presentation on ga

8/9/2019 Presentation on GA

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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





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


57/177

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


65/177

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


66/177

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"


68/177

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; < !; < ! + +


69/177

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!! &&


70/177

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.


76/177

Ma%e Selec%io Ro!le%%eMa%e Selec%io Ro!le%%e

11

34

5

1

3

27

<

24<

<

11


77/177

&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


78/177


79/177

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


80/177

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


81/177

-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


82/177

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


84/177

Co'arisoCo'ariso


85/177

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


86/177

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


87/177

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@


88/177

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


89/177

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.


90/177

.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


91/177

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


92/177

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


93/177

,!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 &


94/177

"'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"


95/177

/ENETIC A./ORITH/ENETIC A./ORITH

/"%"rati/"%"rati% 0% 0

/"%"rati%/"%"rati%BB

I%di!id'a


96/177

CHRMSME 7GENME9 - THECHRMSME 7GENME9 - THE

GLBAL &TIMUMGLBAL &TIMUM

&TIMUM SLUTIN

1 1 1

T=E +EARC= +PACE


97/177

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 #


98/177

GENERATIN #

Geera%io 1 11

2 1 1

11 V

1 2

To%al

Wors%

A5era+e

Bes%

DARWINIAN -ITNESS


99/177

&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#


100/177

.:#&SS.:#&SS

MUTATIN &ERATIN


101/177

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


102/177

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


103/177

CRSS0ER &ERATINCRSS0ER &ERATIN

2 parents chosen probabilistically2 parents chosen probabilistically

based on fitnessbased on fitness

arent !arent ! arent 2arent 2

"!!"!! !!"!!"

CRSS0ER 7CNTINUED9CRSS0ER 7CNTINUED9


104/177

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


105/177

+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


106/177

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


107/177

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


108/177

&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


109/177

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'


113/177

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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174/177

GA STRATEGYGA STRATEGY


175/177

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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presentation on ga

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