ess
JJ.. J Ja"a" =IEL' STRESS MUST 8E LESS THAN=IEL' STRESS MUST 8E LESS THAN
ALLO)A8LE STRESSALLO)A8LE STRESS
OPTIMISE THE )EI+HT O( THE 8EAMOPTIMISE THE )EI+HT O( THE 8EAM
!T-$!! +O-M2LA$!T-$!! +O-M2LA$
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YIELD STRESS YIELD STRESS ^̂yy ^̂yy 6 &7B6 &7B22HH22991:21:2 : _\ H % ) ` : _\ H % ) `
BUCLING STRESS ^BUCLING STRESS ^""
^̂"" 6 _\6 _\
22
E 7 )E 7 )22
% %22
9 : _@ 7 B9 : _@ 7 B22
H H22
9`9`
W 6 2 \ ) % 7 BW 6 2 \ ) % 7 B22 H H22 99
.S:.#% O SE;ROE:.#&.S:.#% O SE;ROE:.#&
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UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU
cc 2/S:RESS ;&,M2/S:RESS ;&,M cUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUcUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU s$bro$tine $nc
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rho63rho63 piA6dQdatan
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CON9-/ATE /RADIENTCON9-/ATE /RADIENT
d = 2 -%its H =B -%its W =d = 2 -%its H =B -%its W =
B8 -%itsB8 -%its
/"%"tic A
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APPLICATI'N+ '0 4A• ac)ine Learning• +peec) Recognition• Criminal +uspect Detection
• usic Composition• Training of Neural Netor3s• Aircraft Design• Tur/ine Blae Design
• Protein +tructure Determination• Biing +trategies • Image !"#e$$%&g
, enetically optimied three/dimensional , enetically optimied three/dimensional
tr$ss 0ith impro+ed reG$ency responsetr$ss 0ith impro+ed reG$ency response
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tr$ss 0ith impro+ed reG$ency responsetr$ss 0ith impro+ed reG$ency response66
-s"d fr sat"
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ROBUST $AR"ABLE REPRESE#TAT"O#ROBUST $AR"ABLE REPRESE#TAT"O# TOLERATE RA#DO CHA#GES TOLERATE RA#DO CHA#GES
PROPER "T#ESS E$ALUAT"O# EASUREPROPER "T#ESS E$ALUAT"O# EASURE "#CREASE SHOULD LEAD TO BETTER"#CREASE SHOULD LEAD TO BETTER
SOLUT"O#SOLUT"O# SELECT"O# STRE#GTH A#D TPESELECT"O# STRE#GTH A#D TPE UTAT"O# A#D CROSSO$ERUTAT"O# A#D CROSSO$ER
PROBAB"L"T"ESPROBAB"L"T"ES POPULAT"O# S"MEPOPULAT"O# S"ME
GUIDELINES -R SELECTIN -GA &ARAMETERS
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'EPEN'S ON PRO8LEM 8EIN+SOLVE'
8ASE' ON EPERIENCE AN'
'ATA 8ASE ACCUMULATE'/ 8AR8ARA MINS;ER /1BB00
HELP TO ACHIEVE
CONVER+ENCE UIC;L= )ITHLESS COMPUTATIONAL E((ORT
GA &ARAMETERSGA &ARAMETERS
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NUMBER - -UNCTINNUMBER - -UNCTINE0ALUATINS N 6 G * &E0ALUATINS N 6 G * & G N!"er o/ Geera%ios %o Co5er+eG N!"er o/ Geera%ios %o Co5er+e
& &o'!la%io Sie& &o'!la%io SieG is /o!) %o "e a''ro*ia%elyG is /o!) %o "e a''ro*ia%ely
GG b 2 L , O L O is %$e "iary s%ri+ le+%$b 2 L , O L O is %$e "iary s%ri+ le+%$
'%i! &o'!la%io Sie is'%i! &o'!la%io Sie is && b 1. Lb 1. L
Hece NHece N bb * L * L 22
GA &RBABILITIES 0ALUES &cGA &RBABILITIES 0ALUES &c
a) &a) &
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a )
Cross 5er &ro"a"ili%y &cCross 5er &ro"a"ili%y &c
&c 6 7 S#19 : S $ere O S = is %$e !"er o/&c 6 7 S#19 : S $ere O S = is %$e !"er o/
'are%s c$ose /or a%i+ -or S62, &c 6 .4'are%s c$ose /or a%i+ -or S62, &c 6 .4
M!%a%io &ro"a"ili%y &M!%a%io &ro"a"ili%y &
& 6 1 : && 6 1 : & b 1 : Lb 1 : L
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GA STRATEGYGA STRATEGY
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As GA 'rocee)s, !"er o/ /!c%ioAs GA 'rocee)s, !"er o/ /!c%ioe5al!a%ios are a)e a) a $!+e )a%ae5al!a%ios are a)e a) a $!+e )a%a"ase is "ei+ crea%e)."ase is "ei+ crea%e).
Ca e a(e !se o/ %$e alrea)yCa e a(e !se o/ %$e alrea)ya5aila"le )a%a %o e5al!a%e %$e /!c%ioa5aila"le )a%a %o e5al!a%e %$e /!c%io"y soe o%$er !ic(er e%$o)s So"y soe o%$er !ic(er e%$o)s So%$a% a/%er say 4 or V +eera%ios e%$a% a/%er say 4 or V +eera%ios e
!se %$is !ic(er e%$o) /or o"Kec%i5e!se %$is !ic(er e%$o) /or o"Kec%i5e/!c%io e5al!a%io/!c%io e5al!a%io
NE%&A' NET(O&)S NE%&A' NET(O&)S can be $sedcan be $sedeecti+ely or s$ch p$rpose6eecti+ely or s$ch p$rpose6
Cocl!siosCocl!sios
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GAs are 'oer/!l o'%iisers "ase) oGAs are 'oer/!l o'%iisers "ase) osi'le r!les o/ a%!ral e5ol!%iosi'le r!les o/ a%!ral e5ol!%io T$ey ca "e a''lie) "ee/icially /or 'ro"lesT$ey ca "e a''lie) "ee/icially /or 'ro"les
$ere a%!re o/ o"Kec%i5e /!c%io is$ere a%!re o/ o"Kec%i5e /!c%io isco'le* a) !(oco'le* a) !(o
T$ey ca "e co"ie) i%$ so'$is%ica%e)T$ey ca "e co"ie) i%$ so'$is%ica%e)so/%ae %ools, %o 'ro)!ce "es% or o'%i!so/%ae %ools, %o 'ro)!ce "es% or o'%i!aero)yaic co/i+!ra%io )esi+saero)yaic co/i+!ra%io )esi+s
T$ey +i5e rise %o )a%a "ases, $ic$ ca "eT$ey +i5e rise %o )a%a "ases, $ic$ ca "e/!r%$er !se), /or o'%iisa%io %as(s, "ase)/!r%$er !se), /or o'%iisa%io %as(s, "ase)o e!ral e%or(so e!ral e%or(s
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