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Genetic algorithm based two-dimensional and three-dimensional floorplanning for VLSI ASICs

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Material Information

Title:
Genetic algorithm based two-dimensional and three-dimensional floorplanning for VLSI ASICs
Physical Description:
Book
Language:
English
Creator:
Fernando, Pradeep R
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Physical Design -- 3D Integrated Circuits -- Evolutionary Search -- Placement -- Sequence Pair
3D integrated circuits
Evolutionary search
Placement
Sequence pair
Dissertations, Academic -- Computer Engineering -- Masters -- USF
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Dramatic improvements in circuit integration technologies have resulted in a huge increase in the complexity of circuits that can be fabricated on a single integrated circuit (IC). The significance of the performance and reliablity issues of interconnects has increased greatly demanding radically different solutions such as Three-Dimensional Integrated Circuits (3D IC) and Optical Interconnects.Three-Dimensional ICs are an elegant solution to the interconnect and device density issues in the current and future technology generations as they provide an additional dimension for packing the devices. This results in a direct reduction in the chip package area and the total wiring required to complete all the interconnections. More importantly, the number and the length of long, global wires are reduced significantlydue to the availability of the third dimension for routing purposes. But to fully exploit all the advantages associated with three-dimensional ICs, a good three-dim ensional packing of devices is needed. This greatly increases the importance of Floorplanning and Placement stages ofthe VLSI Physical Design process. There have been many initial attempts to develop a physical design framework for three-dimensional ICs but only a few of them focus on physical design for three-dimensional macro-cell based circuit designs. This work develops a novel genetic algorithm for performing both two-dimensional and three-dimensional macro-cell floorplanning. The genetic floorplanner employs two novel crossover operators. The first crossover operator (MTOX) is an unbiased stochastic search operator, while the second crossover operator (HOOX) is a heuristic operator that searches for floorplans with good area usage. Both the crossover operators can be applied transparently for both 2D and 3D floorplanning.Three mutation operators have been developed to work with the chosen floorplan representation scheme, namely Sequence Pairs. Despite the use of a comparatively s mall population size of 200, the genetic floorplanner achieves reduction in footprint area and wirelength for both 2D and 3D floorplanning as compared to some of the recent works in the literature. For 2D floorplanning, the genetic floorplanner achieves a 12 percent average reduction in total wirelength as compared to a Quadratic Programming based Floorplanner for a small 2 percent increase in area. For 3D floorplanning,the proposed floorplanner achieves a 11 percent average reduction in total wirelength and a 5 percent decrease in footprint area as compared to a Simulated Annealing based 3D floorplanner.
Thesis:
Thesis (M.A.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: World Wide Web browser and PDF reader.
System Details:
Mode of access: World Wide Web.
Statement of Responsibility:
by Pradeep R. Fernando.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 64 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001795215
oclc - 148053257
usfldc doi - E14-SFE0001549
usfldc handle - e14.1549
System ID:
SFS0025867:00001


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$-*E.M441f57E*n/) > 52.CnA.Xcn/-*,On/).n/f$R$P.n/ = = g CB "h*"‰ ‚kK*‰7"ŽMb‰"ŽK7L7c : n'.{5d.,X$$)E(.Xcn/,KUn/).n/F'()*P Rb1n/‡. = XcJ5 .†nnE = .‡57 = Un$+BRŽHJOA6n/n/4k$).†n$Un/nd5 H_+)(Jn/UnL4*$(UM5 = {.J.Xcn/M„.J'Kn/)*.n/M,gX = Jn+Byf.Jn,4*n4*E R 8d9L:3; nnE*Mr'nE'.J57)Z f. n/)*B "h*" pHO•7)ƒ‚+)*‰‰"x : n'.J5VX3n/n = 6.).6nn/.‡y*1KR4n4*!EnU < )Kd02 n'.._ < )*K 8 )$dn.P 9 $*n'..B < )OT02'JnCe f'. > E ffnn/)EOR57frXb$U)E-n/)*A-/1n/52n*.) > n'..B ; < )*K02 : n'.._OdX3n/dJ) 9 _3Œ_*F¢6$d*En/ =3> †n'.C5‰n/_ : ¢“ŸgUBTE*n/!.CnU4A$ =O> (5‰n/R5Ved*G.r)$6. >H=3> J.$!5‰n/5 : f.Z f GL = JŸ$BŸ$B "h*" r"1g3Z)1"Ž"Ž3,‚+)*‰‰"x ; KUn/).n/dn.‡n = C.)PG Ty > _1*( > < )ORfn^c. : nF @-*En/-n^3 : n..B—@-E*n/-n^3.6n.($(G4k4*E'$ > 5 $ME.J$44*'n = > y.d57E.ERnU.) > .$)" f.)E.EckC57). .X,n/)J/1n/F5n..BŽ = Ÿ$B£i.†,@-En/fn^c.(n. 4'n4*",/1n/R) = G.C3n+,) = •On/)n/B "h*" r"1g3Z)1"Ž"Ž3‡rgxcJ‰"Ž•bxb„u"3bL"ŽŠ7**yc"x3b.Z7Š"L 0.)”.( = ZX( = _+Mn$M$M.Xcn/(n'.‡*n/d.(.Xcn/†. > ) n*4 =3> En.H.‡$,5!,nU4…N3E.$'n > *…G4*3*En/r,'.$MEn/) i

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Ž = JŸ$BŸ : n'.(Sekn/-)%RXcn/ < $n/nr‰@-43E*n/G5[)nib7 ? $J < )Of02 : n'. : n ? $J 9 .… 9 Ÿg : Œ.7Œ“ Ÿg : M$†R..M-'n^c.r7¢K Ÿg : : E.44* > 8 )$H`*e- Ÿg : f..)' 8 )$y`ŠUK Ÿg : : E = $r%4*'.A2 : %Xcn/ < *$n/'n @f*n/‡‰@ Ÿ M$ < $4*nn/‡ < Ÿg : M$P% > * Ÿg : < 3n^y0NOEn > • : % > Jn ? Z Td%d4Š$)741f)$Zr ? Ÿn < 4GfA‰d Ÿne < E.Orrš Ÿg : ? Z Td% > Ÿ < E.O!%R* > Ÿ Ž = JŸ$B£i : n'.(Sekn/f) ; On/).n/ < $n/nC‰@-4*3*En/G57)ni$7 ? $U( @-E*n/,-n^3 : n : n ? $J Œ+\ Ÿg : : 4*n..\ Ÿg : -n^3.\2 Ÿg : ; O > f..r)K\ Ÿg : < $Un/n4k W 9 Œr@-n/M4kfE!+\ e xxŒ < $4*nn/C41-E*!.+\ Ÿ W .41$A@ < n/)Of4k-E!+\e e @-4k$, fM@ < > 4k-E.+\e < )^y.)' Ÿ 9 cn[ : n ; On/).n/ < $n/Un 9 .+\! Ÿg : W .41$, fM@ < .' > Ÿ @-4k$, fM. > Ÿn d = ; On/).n/ < $n/'n 9 .+\! #%$ W .41$, fM@ < .' > e&#%$ @-4k$, fM. > #%$ n

PAGE 15

.†44Š$)$). > .)E)J.X3'n/BC)* > _Š'Kn/)*.n/rn‡*En/d. > )E.).3n7bnOn/)n/_T RH.,)!. > )E.).A) = On/).n/"–Tbkn/ =3> On/).n/"n.BL.)E.)F.f5‰En/) > 5+CnnE H4k$)Mn$Un/nn = {4X =3> 5[)g fƒ.n.4'n4*_ n*.) > n'.P'V > nn/)(4* =3> J > E*.U = !n/)c#`U./1n/BTRT. n*.) > .$)TXbn/_c)(R5k.RE*.U = "/1n/ = n/)(RJ-4))En/ ›E!$B -nEO{$/#`5'#`./#&$…n*.))5‰ = 'n$— T$#&*()†n4Š RE.4 X > ,56(P = gX.X3n/' > Bf.KUn/).n/)A.nnE*Gn = = ) > nIGO(.r > 4k = G)G.-4*nU.-G4kn/-U$)gŸ/V\ 9 3n ; On/).n/!#V$M. Q `ŸM fT*$-$rJFF.!.!*GE ‡n/).n/R$Yn/O-B ; O($ ; On/).n/J#r$J$,57)E.GZ Ty(! > F$, 'JyFf.*B M = ; KUn/).n/e#•*$VXR.–n/)J4*$ = !C.-n4J¦f($-. > 57)EG'H.CE.44k!(Ž > B -.T.e.*•5c.VcnK*rO($TKUn/).n/•*rRnV fd.VnU.) > .$)Crn/–.Ž(4*n/+)C415[Fn/–•J'JhB+-–) = )'Kn/)*.n/xgX 6EnH$f.*Vy._K3E"41).CJ > nU."‡.RnEO"‡5‰E.E. n*.))gŸ`B %dE.RCn*.) > n'.._Kf.*e5k.f) = *On/).n/T f'.$44)nUF.fnš# )(—57‡4Š$B-P(4*'M$†.yX3 > 5-.HOn/).n/† R–*n/ f,n.) > An/C.6. > 5eP)* = .(*JA.)E.)A.C RB : *n/P.†.Xcn/M$(Hn•_+.P$X(.5T.P) = 2KUn/).n/Mn/ Jn/)E4*† fJ.-n/(X3 > R3E2'(r$f'n/-†f. > )E.) .†On/).n/ f.„n/)(4*$y.†. > .)E.).†.Xcn/BdR.†.Xcn/6 > n/ f„n) > n.._k.(.Xcn/(n/)EOd'n/,EnU{){OE* = R$r ¤

PAGE 16

)P3E = r5!) = VOn/)n/P R = F..ƒA = ƒe.yn/).n/)* = /# & "‡.-nnE–n/)(4k).KB2@f4k$Vn = -E(CJ)$-.f.' > †) = R.._ = E.M > n/)*E((4kg "P*n4$cB < 44krKUn/).n/C*g -#`^{%dn/nrgX = y44k)yJ.n/MXc > 5x.MOn/)n/BVE.!E"'^ < 44kSTnš# )J$)( f' = n/)JR)*I*nO2*E.-C$Xf4ŠnJn.rJ.-5‰E.E.!nU.) > .$)B Q ZX_-.n/.,4k$'.57NOEn > *.An/'. E.4*4* > X)$‡$6nn/)(4*rn*.) > n'.A).A f.F4n/‡5!OEJ)E ).._2) = TOn/)n/6'n/P.HEn/XFn/)E.4*'.,/kn/B-M$ > n/ .C'(4*n/!52n/)^GHr.)(RcB %4*T."ET5*n/44kŽOn/)n/L*PZ !#`^rn/n_ ; On/)n/L$T4n/ n/${.„4k5[UJn/„5CnnE‡.„57EE.AnU.) > .$)B02)E.Ÿ$BŸ n/)(4*$M.J. > r5T4'J¦On/).n/C{.()$r R{.(4){5". n*.) > .$)B 0L)E.JŸ$BŸCf.rSekn/-5 : n6){d$P* ; On/).n/% > P‰@f4cEn/H57)Ÿ/7 ¨

PAGE 17

.)E.)…$nUƒ'.JX$$)EC$65 892:3; )n > n‡*C.4k'X3'$J. = gX/#&(O).HE._)Un*'.V$..‡CI**J).$#`ˆ)E)e57TRE. (57VR. 4* = J24*n/(57V-57EE.-nU.))BTd.!5k.fUn)'E.) 44k),.{KUn/).n/H4 = JJ5P.„nEOy5‰E.E.n.))G -.r%'()* ; O$)xŸ`B "' uPŽZ3KUpG)(…3"L7Š"Ž*"r"1g3*b.g3s67bKL'b -./#&%d(*) ; K$ < nET!GO$,nnEy fnUHn/Xr.Xcn/ $P5[)E*AG Tyd(C4Š.Bn/)KXO)2! "$#&%d()•nUnEff/cn/ > ). = )‡24Š.f† RnJ.Rn/X.Xcn/–.BeR'c.R > = ZXf'–.Xcn/-4*f$ .J(V > CE{57COn/).n/)*B6fOEM,n$% ;< n/)'d5"X–n/)OXK)* & "$#&J)LO$nnE*dn^)6)„45–6BrSVnUXcE*k& "$# J)ŽnnER > rA†n$% ;< dn %X3'n/ 9 > U‡"YE Œ$57G„. fU. = & ".y.Xcn/F > C$yn ; O# 9 > ; On/).n/ ; O#`Œ$5[ 8 ; Œ 8 UB+-OE*fHnZ#&%'()* ;< ‡XnLn^c.y5V6E4*r.X3'n/P > $ n/)J6En$P fGnU„.f.)E.) ; K#`Œ$5[ 8 -$$C4*O = & "$Yn/O .Xcn/r > B "'+"‰ tyŽc*"1g**cJ*RuPŽbOKUpG(c"Ž71"x*"r"1g3*b.g3s†[bKL[Z -/#&%d() ; O$ < nE6$ = n/)J.{n/.) > 414ŠE$†—.GnE.# OT*E >P= nE-5+.T3E()EV.XbO$gX!n/)OXK)* T$#&*() ;< B < E.K > f./#&J)xKU$)AnU.))$ = .yE‡4*3*En/Pn$%ˆ(†# > n4ŠgŸiZ–d.(.X3'n/† > dPE*n{).M„,n$% ;< f.{n/)(4Š${,Gi$% ;< fy.MJM5[34O$cBV0.34O!f(".d4cEn/"5x.M f'.‡*G.)OT5L. 4*n^b$PNOE*H57-.Pi$%Rn$%nU4•B -/#&(*) ;< eM57‹†)OT)'E.)6r.!) = .KUn/).n/–4 = J 5‰n/y'(.d% :Q ‡*.)("n.) > .$)Be-.KE*) = *†.RXn n^3f5..Vn/X".Xcn/V' > L+$Ž.T3E = •5..$L.) = U+5[Žn6 m

PAGE 18

,)$ƒA(cE‰.4kƒ)XM56.….)$nU > yG*n/ nZ#&%d() ;< †(n/)(4Š${5[)E.(iZ#&%d() ;< B-.HX$ = > 5R. U,(*)G57f)E.F.4*-*En/C.6OE* = R*A.A5–) = ŽOn/).n/ .†nnE = .y.).•Bd@RJM&inb–n$Un/¦{.† f.A* = E.)!5 On/).n/e'6Mn$% ;< EJR.)) = TXn.On/).n/e*P4*n/6E*n/) y.MXU$Py+ f.B202)E6Ÿ$B£i†.g f• fy* = E.)(57 = AiZ#&%AnZ#&% ;< B 02)E.JŸ$B£iJxxŒ.-',i$%An$% < UnEM‰@-43E*n/H5[)‘inb7 + *.Hd`B'nb¤)–(c.„.Jn$%KUn/).n/ME'.yHn/) = $){5 = {.¦)O XnL fBf‹n/). = rEn/)A = cnLA) = xOn/)n/d. G4'n/G/34kn/ = E.GG.3E = G5†.Xcn/ > U,/.n/.› > _d. Xn3On/).n/2n$4*n*n/"4*3*En/C6n/TC.VcOn/).n/2n$4*n*n/B ¡ X._1f "R = X$R.6nZ#&% ;< f TP& "‡y.C.$).5e. i$% ;< -HF!5e. > G4k57J*n/B j

PAGE 19

02)E.Ÿ$B£nRŒ.6%' = E)M57LR¦)O3ŒL'Pi$%6n$% < nE*T‰@f4cEn/ 57)nb¤7 -/#&(*)1O$)G(4*)(!.M5‰ = 'n$)y5 Q cc# : )knUnE FJ).)'ndn$% ;< i§Z`B--.C)+A*‡n/)(4k).On = M5‰ = n$)A4Š$$ $5[A. = ).,.ME.J41nI*nd "$57# = )'.(n) > Bf-.PK#` "$57 = )rK57n/dn = EJ†)'$f.RXb$)EV6y) > UT3E"$E.' > Xc$6M$)AE.!'GJcc#&)k.)B "'+" F3*‰),).Z71"*fu6xb3)UpG(c"L7Š"Ž*"r"1gOŠZgO“s67ZOŽ[Z -F$yOEJ)ErU$Xr„(4*(KMFXnTn^c.5-.Xcn/C…AnZ# J) ;< B*ŽE.†n$% ;< f$64cEn/AE.(4Šbc'x(.cgi¨ZL‡4*3*En/r.Xcn/ )J4F514*/#`57 = n$JE = $V$VgXf.fg "TXX3n/-' > B–f.!n*N3E. $‡X > .-FnE*rNOEF.)c#&n/)OXO)"(.cC—n/) > N3E4Š(KB Q gX .nƒ43n/J5r.„nE.O‡' > HPE‡.HJ$„.E*. > ..Xcn/y §

PAGE 20

On/).n/BV%dE.rJ.P.O!.-FnE*"524cEn.†(ECn$% ;< _..RU$X (4Š(O$)J(.c–*X = (4*4k)($V'nE.Œ$57#&").Hn$% ;< _K-)E.)c# 8 Gn$% ;< _• < *4 : n^c..BCL.((.cdn = = ) > n'I{OH.†& n$\ ? n^b$)‡Žn'NOE. ? n^b$)„R44)nU.PXn > n^4/#`4Šn^$$ƒ T$#&*()–O$—n# nE*Bƒf. ; O#& > ‡KUn/).n/)($,nXE*.„/3U!O#&n4— R *$dn/)*.n/M.†$444U$P4Šn^$$(4*R5V.†n/41)*.HiZ#&% nU4*B 8 'n# Q{ B ? n^$$ƒXrnZ#&()KU$) Ec1U!5[)’4kORKUn4 = f'.H-.C3E = -5eKUn4AX3f$CF =O> ; 4*!gXb' = MH.r4Šn^$$Pn/•B Q ).)ndxnUN3E. Q ).)n2f4*4)nxEe5‰E > #&O$dnU.))x f.–E*.4*n^$$M T$#&'()* nnE_K.V'n/-V.fK"$57_3$Rn^yV43n/()J4‡51nUFB ? n^b$)†'–.).R) > f.F'.fX3n/ > UTgX = F57 = Un$J"n^GO F.)M())nMnZ#&'()*1*df $5[B Q ).)*n ; O$)Gn*XGEP"Œ$57# = )'.P!-*c#&0257 = Un$) n*.))B Q ).)'nCnZ#&(*) ;< $†Xc.,O ŽE.Hn$% ;< 8 n > ; K$ ;< r†i3B£¨$% ;< gnZ`ByŽE.Fn$% ;< CEF-*c#&02'n*.))6EnU : n/X S–4Šbc'Žg -r@fn/ > ¦$){G57 = Un$J.Xcn/( > r)45"{/.'.GE = # $Bi3B£¨$% ;< !$r(4*(K =3>y= )*.P& "Jf(rn/)OXO)ŽiZ#&*()k .VE*.R "$57# = )f2. = )-n))Be-. = )'.fn/).I)E$)6 f F2.fn = > 5k.i3B£¨$% ;< B2")*.Mn/).I)E.U$)V$fnI(Or.-57)Z f. 57)E.> 4k-.4k'.P), f..-)r = G.r = '. = )*.G$r*44k+\ 0*n//#`$#&0n/ n^K#`$#&n^

PAGE 21

' n^K#`$#&0n/ 0*n//#`$#&"n^ @f5OB2&ib¤Kn/ = e57 = n$)MnU.) > EM-4cEn/en' = 2./#&'()* ;< -E'.(E = U$M'.P$44*)n.B " €*Z7c.Z7Š" -64*J$ > (X$$) = dd "^„'d.Jn/n.H5"' On/).n/H.AX$$)E*F/kn/H. > gX„).„nnEF.)4cn/B-. n/.r.)Fn/-5•'Kn/)*.n/T*J.n/J.Xcn/f > *VEJF. .57(34*r$Jny$G3E = †5d.X3'n/P).)Hn4— R.)E. n/)(4)J,) = ${On/)n/PN3E(KB„-3E6n*.) > n.„ E*{GnU.J„.† = Yn/XM5T.†Xb$U)E4*d5T.†4* > 'nŽ.)„4cn/ f' = g C\ : PE*.)Ef4*J¦$)y5eRJGŒ. f.‡$‡n/‡ƒ.Xcn/y > *E.F„'Pn'.'n/P.F)'C5 $CgX3)Be-OE*–XFPJ)JJnU4y$CJ4*2C'$f3E = –5+*) n/)J41)K6$†n = ‡IC f.H(Hn*4•BA-3ECNOE"(4k*n/FPE* = )XC = Pn4C$f*r f.+BxE.LxVOE* = x5.n/)(4k).OŽ = –4*n^ 'G(n4,'n/_.rn/)(4*/. > 5ŽM4* > n+)y4cn/-Jn/B–'n/!C.G57fGr-FnK-*O4Š.B M = ; KUn/).n/4*J¦$) f.Gn.{5RJ¦(d)n ; K$)n))J{†… '$En/)44Š$)$) > )E.).Xcn/B›.)E).{On/)c# n/-$rJn+_c'-n†"F.Xcn/M¦$-$MX > F1 f. n/)J4*$,J.d5".JOn/).n/C„.JnnEB6-†)244Š$)$) > .)E)G.r* = n/)(R()R.)) = R R.,n/)(4*$,J.P. > )E.)H.MOn/).n/!f.g Ry'y02)E6Ÿ$BŸ$B"S–XH.ME5Ž4k$!nG) > Ÿl

PAGE 22

'X3'$Jd4 = ”57r.F./cr57 ‹n*.) > .$)BF-3Ed.‡.M5 F) = TOn/).n/ = n/)(F.y)I*nKM5‰n/(.G :3; ….)F$ 4k57J*n/f5Ž6nnE*Be-OE*V*En/)y5•.d.y5•.d) = 1'Kn/)*.n/ '-(rJ41K!,En/)H52x f+B 0O4UKRf Q *J¦$) f.X#&n/'.414ŠE$ > 56n$% ;< HG)E)) = 'Kn/)*.n/ 4* = J!'‡M57E.EMn) > .$)f-OcEn/y.r.G57f†4* > n ),57( "^G,57dn$% ;< B ; „n$% ;< _Š.C4*n^b$($‡fJ. =O> R$V.Xcn/f > T f'.(F'$V.Xcn/f' > .)OB2fOEV34*L$ = n/r.r41n/f$)!5ek.P.X3'n/r > R!..•B " v(ŠOb•70/*fMb*VŠ3Dyc"xOZ7A-7+ŠZ27*"Ž"Ž3 .)E.)cn*n„4k5[UJn/{(3ginZnb¤rgX4n/${ f. > Xc.)x fM.TE–5.-./#&%'()* ; O$ < nE*_r-FnK•4Š > n)) 3)P$FN3E'¦J.y4kK'VgX3)B,%)AnnECHd)b# : n 6N3ET.ME5Ž*$nUn1(.c ;? J3E*V(*fd*) > *n/ n/)(4*/cR5".(4* > n2.){4*3n/B6f.†EOM > )EC.)*R RLn/)(465 $r!5ŽJn/3n/'!$!nAXk5Ž.r)H$Un > BV-.d5‰n/!$ > *n/ .C'(4kn/d5 Q n/cn/•0234*'.6H.6 :3; UcB -r44k)A.n6’5[MnZ#&(*)•Fn/$#&n/ŽO4*'.(Ef(4* n/)gX24k$Žfr-FnO > $UnP5[LOcr*O4ŠBxf.–.nT4k$L.X4k "^U4*$O > 5[ = …iZ#&*()2nZ#&(*)L34**..B6-.†4k4*E$ & "$#`4k)OPn/)gX†4k$C f*n* = Enn/57E* > E f = $ > n/c.)C = F(cI*JC "^J RJ.N3E.n/4*V*n/3'.r57T34*'BŽf.fXc)$)*VO$# En/ =O> .r*)1& "$#`4k)ORn/)gX41U$f$rJgX =O> E†Fn/) = '$) 5fG.Jn/)gXJ4k$F*.H& "$#`41)'KJn/)gX‡41U$Bƒ-y/c4k(O E*P.g $†.H441)….'nHO4*.P = JjZ¤.BŸ) gX$AEn/)— 0.34OrRc_LmcŸ$Bal$¤OX$yE*n/){xVŒ.+_L¨3B¤K¨)~XU$‡*En/) ŸŸ

PAGE 23

F. 9 .‡5•. 9 ).Œ_c‡i3B£i)ˆgX$MEn/)‡‡xkR W $BT= e†.-cn*n4*n/)Ž5Š$)E*(¨$lKXc.)e'P fC*En/) 57RnZ#&(*) ;< fH¤‡.X3'n/r > Zin$`B "21 uPŽ3g7Hv(b*Š"Ž),).b[1" < *$4,i…4*Oy)( = n„n/)n/4G.$H560LO4Š._*n FŽ*$V$-..J = –E.62.'B < $4Vn = > .n/U = e)( 5M.„nE.O‡$44*)n.yE57F& "$#&J)R/#&(*)!*O4Š JB < $4R¤‡'nE-.r44k)A.nP$44)nUA57f34*'.†.hB < $4*6¨G.n/ = M.‡/34kJKrn/)*En/…*…nEMJEM = .…5[6 .R/34kJKB < $4*"mrXVn/)*nE)*25[).f/c4k(O.EV*JnE* .C*n/)H57-5‰E.E.d "^ŠB Ÿi

PAGE 24

s6AtHru6qd‘ -GwpFtH€qdwAutH}sJvFws6qdru(‚ k"h G}-‚+rys67ZKL[FpH3g[1" 892:3;V< nE*–%) < > n–X3(K6C3E = V5+ T#&.I*.J$"".Z f = g C\ : > : 4knI*n$)‡yf.MI!45Ž 892:3; .)Gn > nCF = ,Jn/)J4/# Xr'5241nI*n$)57-.r.G > GB RnUn/E.O%)drdn/–." > ›4knIŠn$)•$V = .r = ne$Unn/E '-.)H5[-C > GB "gX3-F0*En/)f%R)—ƒ-. = gX3!.)$.OI†,J 5‰En/)kET5[)  = nd > $n*n/E.MH.MOn/)n/) = & GB 9 )n!%)6 ; †24x_K.!$r*(n/)K)g 51.X$$)E25‰En/)*3E*2 R > ˆ$R.UXF$".R@f)xU57TXŠJ•BV-V.n/4*)(5• > !nG,@2 9 .n/4*)H,".' > .n/ = HE.(($. $r%/# n/4) 9 .)E*$K‰R% 9 UBŽT3)„/c4)R*AF.‡'.5[UJ$)A$6 = 57-.CXb$)E!E!*GA$)'-.r*.$#&X+4knIŠn$)B < nE-%)HHf. = O)G/34*)*! = .G.6)nr)A$P$6n/)c# XK„nnE6.n/4*)+B,-.ynnEP.n/U4)' = E*M$^c.„.‡4k57# Fn/CG4kZ T-NOE(O-OJnn/)EKB Ÿn

PAGE 25

' ? > nV%R){-. ? > n–%)…$Hn/)KXPFnnEr.n/4*)O )Jnr.n/4)ynH < nE 9 > )E.BTf.M > )E.!52(nnE*"n/ = ". )JM5T.†Xb$)Ed.X3'n/*KUn/).n/M„.(4*n'.) = T.GB fe)(Unf.n/4)('–EFr4cEn/-435768-$"$fE =3> f0 = 'n$) 5‰n"J4cEn/d.rnU4*B–fOEM4* > nk.)G$P*-(n/!J4*n/!) C$J,.M4k5[UJn/M52.M5‰ = n$,nU4•B 0* = n$)AA-.† > )E.M$y5[)'.64* > nŽ)„$Jn/)KX…KHy 5Ž4*.).$4*'nfJ^c"$!n = E‡†43E*n/fn,5x.d.Xcn/MH( > f)G.C'n/)y "$57fF4cEn/d.CE4*n^$$AnU4•_.J4* > ^c.g R,:9K<;B ? n^b$)6Fx'.6-.!4*3n/J'n/)† "$57T'–n/(OC*XcEOn4Š– 4Šn^$$+B"02*k.(52.rnU4A!). = 5[M > $C4*41‡J.PJ$^B -FI*V)(65!.yn4—.gX3' > .4k)ƒ. ? > nT%)—$GP6 .MI**+$ = 57M57 = n$)+Be) > _34* > 'n+.)Gr) > $C$R. fHCn/E+)(Uf5L.CX3n/f,On/).n/fH.CnUnE = .(.)+B k"' r1x7)*!pHc7Š"*-,}!‚+rys67ZOŽ[Z ? > nL%R){$(,. 8d9L:3; %) < > n6fP43n/R5V.UJJ. 4* > nT3n$)*C5-yn/X,X3n/†ƒ.HOn/).n/)UEn/E. = & ". ….ynU4 ™ 6 > )E.B„f.‡4*E.M{.F4Š > n".)ƒ$G6AnnE*P.n/4) f 4)*-J'.4knI*n$)*B-.'.4*E.JnUnEJF4cn/—F5M T#&.I*. 4*-fg fGG02)ECi3BŸrJ = ,G4'J¦GnnE*! > )E.B ? $).Py%n/)(4k))G52.MgXUx > ’'KF(4*!E = #& > J 0234*'.,* ? n/(OP02*.,. = †.)c#`gXU$44*A4k))…5[†nU J3E*MH.C.)H5[RJJ'JŠ$Fn*4, > )E @f)E..C < ).n/'.PUJT5xd'Kn/)*.n/) = & "G.4*n/H(cc# E*-E'.6FJ1 f. Ÿ/¤

PAGE 26

' < )(4*n/)yH@-En/)G5LE*OEG4*n/CHCn4, > )E. S–3Un/)› 8 I*n$)Secn/)›5†.… > )E. ™ ,5‰En/)* > . $)'-.rH5‰En/)* > 0L)E.Ci3BŸ ? > n•%) < > nM5[ 892:3;!< nEM‰@f4cEn/H57)imb7 k" -7+*bL7*"L"Ž‰"ŽƒŠ"xr7)5(c"1 -F02O4*'.‡4ŠFr.‡n/)*…$y5 892:3;M? > 'n–%)…*….r f 4k))*.,T.‡J3E*r = '.…57).y4*$).G4**‡—„JF = )E $cB--r0LO4Š†* ? 'n/(KR4*RXPgX'$44*.F = Y¢n/XRffn/)†# () > n/)*.‡$".d0LO4Š4* =  TP.'¦FXU)‡5+. ? n/(O Ÿ¨

PAGE 27

4 = GB2"EV.d$R& "PnUn1kn/ = & "F.d0234**.M ? n/(O 4*\ f.-02O4*'.f4**-nn/4– TP > 4ke51J3E*2Ve4*E._)( > 02cJ 02/. = dJ3E*B =?> A@B;C9‡:DE3KF9 Q cE-$M.C(cE" f)r f,.)O-$CI.3•B =?> !;r@Š 'JR){.(R41n/r@R$ H.PfJ5Ž.P(3*EB ; n/)O_2. ? n/(Or4*Fnn/4P) > I.3…(3*EMC.4*E.BJ023# 4Š(4*P fk4n/.C. ? 'n/(K4*C52/. = = 3n^3R$64ORA. )E4*E.!52. ? $)*.†4*B 0234*'.ynnE$r.†F;n!3KAHI;J4k))5L.J(cE{.(nUnEM R4'J f'.–y.)OT5["ny5•.R/. = = 3n^3"JR.4ŠE.B ? n/(O n'nE$-J3OšLK3I!241))"5ek.‡7I3Š"J3E*B k" MZML75( x*N({Ž7.Z71" -r.4*E."Fr0LO4ŠC4*Cn/)5 F-5L(3*EOG&!‰$P68K\QR_SQ _•BBB-_SQ R.)UT`,.)KCVT`5ŽnU(cEQT W 44kC‰@OW T " 9 g "6‰@:X T = )E*)G.r4kn/f@f$F5[-nU,/. = dJ3E* 9 !52On/).n/)* = & ",.CJ3E*^3g fGf.C.'5Ž.PnnE --4 = ‹5•0234**.d.T f(..J'$)J5•F4J*4*n^c.P5• .r(cE"'‡r.4*E."nnEEnH$!r$r.†gXU$4* = & "A > & "J(3*EB -.f4J > 5+.-34*Fe.' > (E. =O> .R$C5k.J'PEDn/) Ÿm

PAGE 28

$ = )E-'•.6(3*EBŒAP.XOR5e6% :.Q )'(_* f.(n$ .….A = Y¢n/XA5‰En/) = 4J¦•B ; 5d/c = G(cEJ$,4O‡'. .4ŠE._O*O4ŠC*  R1)* > n/)(4*E.M R.yG.)O5[!nU /. = !(cEEn(*$V.fn/)*O–n/)n/*.r. = )E*L)J.R4kn/–$C*(. $(52.rn/4k)6*/c = J3E*M$C$I+B k"21 s67*)YL).Z7Š"*R-7+*bL7*"L 0234**Mn = JnI = ) > KA& "n$ = )F(.c…E cn$ = cn^cdH.d4k))„.†34*„ > )E.B6f.P T,n$Ur5TO4* $ : n.6 : 'n/ = M0234* ¡ )c# : n.6 ¡ )c# : 'n/ = M0234*B k"21+"‰ ‚+‰7K‰"Ž—-7+ŠZ27*"Ž : 'n.†02O4*$r)M34*"$Rn = M = =3> nE.X > 4*$). .†O†n/.)(*$rn/4k)H.JnE.Kd > )Er4*n/ = .Hcn${GGE = # 34*•BC-.†4*$).‡CnE.y5".( > )E.C$GM'g "{) > '{.(.¦)O -X'nxn/)BeG/cJ4*M5e : n'.60234*'G!.Z f,G02)E.Ci3B£i$cB b c d e a c d b e a ( b ) ( a )0L)E.Ci3B£i( > 4k!5e0234**\-‰K : n'.60234*' = ¡ ).# : n†0234*' Ÿgj

PAGE 29

k"21+" w,1"+‚•‰[O7"Ž-7+*bL7*"L ¡ )c# : 'n.A0234**C$H34**r$†n. = F43E*n/ =3> n/)(4*HnEX 4*$).‡5TJ > )E.r4*n/B6{/.(4*(5" ¡ )c# : n.y02O4*{M.Z f{02$# E.†i3B£i = B ¡ )c# : 'n.J0234**-N3EPPEnUJ6n/)J4*/,4K$)nU.(dEnU -rT)E*. : 'n//#&.r'x‰ : r/Ÿ§ZŽ,. : N3E.n/ ? Z :.? /ŸgjZ•4*O$)B k"[Z -7+*bL7*"F3LZcc"1g.Z7Š"L 0234*ƒ@-4K$)†4* > —'(4kK6)y†. > gXG„*n/C/kn/()—. EO(k5c.e*O4Š"UJBŽ0LO4Šd4K$)*•n = = ) > nI O!& "Rn$ = M)r.• = > R4O = : 'n. ¡ )c#&n'.O4*B f.‡I*†n$ > n/)*65f)H4O$)nU.(($(n—) > 4O : n.y02O4*B : 'n.FŽM ¡ J¦ ? )I„Sec4)R57'LE*. n$ > B f.(n/)n$ > n/)5T*O4ŠA4O$)nU.(d$rn4O = ,n.†,)c#&n'.P*O4ŠEnU,-. : NOE.*n/ ? f,ŽX < $# E.‡$4ŠB‡f.(n/c.G5.J*O4ŠMO,.‡4K$)*rF./# n/cC5xR4*O$)"†5[ˆ.34*‡$Mn/)(4*/k_3(/#&n/)E*J.P4$# n/BE.6.y4K$)ƒnU.(64KP.yK‡65!34*r$ n = C¦ f.6J3E*-.†.4*E.-nnEB-OE*f„r-FnOR*O4Š. 'd)E$O,I*„).†5"4k) = > J > 4Je)E.)dn/)O.„'M$ )E.)—4*n/_– R.†A*O4Š.6E.„n.A4O$)6„I*— 4*J•)'E.)H57)A‰'n.OTE = !5LM4Jk34*'B k"[Z•"‰ ‚+‰7K‰"Ž—u"bOc(*"ŽwA*N(*‰),)3f1/nY]\q:\•Lb3g[1"Ž : 'n.0234*†n = G > 4KE*.*$ > ŽAEn/E.,y.Z f 02)E.Ai3B£n = B-.,O!3.†5. : n.„x,4KJ…nE.(5R,34* > )E.V f*nJn = !."C.¦)KŠnE.g‰ŠL"rXnŠnE.g7XUBV-.-$5+.c.V4O Ÿ§

PAGE 30

.,(cEP—.G*O4Š+B… ? )¢#.JŽXU!5. = $ > > † ? )' Sec4),*$4Of : n.J0234*'+BR-C) > = n^AR.(n^,5V‡)./# $#`).An/4k).n/ = Tn.„34**6*41)'ƒ/34)B—-*†. = n^ n = gXn/)( =O> .57n.(†457n/ = & "GX'n•nE.!G.U¦)K+nE-$!. (JXhB(-.(.U.y5T.JnEMEM : ^ : n'.yŽ( f(.GF.c. ‡–)K–nUJ*X.f(nE.T' = `B ? )-.VŽgXŠ51 : ^ : n.MŽ E*H6E*N3E. ¡ J'¦ ? )'HSec4)F57!X > n'.C34*'+Be0LO4Š JHn“E„.(4* ¡ UJ¦ ? )S–34)y4KG{n. 34**"'H.-4'J¦$)H43n/EB V V V H 5 6 7 8 H V H 3 2 1 4 2 3 4 1 5 6 8 7 ( a ) ( b )02)E."i3B£nC‰K : n.!ŽVy = k0234*r5[Ž. ? )CSec4)R Ÿin$.¤Xc*¨mbXj$§$KX3X3 k"[Z•" ‚kI^•Ž3"Ž)fŠ[H‡OLZcc"1g.Z71"*f-7+*b2[Š"Ž : N3E.n/ ? gŸgjbEF& "N3E.n/g_a`"b_eŽM{4*OP.y4k))*–$)4 = & " > & "ƒ(cE(.,*O4Š+BSTnNOE.*n/n/)'(5M4k6E.$)5 (cE,*(B›-N3E.n/y$„ = .E.ƒ…43n/‡n*..B-.I N3E.n/K_ ` U_bnM. ? )XK ? +NOE.*n/–x.Vf#&N3E.n/_$)XŽ.V5[¢#`$#`)K•U. 5xd)c#&On/.†cn15Ž(cE$)'T*$"UEy5[)ˆ.M)Ec#` Tn/U.!(. .6–n/U.25*.!(cEBL-.n/)(N3E.n/K_ U_)n6. ¡ )$XK ¡ –N3E.n/ .Jc#&N3E.n/_1)XfP57¢#`$#`)ORU.f5e.6.)c#&On/'.Fcn•5e.P(3*E ™ $)**$"E*–57).c#` "n/.P)Ec#`!n/."5•.d(cEB2-.& Ÿ

PAGE 31

N3E.n/Ž).V$"E8-FnK+R = M.V$X–4k))k5.. = cn^cxd.VO4*+B E.2R*CNOE.*n/KAdrŽx > ECd4KL."O$)L5.!(cEBx-3E .rOM*O4ŠH > )E.n = r.g f,E'.Pr.CNOE.*n/g_]`Tb_eeedrUB fgfgfgfgf fgfgfgfgf fgfgfgfgf fgfgfgfgf fgfgfgfgf hghghghgh hghghghgh hghghghgh hghghghgh hghghghgh igigigigigigigigi igigigigigigigigi igigigigigigigigi igigigigigigigigi igigigigigigigigi igigigigigigigigi igigigigigigigigi igigigigigigigigi igigigigigigigigi igigigigigigigigi jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj jgjgjgjgjgjgjgj a b c d 02)E.Ci3B¤‡0LO4ŠH5[f. : N3E.n/ ? n = •_n = k"[Z•"+"h ‚+k^•Žc"x){R*7HpH3)+2‰"x -dNOE.*n/4Š4O$)GnG = MEH ? n/(O-.M = )E.dR#V c#2n/3*$V5•*.d(3*E–n = fn/)(4*EF57) .NOE.*n/f4*gB2f.f*) (.cxŸgjZ–,n/)J4*E.J.Jn/3'$M5".J(cEdn/)UEn/rn/)UKMU$4*d57) .yNOEn/‡4ŠC—EC.yn/)*OC$4Šr{nnE$‡.HJF = )E*. = $(57-.CO4*Gn/41)*.6J.CNOE.*n/r4*Be0(3-$fEr). n/)J()E = NOE.*n/dJfX = G4*4k)xnnZ`B k"[Z•"+"' sP1"ŽgZŠ7"1HHZ*LLJ€DKbx+ R¦)OVXn–$) = T—(cE†4*UMn = J.X5[).F(cc# E ™ 4k))f = „.(NOEn/Br-.P'$)dn = 6EAGn/)UEn/M.¦)O ‰{X'n[n/)'Kd$4**B6f.PXn/r„.J.U¦)K7Xn[n/)OU$4* n/41)*AG.((cEf„.†34*•B„.(5[U X/{LHX/‡Y.(.# ¦)O-n/)UKF$4*J4*P$F(cEH!'(5[(5M(cErYJ.,*O4Š+B-. Xn/d$6 ")K„ f,.6 f.*g‰.)OU"5e.†(cEB--.P).4*$A57) i$l

PAGE 32

)E.Un/F.c.†A.J'.^.c.J{*d T)Kƒ.¦)O&7Xn7dn/)'KrU$4* > .(J*J• R.x‰.)KU-5V.†34*'+BrxHI**A.†4k))f5T.(X3*E = cn^c „.(34*'+_+.().M4Š$„.Jn/)UKMU$4*d57)”.J)E.Un/(X/G$ (cE ™ X/G'-n/)(4*E.•B k"[Z•"+" }TŠ"Ž*c/GsP(l(…Š"“‚+]MLk^•Ž3"Ž)€DKbx+ Œ).HB&nnbe.A*$yn/)J(){E = NOEn/ = & "„.m_a`T_1E_e—NOEn/ n/41)*H4*$“'..¦)Orn/)OG$4*+B-3EH. 9 ). < )F() : E = NOEn/C5–m_a`V_+E_eN3E.n/ fx)X6.P R.,5T.6O4*,4O =3> .JN3E.n/(4ŠZ_ ` b_ UB(-.((cE$( T)O fM f.*f, = {. f{5"J34*+BJf.J.)OM5.J34*n = Jn/)(4*E.ƒ,F$d57) E'.R-Xn_ ` N3E.n/B2Œ).rV•nn*.Xc(F(7x2Urn/)(4*E-. .C5..V)Žn/)JJ)PE = #&N3E.n/VC")K6N3E.n/–4ŠBŽ > E.= n/ $nU,PEn/E._..r(rn/)J4*/. > 52.r* "fEn/GH(‰+Bo!‰qpOŠUB k"[Z•" u"Z*"L[Z7*…s67ŠgxbHZ*LF3LZcc"1g.Z7Š"*f-7+*b2[Š"Ž 9 F < .*Ÿ¨$Š44k)‡C.ZXŠ$4*4)ny5+4*O.r34*'–E'.M& "†c# XJn)E.(U$4*g‰ < rUB•ˆXn– < ˆ4KC.JXn–$) = T…. (cE6{.¦)O < 4K†H¦)OT$) = & ".H(3*EB -.„Xn‰.¦)O[‡ < ‘y = =3> I**.„UX„n)E.5P.{X# n&‰.U¦)K7Cn/)*O†$4*Eƒ. : N3E.n/ ? ($44)nU+Bƒ’4*n/(OJ rn/4k)y < dr$Jg f'0L)E.Fi3B£¨3BF-J.XbO$F5! < ddgX : N3E.n/ ? !"$!)Jnd$) = TA(3*E"" = Xc)E57).M < †Bc0*(7 (.cM "‡44k)57CX$E$,.Fn/)P5!,34*{4O…E.G.F < 4K$)+B icŸ

PAGE 33

rs.tvu8wbxzyI{|n}~r.€I€FwbS2‚Fƒ„‚FƒV…4s.†b‡ˆ€FwbwbxC‡‰B€vƒV…Vs2ƒ8tŠˆ:‹ŒŽxrVwxC‡‰xCƒ0†b‚N†bs[€vƒ )‘ ’”“)•–a“)—]0™S–š0›EœŽ™Ÿ œ”œ”¡£¢J¤)™Vv›5¦›5–§ ¨[‚FPxC%xCƒk†‚FƒV…ŒŽ€vu8†bs2ƒ8tz‚NwbxO†b8x:†<€%€v‡‰†s[%B€Fwb†b‚Fƒk†SV‚F‡‰xC‡s[ƒ%†bVxO¨k5‡bs[r‚FSxC‡bs[tvƒP5r.x ‚F‡m†b8xr…VxCrs[…8x†b8xƒV‚FIuV‚F[s[†€F:†bVx[‚nF€vu8†%s[ƒ†‰xrw‡m€F:†b8x [‚nF€vu8†%‚NwbxC‚‚FƒV…†b8xOs.ws[ƒ8t wbxCIuVs.wbxCxCƒ0†b‡r{gu8xO†‰€z†b8x[‚NwbtFxOƒIuVBxrw€F…8xr5s[PxC‡‚FƒS…ns[ƒk†‰xrwP€vƒVƒ8xCP†b‡s[ƒ‚Jkgrs.wruSs.†r0B€F†b †b8xC‡‰x SS‚F‡‰xC‡‚Nwx Ss.tvV.P€v%S[xP‚FƒV…Fxrwbl…Vs[nruV.†r{ŠŽ8xtFxCƒ8xrw‚F¨2‚FPxC%xCƒ0†%‚FƒV…ŸŒ:€vu8†bs[ƒ8t SV‚F‡bxC‡S‚CFxBxrxCƒ Vwb€qFxCƒ †‰€mBxC.€vƒVt†‰€%†b8x¨gV‚Nwe…r2‚F‡b‡€FšVw€FS.xC‡nyFnA{Š:kuV‡‚Fu8†‰€v‚N†bs[€vƒ €F†b8xC‡‰x†<€SV‚F‡‰xC‡Žs2‡wbxCkuSs.wbxC… †‰€€FV†b‚Fs2ƒ„xrnrs.xCƒk†:[‚nF€vu8†b‡:s[ƒ„‚wbxC…VuVPxC…„‚F%€vuSƒ0†Ž€F†bs[xF{ [ š§nœ¦™8§q“)œ–œ"m“)"70]“§' ›5C“)•– ˆ€vSu8†‰xrwŽ}s[…8xC…„xC‡bs.tvƒlˆ}Oz†‰€I€v[‡U‚Nwbx‚Fƒ„xC‡b‡‰xCƒk†bs[‚F”S‚Nw†U€F]†b8xzgkxC‡bs.tvƒ4Vwb€5PxC‡b‡r{ ŠŽ8xrr‚Fƒ¦BxuV‡bxC…¦‚N†z‚Fƒk‡b†b‚NtFxn€FUrs.wruVs[†…VxC‡bs.tvƒ†‰€4€FS†b‚Fs[ƒ¦‚4IuVs[E‚FƒV‚F[I‡bs2‡€F†bVxnru8wbwbxCƒk† …8xC‡bs[tvƒ€Fw†‰€„xP5S.€Fwbxm€F†b8xrwJ…8xC‡s.tvƒ‚F.†‰xrwƒV‚N†bs.FxC‡C{4€Fwxr€nFxrwz†bVx‡8xrxrwJ‡bs.rxm€Frs.weruVs.†b‡‚FƒV…E†b8x xP8‚FP†bs[ƒ8t…8xr†b‚Fs[[‡zwbxCIuVs.wbxC…lk¦†bVx¨05‡bs[r‚FxC‡bs.tvƒSV‚F‡‰xwbxCIuVs.wbx†b8xxC2s[s[ƒV‚N†bs[€vƒ€F:IuV‚Fƒ s[ƒk†‰xrwbFxCƒk†bs.€vƒ4‚F‡:muVe4‚F‡ŽB€v‡b‡bs[S.xF{ }‡†b8xmP€vS.xP8s.†„€F†bVxmrs.weruVs.†b‡Ž†‰€ Bx…VxC‡bs.tvƒ8xC…s[ƒVPwbxC‚F‡‰xC‡:s[†b4†‰xCSƒ8€v.€FtF‡r‚F[s[ƒ8t8†b8x ‚F.tF€Fws[†bV‡)€Fwg‚Fu8†‰€v‚N†bs[ƒVtOrs.wruSs.†]…8xC‡s.tvƒz‡bV€vuV[…J‚F[‡b€eV‚Fƒ8tFx†‰€‚F…V…VwbxC‡b‡]†b8xƒVxrs[‡‡bu8xC‡š‚Nwes[‡bs[ƒ8t yFy

PAGE 34

E.d(.r'(4ZXHn.))BV-U) < %DO)'4J$U > 4J¦‡r$ 5Šd.)+B2R2.nU.) > $44)nU.†.!% :.Q )(_.!. < %3)e. E.rEnU…C41Z Tg_LƒOn/).n/rNOE(OB‡Œ‡.XOC5. ¡ .)J c_57cnE-5[PJ) = +On/).n/_n/)¢#`^1_*H.UJ+EBe%EMJ. ¡? #&$*.!52.r4* = J_c3nUnP$n(.c-E*nA : 6E$G.'.J .'nrRJ!$r5[NOE.O > EGJ4*3*En/d4J+nUnE> )E.B k"2 yc"xOZ7AtH7**$[Za(… ”.nH`ddP64F¦$)ƒn'NOE.H$(E6{cn*nH$nU $ > (X$$ =3> .4cn/L5Š$EKX)'E.)+B–.n*JL T!OcEn/ =3>m )*(f)'xg*6.rŸ)jbl– R. = g "()(!5‰EJKc4Un4*•57).!. > 5c.nŽMX)E.)+B2n–Fk …M4k4*E*$ >-= nEe5c.•–5.E_ ) = "4k4kn/X_V = E_–J'JV4 = 5[F$)…NOE(OgmZ`B W ^ .McnnP$nU$)$R4k$(E.Fy.)C)E.)+_knPJ JOHHOd4k4*E$)‡5Ž)E.)Tf*XcE257)ˆ f'nHH4Jk)'E.)H = +B–-3Ef.nCRUJ!$P(4*'n > 4*$'kG$E.B k"2+"‰ vJxZ(ƒ,K.Z7Š"G‰"xyc"ŽKZ7AtH7*Šb[Za(… nHRUJ6 "^…)„4k4*E$)ƒ5f*XcEd > 43E*n/ = Jc# XcE*MnU—.$)…I* > E.U., = P'XcELn/)E*K—6. )E)F†.4 = GBVd"$$ fyH'.4k4*E$)F5Ž*XcEB•-.d 4k4*E$)P > n/)–51dI.cJ3E = 25k)J > .U$F*X3'EB•fLc# E.–$J > XfX3*EL fFXb$J.dn/) = $)T$4OTF.d 4k4*E$)J$ f'*.4y4cEn/X$$ > '.C > 4k5xI*"*XcEe'F.d5‰E.E.R.$)*B -.C4cn/!5eX)E.),,$EC-PE*$ =3> CEr52.C > 4k-524k$f$ X)X†.†X3*E,6*+4k4*E'$),O‡I*d'XcE'"',.657EE.Cb# )B6R+4‡*X3'E!$(4*3*En/ = {)n/{4k$M4 = = -„X > .$)AE'.†.rJZYf > 4k!5L4k$\ in

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' @f4cEn/) < )ZX Q E.$) ; XcE'•$!n/†57e.4k$)257)D.4k4*E$) = P)†2I.LX$E. ‡.$k4*.r4*3*En/J4Šn/R*XcE2F.414ŠE$)( R‡g I.Be-3ET. 4'n4*R5eE.XcX$Š5L.rI*fG$Er!6E$AH.M.nC,BTdRRn = = ) > nIGO(& "F > 4k = G)G.r4*n/(Of$ > E*+\ : > # : $†df d.$)2dB : > : $MdRV4cEn/$+457 "V(3E = eF.!O!4k4*E$)6¦f†nU .$)+Bf-3E-)* > FE = f5e.P4k4*E$)A-4Šn/'GX > .U$)+Bb# )dL4*n/".O"414ŠE$)C fP$k4*.XcE*+Pn†.$)+Bef57 Jn/',OE* = !52.$)*_..6dD)E.4ŠE.!. = -*XcEŠ-!n/)E*K .(I**L)E.)+B6-I**L)E.){n/41)*G. = M)E.)„n/)E*K…{. Or$nU+BT, = n/-4.#&Xx)E.52(.'nM4J¦--.Z f,G02)Eri3B£m3BGenetic Algorithm Template() { Initialize Population; { } Crossover(); Mutate(); Replace(); Select Parents(); //for Crossover Operation; Update_Best_Individual(); for N generations do Output Best Individual; }0L)E.Ci3B£m( : > : $6d.nP4*J¦-Ž(4*$ ib¤

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k"2+" sP(…–Š"Žc"1ZJ*-—yc"ŽKZ7{vJŽZ(…),)3 J4*.nrU f'1*XCM5[)g f†n/)J41)K\ 4k4*E*$)y5e.)_ *n/3'.J(n*G_ I*.!5‰En/)•_ n/),(nUG_ nM4k$_Š n/)O)x4*$(B k"2+" r"x27•7LŽ*qd"x)+2‰"x n†RUJR.y "^,)„.64 = *n/dn/ > B ; dd T^ )—n/3*.,5R.‡4* = ‘n/y3EPFJ¦.H.H()EO65f4 = ‘4knI*n .57J$)..+BySVn—*X3'Ex'.F)'E.)4Šn/Fr…n/3*.G5.F4* = n/Be-.f*n/3'.PnU.(d.)E'(457 = > J$4ynG.r†6EN3E.-*X3'Ec .64k4*E$)•BR-.6n/c.yn((.)E = C > G.n/36H$d.6I.R5 .C'XcE*n = rn/)(4*E.AE.(J'J1(( > H'(M)E.Un/B k"2+" -[Z"Ž3J*-Š"r"ŽL7•72x* STn*XcE+.†4k4*E$)Ad{n/c.y5V6)'E.)„H.†4 = = )X•B–-.dI.52,*XcE.6E!*n/!.rNOE* > 5x.r)E.)yJ.d4 = GB : *n/e.nVJ•5[)g ƒ*$E.)n/)+_b.VI+X$E.–5.C'XcEZ f'.n. f.eV.e2 f3E.X3X.)E.)†.!.$)Be-.I.25ŠJ*XcE)F > .nr f..d.f.†*X3'EŠ f = CnU.){J4*$O5[dJ$.‡52I.¢# = 4*$Ofn/),nU.(f$CE+B i¨

PAGE 37

k"2+"[1 ‚kc7O)Z7Š"€DO$xŠ"Ž‰C( : n/) Q nU '‡„nU.(E =3> .'nRU n/G& *X3'E57M.(43E*n/)Arn/)gXC41U$)B6-.64*E.4k)65V.(41U$) yZ E = U.)F'„I*y*XcEF—4k4*E'$)EX3X57,J > 5‰E.E. .$)BM-3EfP4*$KdX3*E57R.64k$)R$P.U > n/ = ).,I.HX$E.B’-H f'f4*)(…EX3Xb5†I,..$+4U. .)E*JFCIX3*EL(.R57E.E!.$)*B Q > n/)F(nUF–/. n'E.F44k)$Jn/)+_•)E( f.en/)+_x*{.^O# = n/)+B(-. n/)(n*'Jn.) = ).,$E,5.,4 = = .{4J¦ .R57n/RnE*.6n/)(4*E.$),(r,J( > NOE*(OB k"2+"[1+"h ‡ŠL7KZA|~x3c!‚+373Z7Š" ; r."@-)ETŒ. : n/)6n.J_bV4 = = > *$Ž6XcE*g f' = Vn.) ed4*$Oe.4kL)†.44k)C51.!X3*E ™ +IL f.(n/)(4*$†M. I.!Xb'E.M5ŽCnE.O!4k4*E$)+B k"2+"[1+"' u"ŠŽ$"xS(…3"1,‚kc7Ob[1" ; CŽ)E.JK : n/)+_$F'XcE'Š$")J > n.)657)“TnE.KŽ414ŠE$) ,4*' > 'H)E.(Or$)MnBJ-.† f*.d5T.()E(OrMn/ƒ .r4Š$KBT›)E.U(OfOX)X3'.†{'XcE'V!n,Gk#` > )E.*(KB k"2+".Z yc"xOZ7vJ–3b.g*$ -R T(()4k4*E'$V > 4k"5x.n4k$$d.dn/)gXfy6E.$)H4kb# B–f.Mn/)ZXf4k$!4k57J64 = = 'n-/cnU.M5Ž'.5[UJ$) = & "G& *X3'E5–64k4*E*$),H43E*n/6y. X3*EhBf-6n/)gXr4k$Mn/ & "y4*$OR*X3'E"57)’.P4k4*E$) = ,)„yn/)n.JB ; f.A4cEn/ $+4U.A*XcE =O> E.,n/ƒ.57J$)5[).FI*r4*$KC*.‡C5 im

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.6.57J$)G57) .Pn/)A4Š$KB-fOEf.C$+4U.J*X3'Ek.U!FE = f5 44k5[) = H5e-4*$OB -H6E.$)41U$J > 4*n > 4*n^3({U.)*X3'E–57) .G4k4*E*$) 4k57JL(KXU)P–)(.e)4k$)P)6.!*XcEnU.)())JB–f57 n/'3E = J5d.U$)_.„n/)ZX‡4k$‡Jƒ4cEn/G$+4'.{$ $JX > J'$.J4*$KC'XcE'B6f.JPE$)4k$P4* > CAn/ne)J U.)†.nGF$(4ZX3'.y*X > —.GnE.K†4k4*E'$)ƒ$( (B–-OE*!.r6E.$),4k$R.4*4XKfn/)OXn/6Fcn+4'J+)E.)B k"2+" sPbŠcŠOvJ–3Z.Z*$ Ž)–.n(*J T^) = $ > n/3*.)5T64* = ”n/B -.ydPE…J4*(n/)ZX†41U$PEnƒC. W 5[ < )ZX(.Gd./# 4k)O < )ZXRJ4*3*En/d.M$k4.(*XcEhB k"2+"1"h G"L*`*N( sPZ1c*3 W 57 < )gXJ4k$F)X = .G4*$O†NOE*4 = = > 4Š†) MC,J$k4..B ; ƒ,(4Š((4*JK$){5.‡E57~n/)gX641U$_ ) = $ > 'H.$ f.N3Ed..5P4*$O ™ n)())(B ; 5V = XbE†$rH4k))„!5T.J.HMlc_•.{6F$M4k)) 5e.6$k4*.FnU.)())((-I*'G fA.6 WJP57) .PI*f4Š$KB ; 5eCX$E. 6Ÿ$_k.„.6 W .65[)'.†n/)4*$O f = †E+B W *5[U6E.$){fyX > E.4X4k$ZiŽG*!F)C.M.nP.57J$)G$57RJn/,3E = -5 .$)BVG/.(4*M5L.CE*5[Uˆn/)gX4k$R'!.g R,G02)E.Ci3BjOB k"2+"1"' vF"Ž)–1‰"1HsPZ1c*3 -yd./#`4k)O < )gX†4k$C*.)J > .$†A.)JnE.¢#`4k)Or) = …. 4*$OP'XcE' ™ n)())(B,-.JIUM4*$P5"FIM4*$O ™ PnU.)())J‡PE 576‡IUP4Š$P5f.H$k4*. ™ Pn.)J))(B…-‡n/)4Š$P5f.yn/)4*$O ™ i)j

PAGE 39

A T C G A A T G A A A T C G C G 0 1 1 1 0 1 0 0 A T C A T G A A Parent1 Chromosome Parent2 Chromosome Offspring Chromosome Random Binary String02)ECi3Bj ; EU$)y52Ž) W *5[U < )ZXd4k$ n)())(-'eE65[e-n/)†4*$e5Š.!$+4 ™ LnU.)())(B–02)E.!i3B£§M'E$ .r)/#`41)'K-n/)gXR41U$)+B 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 Parent1 Chromosome Parent2 Chromosome Second Offspring Chromosome First Offspring Chromosome0L)E.Ci3B£§ ; E$)y5ex*)•d./#`4k)O < )gX k"2+". |*7•7"ŽM$7"ŽK72[{*dyc"ŽKZ7AtH7*Šb[Za(… -" "^c.d4'n4*T5Šn!*Je = ()† TC._O( > .-nJ > ZŽ*G. = E'. = cn^y. > mb`B i§

PAGE 40

k"2+".•"h u6x‚k$ŽI(…ƒu6x3*bI( n.Jy—J'$ > (4*'$„.n/ = …ƒE = y5C'.)J f'J$($ n/4k))*!5e.†..B-f.P3E = f5–I.c,4k))*!$d$P = Pn/)(4*$A57 F$RMn'.yd.M5. : nU.JcB‡f.J*n/ = T….()E.J)CI.c 4k))*"'-nH.P%RIŠ. 9 ,5L. : nU.JcB n.F R ^c{I.c…4k))P.$J nU.J{n/)(4k)„().{.G5'# 57K(iFHnU.J$„$(n = ‡4cEn/+B,S–3nE.)ƒ5-.ny$Ji X 6E)E!nJJn/)(4k)*B–-3E.P.'nrR$UnAn = 4knX, ,'PE.)Edn/)(4k)J).AnU.J$GA'n/(.‡OE = M5Tr*n/r .r4k4*E*$)+B k"2+".•"' u6x„œ†Ž‰7L‰"Ž—œ†7+7G•–*ZŽ3‰ E'. = 3n^3d$(nU.J$H f)AIXbE*„JL.I*‡.*BM-. E*. = 3n^P > 4k.'L$–$–U.)L f†)†I*.LXb'E.en = !3n$ =3> †# 4*'. = E'. = 3n^3" fy)‡I.VX$E.yn/) = .P. = E*. = cn^cT/1n/X > B < )gX!4k$UyJn/)Xd. = E'. = 3n^FE*n/E."$4O!‡. 4*$OB Q E$){.$Cn > = E'. = 3n^3BP{.(n/)…(n* 4ZX3'.x5‰XU = = Lg $ = E'. = cn^cŽ RP*)CI*.ŽXbEBL > n/) = '.4k$F f3c(nU$dYEc3$4k)F. = E* = cn^c(ƒ5[$k4*. '.)_k.†.n†”.)E = ( = 6GI* = r'XcE'!„n.U$) '.†g $f'XcE* fH.C4JkIB k"hI ‚•]((Z -*2n$4TK3E*n/P 892:3;L< UnE2%R) < > n! = > nE*P.!Xb$U)E 4*–5+. ? > 'n*%) < > nB2f.R0234**.4*R5+. 8d9L:3;e? > nŠ%R) n > nM "f.n/ = HH.kF(4*¦r(4kn/d5L.M0LO4ŠP ? n//# (OC4**Byf.(57E*(O = *….nJ = …4J¦$)n*N3E. i

PAGE 41

"A.n/U = . = nH4Un4* = 'ƒdf# = 4J¦F TnE 4k > .PKE*) = y.M "^c.(52‡df# = ,4*J¦B n$l

PAGE 42

s6AtHru6qd ptHwp*p-}-vHvJyr}"tHwAw,rwe‡qd}"tMuPqdp|”vFyz --.*O4*'.RF4*n/(O–4 = J = )Mr. ¡? #&$UFn–5+4 = # JB Q > .E.Un†4'J¦$)…n'NOE.6gX = 4*4k)„n^cy.‡1O X$$Oe5k.-34**.d(4*'n/(KV4 = FBŽ-*en$4*V f'3*nEe)(-5k. $/#`5[#`./#&$MJ57-. Q n/$#&n/Ž0LO4ŠP ? n/(O-4 = JB +"h F3•70/*R*p-7+*bL7*"L"x3$ "$#&J)0234**.„ ? 'n/(K‡( "#`$Un.4Šn$B Q > 4.# J¦$)n*N3E.CgX = ƒ$44*{.‡i$% 0LO4Š‡4 = ~57C4'J¦. X$$)E = Yn/X†57E*n/)EnU$G„ f+B@fn/K > _•.† = Yn/X†57E*n/) $(n*.).H57)'.†)*L$yJndHn/M.(On/)n/d'E.R5V.†5‰Ec# E.HnU.) > .$)JEnU((4k$E.,n/)¢#`^ŠBE.{B-.X4k H.n('57M.Jeg "$(*O4Š*ŸŸ`B6-.FLg "$J34**.J57 ./#&*() ;< d r441)„'Ÿl$`B(-dn/)4OM)((5".(n*N3E. EA,i$%02O4*'.P ? n/(OfE.(n/)KX*)•n/)(nB +"h*"‰ ‚+({L[gOtH"Ž"Ž3*‰7"Žƒœ6*OtyŽLb*$xc : 'PE'$R*..*Ÿ/¤$rA.)J¦…$nU = …4*J¦$)n'NOE.B ; = /# ).)6{.Gn†5f4 = = 'n$_2$Xy4*J¦$)UJB : 'PE'$ƒc# .'.„'(4J¦$)—n'NOE.G*$JJJn6.,*..„4cn/(E5[FJB ; ….y.'.,4cn/6Eƒ = …)c#&NOE* > ('_2.yJTPIC( =O> .$‡R‡‡X > )A(4k$E.6,.„n/3)g f„Z f > nn/.‡yyn/3). nU.EEK'-57¦.…41)'KJFn+B“‡,5M.'.4cn/_!f. ncŸ

PAGE 43

()nE*!52.C(Ž6.g fAG.R > #&$Pg ›. > 4k)))X3( A,*$+_Ž*E. = ((`BFP > 41)'KM5.J.G43n/_x.Fn/)'n/XJ. > 5 2.‡()nEM'{.F(–I*.(.JN3E > 5.J(T{.J4k))5!2. ()nE*FdJ+n/)E.d.Mn/).I*)E.$)y5xd > ,B ; H†J'$TJ*._c. : 6E$6.R4'J¦$)†D/cJ'.2n/).I)E.$)L5*.! > $eX > (4k$E.'KX$. =3> Mn/3)dn.E*!†Xb'E$e.-N3E > 51.-n/).I)E$) =3> cn$.yFn/)57E*n/), R,nU„n/)I)E.$)•B-SVn{n/).I*)E.$)fy)E.)G .J4* = ~E*.Cn/)'.$)….Fn/)C57E*n/)rA(E.F5"FNOE* > 5. )E)+B : 6E$G.'.(!n$Un/¦ =O> .r4*4k\ : )E.) : 4Šn/ Q gX : < O)'. : n.*E -)E)4*n/{n/)'F5MAO‡5r)'E.)F = A$Un. =3> : f# 4F¦$),).BRf.P¦C5–.†)E)A4Šn/6R.4k.Of).6n/3*.FEA57 .†)E.)+BR-P(ZX†dn/)*R5–.†5–4kE. = $)-M(ZXd$n = 6E )G.PnE.O-)E.)Hn/3*.(J = ',J. “*n/3'.(n/4k)'.†FJ.) = )E)+B2-.d(gXM!.F.T.Rr-‡nn > 5• : 4*J¦Be-n/3).6nE .nd.JOE* = d5")E.)X$E$ =3> : ‹4*J¦rn/J.J'.d. ./#`$ = & ",CNOE* > 5L.C)E)GH.rUEc#`(d5L.CUGB : 'PE'$P.'.f = PE*†Enn/5‰E > 57e)Xc.-0234*'.-* ? n//# (Oe4 = JB ; –n = !E((n/)$YE*n/)† f†c51.-$UEn/E.–n/ = 6†. 4Xc)E"n*$4-H.!$UEn/E.BT-.dn.)n/d5Ž.M$(En/EI*.".d$# E.)F4*n/ = .C$Un.+BT0.!n/_c5+Cn.CR6.J¦J4k)†/c4) dE•_Š.()'E.)„4*n/('n/H.(d5V'Ln.FO4*B ; 5–. : N3E.n/ ? JF < 4K$)(E•_V.,)'E.)4*n/,'JPE*n = Fn'E.6. .)c#&n.‡34*d{*)„G.J'n.F*O4ŠB6kOMM5T4kE = $) 4k$)V– = R.I*.(J.f(ZX"nn/rC.fO4*†4K$) = ni

PAGE 44

Eƒ57P.H$nU— = F/kn/X,…r-FnOB Q E.$„†&ŸgjZ"44k)ƒ.F57)Z f. !5L(gXf5[!. : PE*$HR. = y34**.T*$-E : N3E.n/ ? 57 n/c.†.CO4*\ Q ŸyS–cnU.rr4k))"5–i†*.)(cE!HMI-N3E.n/ Q iPyS–cnU.rr4k))"5–i†*.)(cE! = GrNOEn/ Q nP < .M.rUK$)G5e(.)J3E* 9 < .*Ÿ¨$R44k)…'PE'$.'. = 34*'.($HE‡. ŽX < )E.FU$4*4K$)5[CO4*B(! ", > 4kM5".C$F.OI ….‡ < d_2( > @-*En/)y < )E(.BA-F4kE. = $)4k$6$ .I*FC5.‡.P'.‡ < $C….‡(cEB‡-J5[)'g f'.,C5 4kE. = $)†4k$e "-441)J†.f < R# = : 6E$(.*O4Š.\ : "$44Š.†.M. = T„i†)’(cEH.P < @fX6G. = & "i(.)(cE!H.C < Q gXƒ = T“iƒ) (cE‡..¦)K&7Xn[‡ < . Xn&‰.¦)K[! < @f$),5eJJ3E* .)E.).PO4*,4O$)„AP(ZX†$†kO_ŠŽ. : -# = 34**.MEF.‡J‡.'.G(4*'$‡P.F4'J¦$)4*3n/*E.B : 6E$ .(41)f.C = > ‡n' = )Ef5ecn•4FcB : 'PE'$,R*..Jnn/4* .57R)E.)*fE.U.JR4J¦$),43n/ = ){F4* = = > $'R.4kK )(.RnE.O–(4k$E.-(.f*1n/-†.fn/)–5k.-34*' = '.dXbE*$+B -'––f4'J$ > )‡5[T.R = > 5 : f# = ‡34*2CI**J) = > 4*J )E)B nn

PAGE 45

+"h*" •ŠZ)K2[b3g3tyLŽb**bŽ3 0.Un//#&n/G*O4Šry4*n/(O!FT'PE'$R.dnnk(n*n 4 = ~5fP5 = cg‰FUd$nU.—„65-4)BG-. = cr$nU. =O> y4J/34kn/P„$n/X(57n/ = T„.”nn/*.yyRO^ ™ M' > $NOE* = UE 41))-J$.COC > '$Fg !#`. > $B ; ,57n//# n/H4*n/(O_..M(cE"$rn/)'.y = R. = c"H.M.$-n/)*.n/ .”$†n/), = C.†4U.)B < )OXO)L5[Un//#&n/{(.cR4K. (cE"E'.PdJ3E*n/OBT-OE*T)* > .Mn/O!5L.M(cE"$rn/)'. =O> .†4*n/JKM Rn{ER6$n/XJ5[Un/ = T{†41)'KRGI*. = d4k))R57M.J(cEd„.†34*{ > )E.B(E.Mn/†) > (3*E†n/KP$ n/)'.+_Ž.FLO4* f'2X‡gX$4Š = & "ƒ.F(cEBF-.JZX$4*P Jn/$#&n/'kO4*'.Pn = M$M!.MJn/$#&n/!n = 5ŽX$$)E*$41G¦B -3EMZX$4JgX$e4*( RL > C5[)'g .J'Ž34**.F4Š({57n//# n/P*O4Šf64*n/(OB : Xc)E)LX = 644k)6MO$!. n/*gX$4y(ZXbŠ4*f(f34**.4*EnUF"K3E*n.d4*E'X5[Un/ 57REn/)*.n/ = cn^c_*E*.()k/c•57n/fF = A,XAn/'x = E.) gX.r > )E.R$c_*,n/$)G524*E.$#&n/'5[R$n/.‡-4kP.Rn/B Q rV&Ÿm$44k)(d57n//#&n/J4*n/(OV5[V.-Jn/$#&n/4*n/(O 4 = GBd‹I*'.(57n/(dEGEn/6.†n/LgX$4ŠBr-.†.M$†(c.{E‡ $(3+H52.rU)kn'NOE.M(c.•'H!$44)n+B +"h*" yc"xOZ7tyLŽb**bŽ3 nJFPE*$A.4cn/‡5rX)E.)*$E.„ƒI**)E.)J57 4F¦$)H4 = J!!/c4*y'H.r4Xc)EnU$4B"d.nr*J = ).† .dn"5•4 = = 'n$_KU$XR4*J¦$)yJ"J'$V : 6E$‡R..B .'nFFrn… = FE'n/)bYEn/) R > 5!J4Xc)E > nE $UEn/E.B!-rn/)ZXd*A6E.$),4k$UfgXP = rI*.Ann/U.J‡. $JEn/E. = †E*+B nb¤

PAGE 46

8 ¦E.6yŒ.*ncŸk44k)y†d.nd02O4*.V$!E ¡ F¦ ? )' Sec4),4*Or.(34**B6f.(44k){34*'.y*~E = I.cGH/. = d(cE" = E*‡.M34*BLD.gXx$4*†nEXr(.cH "fE r = '(.-4'J.(4*(K$)†5[–nUF*/c = !(3*EBŽf.-n/)ZX"*JPE$) 4k$ "M.I*.y†$) > .J¦F4k)J/c4)V "d4cEn/ =3> 1. 4k$B : N3E.n/ ? P THE*… R—nHRUJP§$`B„ƒ*$4XAd 64$# 4k)$,E& "n/)gXA4k$U,( > ? n/JK¢# = ? $ > Se.n). < )gXZ ?T? SVMd* < )J()…x4k) > ? X3'. < )ZXZ < ? MU_L).G fG 5dPE.$)4k$(…I*.,4*J34*•Bf.,n/)ZXF4k$‡ = ,E C$4X > n.) = ).yOE = r5$4*.$)By?V? S–4k$ Jn.)$ > J†4cEn/)* > J$C$k4*.(n/)(4*$.G4*$O *X3'EB•f. < ? “4k$ 57gXHg $*F†4cEn/y$k4*.P$ fF$"F.M4*$KB +"' F3•70/*fŠp-7+*bL7*"L"x3$ ŒH.dZ f.64k4*E$ > 5x/#&(*) ;< "!†Xc = R)E)y6M) = On/).n/4 = JT5x.MnE.K!y5‰E.E.n*.) > .$)_c6EnUH$nUG = n/)E*n/).X4*.…n$% ;< .)g CBd6E.i$lbf4*4k))c# = > U … = *!n$%”4*n/(OFF$ > AŸ§3B@fn/K > _-%FB &iZe/c.{. Q $)n( > )EMZiibeGE.4*41f.(.)5nZ#&(*)L > )EB %.A Q > nbV.X4k < %ˆO)'d5[CE)J$.G.J){5!i3B£¨Z#&% ;< B Q )r5 .‡$nUƒƒn$% < %O)'C = ƒn/…g $P34**.H4*'n/(K6 0234**.J ? 'n/(KdgXJ„'n/„)I*nn/P'„n$% 4* > 'nx.)+Bf. 4*C4UJ$ > .n'.F.y57O4UK6${ƒ.y3E = C5 ; K#`Œ$5[ 8 P5-.GnZ# J)T > )EBƒ-.Gn$%”02O4*'.,4 = ‘*PH*)T^ƒ5R). (cE‡.rX$$)E!' > X$ = rH.rX'nxn^G5ei$% > B"-*!^c.g f n¨

PAGE 47

L = Cn3BŸP"5 : EJJ$ > 5eSe..(-/#&%d()k0LO4Š. ? n/ )E.4 > 4kd520234*'. d4J¦$)GxnUN3E. d6E. ; 'kn$% ? n/ > R44)n L.4 n$% ? n/ R* > 'n•f4*4)n %.‡* Q > n$% Q n/$#&n/Ž0234*'. : PE*$HR. %.‡* Q > n$% : $Uc#&n/ ? 'n/ Q .# < E.!f4*4)n %d-f n$% : $Uc#&n/ ? 'n/ Q .# < E.!f4*4)n = E*! : ¦ > J^c n$% : $Uc#&n/ ? 'n/ 0.n//#&%dn/{R44)nU ]C > JR n$% : $Uc#&n/ ? 'n/ 0.n//#&%dn/{R44)nU : *Eyf n$% Q n/$#&n/Ž0234*'. : PE*$HR. ? 4k)GR44)nU n$% Q n/$#&n/Ž0234*'. .'nrR 9 > -R)(O"4 = ,B 9 > f)(O"*"†3E.d(4*n/")H.I*1NOE' > 5 .C' > )E.f'HJ!52.M57O4*O-$(52.Cn$% ;< ,(.C3E = !5 ; Œ# 8 B -MX = H3E()E/k!(/cAi$%D34*'.PF"'KFn$%D3# 4**.(Jfdg fAL = Pn3BŸ$B < )'..†.(n$%‹*O4Š,Fn^A5Vi$% 34**_x/.„i$%*$UEn/E.6X = ƒE*{4KP.yn$% 34** =O> E'.„(5di$%”E*n/E.B0.F*n/_"i3B£¨$% ;< 34**.6E*((5 6c : E*n/E.eP4OV 6cb#&' > -n$%34*+_)E*.M).R : E*n/E.!57Vnyi$%“ > B -.Cn$%*$En/E.-$r.AKU$G fH. : 6E$HR*..†34*'.6# *GBM-. : -# = „O4*.Ed‡5[ )LKU > M(ZXr„)A .CJgXCREG57Ri$%34**.6F$nU,57fG4'J•n$%34*•B ¡ E()E*x./#&() : $c# < -*O4Š.ŽX = 644k)C$eE 57n//#&n/ = F(.cgŸbŸnb`_ Q c#&nE.VJ.3*giZ`_O Q $J$n ? FJ. (.cgn$l`B–RŠ../#&'()* Q n/$#&n/+0234**.)rUJT44k)y .C'$E.d(4Š > : 6E$G.'. = G4'J¦$)G(3B +"'+"‰ ybO3Žr"Ž[Z7*"*pC[*)I(…3"1 ‡'n$%›4*n/(OV$"4*n/")) > n/).n/H(cE–n)f.! T4$# 4k) =3> d6E.i$lb`BTf-$44*)nA(4*¦!),.P > )JK-4* = 'n/r E*(!$-5‰ = 'n$)H5eK "$57-Xc-!6EnAn/)-*G.COb#&nU4GXc†57 = nb# nm

PAGE 48

)+B–f.d44k)G(.cGXc.".Cn$%nU4G))GKJnE = nk!nU,5L fnUGn .)GF(3*Edf.Z f,G02)ECn3BŸ$B 02)E.Jn3BŸFn$% < *4@-)) : g f < E = n : MR)‡. Q cEd{. ¡ ; c# n/)n/.J. Q cEC‰@f4cEn/H57)i$l$7 -V(cE•$–.CJgX6g $Ž.•4*J)4k))+E'.-CU$XTU $†(gX†y(cErg $†„6$†P$6.Hn/O(5-Xc > 5fT. .T$TVn/).n/B–f.-44k)F(.cJIVn/)(4*E.T.n/K"5+Xc > 5+nH. =3> EF.†n/KUd5–.†(3*En/).n/ =3> .†.BCd57(ZX3'.‡nU(cE g $‡.„n/KH5M.„.F$„n/)(4*E.5[y-(cEB-.(3*EG f. Jb.6EnE6E$XC)RJgX+B ? > -)XAyEn/P.C¦/#&*n/5–. =O> ")K'.{.H¦/#&n/ =3> {).(n/)O(57n/F„*$6yfOE = †5Rn/) > O#` $5[RX3 R = rJF¦+B +"'+" ‚+({L[gOtH"Ž"Ž3*‰7"Žƒœ6*OtyŽLb*$xc %.y Q > n$x44k),‡Jn/$#&n/x34*!5[diI£¨N# ;< = ,) : 6E$ ..B2f.r$JUEn/E.rEHJn/c.r.Ci3B£¨$%R#`34**-J-52 : Enš# E.{7).{57‡nU.X3'n/ > H'.„n^UB‹-.„(gXy57‡. : f#`4J¦‡ (cI*n/‡*O4Š4F¦$)—…"nA*()B ; —){ "$4*4*. n)j

PAGE 49

(cE = Tƒ& "A$by.y(F > _e $44*.G5-J3E* = & "… T3)J E*$,GkO> U-Z TH.r(ZXP-52.M4*4k)H34*B : *E“{&i)jZ†44k)D/#&(*)PJn/$#&n/634**.A57 : > (#dc# ? n^$$K : ? V)B : N3E.n/ ? Ue TREJC4KV.nZ#&'()*cO4*B SVnUi$%34*'Gn/4k)'.Py( > dH.Cn$% ;< -4*OAE'.(JN3E.n/ 4*gB ; {)AH.(Ob#& > r(gXr'g ".Ji$% : f# = {*O4ŠJ$# *G_Š TKU > r(ZXM "(.„G.((gXJM5V.Jn$%ˆ34*BM-.†n/) 5‰En/)„E =O> : 4J¦ d(cIAH'nE.P)*•J$M$†4k/# nI*nCHn$%34**..B!-.Cn/)5‰En/)AEA "d‡ T)K57E*n/),5V.C57)Z f. 5‰n/\ ŽxRc_ Ž•Œ.+_ ¡ E = -5 ; O#`Œ$5[ 8 0O4UKRfc_Š %dJ)G%Xc$)+B +" ‚+a(l(…g -*+n$4*x4KrrgXXc …53.–/.'.& "$#&()M/#&(*) Jn/$#&n/'Š*O4Š.BŽ! "$#&(*)Š0LO4Š.VE.P4J¦$)FnUN3E."c# nE*. : 'PE'$C.._b0.Un//#&%n/JR44)nU._)(.n"Fx "¢# nE+BR-P./#&()+34*'.RnE,n$4*d$P.6) > Fn/$# n/dn$%*O4Š.FnE.O > X$ = B-*F*n$J„.57‡$n*3) .X4Š(KM57M./#&*()LO4*'.FMnU.) > n'.G4gXc'.y). (X$$)G57-.C4cEn/)y52./#&'()*1'K$nnE!H.M5‰E.E.B n§

PAGE 50

s6AtHru6qd u6Aqˆr‡vF6vH‚•qp GqdwAqduCrbstHrr‡v†tys6 -f44k)J.n VPJn/$#&n/Š34**.–$"n‡4k57 = F& "$# J)T—./#&'()*V34*'..B{.)E.)—.H.!Fn/$#&n/3# 4**.64 = ’OX)X = ,I.c,,/c = M(cE_.)* > I3G$G(cE-$ n/)'.—.,4*4k),Bf.H5[)g f{n/)(/c4*—.Gn,6E# J)134*'.6*G.hB •"h v(ŠOb*‰-7I/*!bx…yc"xOZ7AtH7*Šb[Za( -T441)C.'nV34*'.RDELd > #&$!.nU†# 4*$rf.g R,H02)E.M¤.BŸ$B"RG*14k4*E$)‡5e.4kK > $,*.)c# XcE*Vn/$•BT0.f†I3H3E = 5L.$)_n/)ZXRG6E.$)G$rn$ )E.VE*.M.RXcE*xJ.fnE.K–4k4*E*$)†nn/rC.Rn/)ZX*JPE$) $B!-rn/)ZXd*A6E.$),U$R$P.I*. =3> .PnU.)Xb'E.!57f.Cn/)gX 6E.$)4* = = 'r4kn/X > B-. = (XcE*en/)EO$57J.GI.c 3E = !52.$)-!)E4*E.-!.P)E.)H57-.M*O4ŠP4 = GB •"' sP(…–Š"Ž3"1b(*-Zx…yc"ŽKZ7Af[+ŠZ27*"L"x3 -MXb$)E!n/)(4k).O-5L.r44k)AM-# = ,34**.!$C = g r\ ; X3*EŠSTn/c. ; X3*EŠ02 ; ? 4*E*$) n

PAGE 51

Select Parents(); //for Crossover Operation; Crossover(); Replace(); { Proposed Genetic Floorplanner() Generate Initial Population; { { Mutate(); Replace(); } Find_Best_Individual(); } Output best_Individual; } for N_Generations do { } for i in 1 to cx_Rate do for j in 1 to mut_Rate do02)EM¤.BŸPX'•02g “52. ? 4k)nr0234*'.P* ? $O : n/) < )ZXd4k$ Q E.$){4k$ %!)k.r = gX6n/)(4k).O! f = rnEHH.C5[)g f†n/)B •" r"x27•[2Ž*F3Žbc3"1Z.Z7Š" STn6XcE*ZC.–4k4*E'$)r+4OPE*.-RNOEn/V4*•4K$)ŽŸgjZ`B S–X > N3E.n/†4*n/c.Hn/41)*fGyX$& "$#&()L34*+Bd-3E. )E)ƒ4*n/H5[(.y.nG$n.)'.yn/)*65f‡OG†5Rn..)c# 'n.yO4*d$Pn = (4OE.H.FN3E.n/(4ŠM4K$)… fnU g1 f.)E.Z f.y > UK$)„nU.Br‹./#&J)x34*f4O E'.Mr–5kN3E.n/-4*B26O#& > n$%*O4Š(24K‡EdM–56(N3E.n/ 4*UB ¤)l

PAGE 52

-y > 41A5fnX3*E–n)())(G*$(4OJi$%'34*—n/)' 5".F'B(-.(IUrMdR#&N3E.n/J Rn'M.(.r5"4k)X(cne57r. 34*•BL-Rn/)yV–:c#&N3E.n/ fnUFV.f‡T5•.)$Xd3n*5[". 34*•BŽ-.!*(2'2.-O$)(51. = 3n^3V./c =O> = 3n^P.d5k. 4k)Xcn*B : n/-.dn/).n/X3 > 5•..4*EVnnEV.3""nU._.1XcE* f'Š5[-‡Jn/)J(),!57fn/).n/X3 > '.5[UJ$)+B •" -[Z"xc(*-*"r"ŽL7•7LŽ* -IH5P*X3'E-.UJ.‡ f..H.*XcE! RfE.XcX)E.) .APE*$4cn/(5X)E.)•B0.F T$#&*()34**.._e.,I*.†5M *X3'EkR)X =O> P34*' ™ -2$H.62 f,N3EAH)E. .ROn/).n/)VJ.R.'B20.T/#&(*).*O4Š._bfI.e5• *X3'E*'!( T)KA57E*n/)H5Žr5[)'g f'.†57n/\ ŽxR†#".CE*5Lr$-5ek.P > fG.Cn$%34*'+B Ž2Œ.#-R.(E 5V.(5'#`4kJf f.R5VL.†.M„ > !F.dn$%34*•B ; 5•. = )E = g3"5•.ybYn/K! > fgXU$4•_*,.P f†.GN3E,‡n/).n/R. = )E*. = cfR. F.r• R.•B 0O4UKJR#C6.H4cEn/65.G$( f'.ƒ*.)O†J).".G. > F.n$%›O4*+B2-.-5734OT$P4KT.R4*n^$$M$C5+nU4•B Ž ¡ E = 25 ; K#`Œ$5[ 8 L#+L.!E5*.3E = 25*O#& > eX3'L. ‡n/).n/R'k.C.B SVnU—5-.yI.P57n/U† "†.F¦…E*.A„Jb.6EX$E.B„-.‡I.6X$E.F5 n„*X3'Ef† T)O,5‰En/)H52'k.C.F¦H5‰n/B ¤Ÿ

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•"x"‰ -[Z"Ž3FqRc*‰Ž.Z7Š" --I.–5•F*X3'EK'–(E.FE'.d& "P > 4k–5+(Un_O*( > $C(Un ,-(nB •"x"‰*"h -7+ŠZ27*"tybOƒqRc*‰Ž.Z7Š" : 'n/‡ : NOEn/ ? 64O$)†Eƒ*n/3.H.H34*'_e. 9 ) < )JJ) : E = NOE.*n/r(.cxnnbŽfEG57RJN3En^HXbE*$)G52.C*O4Š = )E = ƒ$cBƒ-. 9L B6f.P R.d{.)Od5L.((3*E„.J > rE*. n/)'.$)y$d)E.4k‡.fy.y4*F†. 9L rR{y$ .r5734O!$(52.Cn$%34*'yn = rn/)(4*E.+B •"x"‰*"' -7+ŠZ27*"|~7Zc73"Žbqc*‰xZ7Š" --x.Œ.(..†r)E.-c.-On/)n/)–6.-nnEe2'J$ E'.J.6 f. > E*5[# ? (d(.c+BRf.6*5'#`4k'(f.A'Rn/)(4ŠE. E'.-.n/KUŽ5*."J3E*•n/).n/ =3> ..B ; 6n$%34*+_b." f'.!N3E J)EC(.fn/)!5L.r57)Z f.(n/)(4k).O\ 5[# ? (R fy'Hn„ > R$-.r.f4*!)E.)+_ ¡ )c#`ZX$4 f.—5-.G. ™ = )E*. = g3('ƒbYn/OF > U†$(.G. 4Š-)E.)G.J.fgX$4x_* ; O# 9 > RXc_5L.r.R4*!6E4Š' > B -f f.F*E.f6.dK#& > XcT'V.n/)(4*E.•B ; y.R+OE* = V5 O#& > fXc-!nnE*$,,E*,H.MI*.!5‰En/)•B ¤Ki

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•"21 r"Ž[Z7*"fŠLL7.Z7Š" n!RJe$e.e$nUJ57)(K4k4*E*$)+BxEnn/57E*.M-# = 4F¦M.dGX6d5"XcE*-.('•4k4*E$)+BM-.(X > 5T. 4k4*E'$)FE."P R.fX$$ > 5•$!n/)Eyn/) = '.'‡65‰X = dF. = ') > Ir*XcEBC-M'd.J4'J$ > )$P.J'Ž4k4*E*$){ .(441)„$4*4)n'd.$*.)J > B6-.†4k))R5L.J(cE = cn^cM = .JN3E.n/C5TFN3E.n/J4*r$(.$—.4kK > *.)F > B(-. O$)y5rnU(3*E$„…)J > .$•BD~U.)-414ŠE$) E$-.C.nM34*'. fk.-n/)OX†NOE*n^c > ‡Jcn+46EGB .)E.)'R{'XcE'J.-4k4*E'$)$.)J > .$+_d. > $5 > $,n/)UKB†-.($Gn/)*OrME.)J$'n > $E'.‡( $H5"L.J(cE„.()X = nUJ$^AnnEBCfRE.d*$JXcE* „.(•4k4*E'$)AgXJHM5V33{d f4kn/d,$G{.4*„5‰ n/)OXn/Gg $(„) = > 4J")E)+B{-.‡$„n/)*O(P6{$†† .f3FUn/XPF$R.$)5–FXC5–*X3'E"-'+4k) = M. 3,/34ŠXJA$CJ > 413 > IC*X3'E-$FX)+BF0.(n$%34**.._k. E52.P$-52k.C' > R!EG57-.r$Fn/)UK!B •"[Z yc"xOZ7{vJ–3Z.Z*$ < )gXJ* Q E.$)—4k$†$y.y) > > 4kP5f.ny4k$6E+B„-. 4k4*E$J'KX)4k$y'JE‡6E.$)4k$gB ¡ gX < )gXH Q E.b# )4k$‡5[y& "$#&(*)R./#&()-Jn/$#&n/f*O4Š{E*. N3E.n/G4*6 T,X4k+Bƒ-y4k$U† T,).4'J¦ = —$ f.,'PE.)E > B!-r.nP4k$R T6.), = EH4*J•4#&X 34**E*.yOcE = #`O4*BP-.†.n(4k$Ur$J.n/U = 2{. 57)g R.(n/)B ¤Kn

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•"[Z•"‰ sPbŠcŠO -64*4k).n($44*)nE*d& "An/)gXC4k$Ud,$n5[C{4*J 34*•BLSTnGn/)gX-IUTn/-iC4Š$K*X3'EL f.)R. R = R4*y)y .r$+4U..B •"[Z•"‰*"h Rb3"1G‚+c[3Z71" ? $O : n/)'P > 4k57( = )yI*.†5fH'XcE'B! 4*$Ofn/),$)f$rJ4* > =O> .M441)H.nM34*'.B ; —.H$ > $_V.y.)F > .$'V414ŠE$)ƒ†„'$GOE = P5 *X3'Ex$TgXRZ IeX$E.B ; 5kC(4*"nfU‹VEJFn/)bYE*n/) f)E(O = ›n/)“$ > _r.*XcEF f.…g !#`IGX$E. f' = A4*n/ f.AIUJ57 .$)B“-.*X3'E6$A4*n/ = 57 > n,n/)O = E.M > OcH.!Z "$*-.M4'J¦$)H43n/B–fn/MM44k) .n"34*'.2E2 Œ/#&-.#&fX$RI.R4Š$Ken/)†n.J! f6) 4 = = > '….yIC57 ˆ$)65-.H.'nF4'J¦$)ƒ4cn/B{-C)X( n*n/r57-X,.Pg !#`I*.-*XcE–Fn/)KU = E.M f*$Xf33G-. > gXr .‡4J¦$)4cn/P.)E.)….P$k4*..B,R5[6P'24*_2.‡414ŠE$) f'1n/)J4d5eJ!5e*XcEV fHIXb'E.-H.P(EˆF*)H.B -6)E(Orn/)$ > d.Jn/){4Š$Krn/)U$ > E* =O> 44k){n(34**.B ; .J)E.*(KPn/)$ > E+_ŽG.)E = # 4k4*E$){5f§,*X3'Er)$…57).F4k4*E'$){„n.J.F& "4*$KP = COX)X„,.6n/)ZXd41U$)+Bf-C¦P5e.C)E.U(ORn.) = A). 4k4*E$)¦yE…'.yP4n/ = …ajg`B„0.64k4*E$)¦‡5rŸllZ i$llc_ajb4*n/ = C.H)E.(O(¦H = y($F§{)E$O,n/)K'OE.)E*(E.44* > 5 33 = E'. = 3n^3Be)E.JKV'–n/)En/J f6'–E = #`4k4*E*$) = ()F. I.!Xb'E.B–-.M TFI*!$Cn/A-.r4Š$K-5[-Cn/)ZXR4k$)+B ; > _K.4 = = > 5ŽE'.C"5x.d& "64Š$K!n/)Hn.J!".(B d.†.n634*fnU.ry4*† f6'x5T.(XcE*!.†414ŠE$) ¤¤

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gXCJ('EˆF)yI._..M4 = = > 52E.†.M)E(O-n/)An.JC n/,JfF.)J*$M. Œ/#&fc#&RX$Hn/),n.(B = gXd4*$Kn/)HU$)!$ME =O> .RnO4*.T5[ = ‡& "$# J)kH/#&(*)134**..B •"[Z•"‰*"' €D+2YL3uz/6–Š‰"1GvJbŽ3Gs6Z1c*3v(VOb.gŠ -CIfn/)ZXM4k$ME =3> .644k)GnC*O4Š.f' = ,)„& nnCn/)gX4k${E›X6.n—*J_CJ > .ƒT$# ? )O n/)gX,4k$G..Hn/)ZX,4k$B-.)iZ#`4k)O‡n/)gX 4k$M)J > nU.O)d& "AnE.¢#`4k)OR*$r4* = „.†4*$O ™ n.)J))(rO .!4Š$en•B–! TM$+4U.d$-4cEn/657).! TP4*$O–ER.-J.3 = Z rB -."Ix$+4RŽ5[U( =O> n/)*n$$.M."IŽ4*$Ž5"I*x4Š$K ™ enU.)())(_ .rn/)*H4*$!5xrn/)H4*$O ™ -nU.)())J_*H.MF4Š$!5x.MI*4*$O ™ n)())(GBƒ-yn/)*$k4*.„65[J =3> n/)n$*$..HIP4*$65 .(n/)4*$O_+.Jn/){4*$KM5T.†Id4*$O_x„.(*4*$d5V.Jn/) 4*$OBV02)E.M¤.B£i(E*$.M T$#`4k)Ofn/)gX41U$B A T C G A A T G A A A T C G C G A T T C G A T G A A A C G A G C Parent1 Chromosome Parent2 Chromosome Second Offspring Chromosome First Offspring Chromosome02)E.M¤.B£i(Ž)+! "$#`4k)K < )gXr4k$ -‡)iZ#`41)'K†n/)ZXJ4k$( †44k)ƒ5[(EH fƒnU.)())J†$ "An/c. = *$ > U.)($ynnn/)(c$E.4Šn$H.y.A'XcE ™ ¤K¨

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n)())(B ; 5kV)(.cJTEF f : N3E.n/ ? VV fcE–J'KX$ ` _ N3E.n/J.JE.G…*E.4*n$)—*ŠZ‡.)5M(3*EH(Bf. Xc)$)FPE = ,(ZX… = …N3E.n/4*‡$F4*OFƒXb'O4*+B Ž‡'J$rPcnnE.*n/P5VEnX3)$)RA†R+4'. ™ : N3E.n/ ? _1.6# )kiZ#`4k)OTn/)gX!4k$!"n/) = '.J fF.R.!n/)gX!4k$ > F. Q 3IG! "$#`41)'KRU. < )gXZ Q R-M-f.Z fGG02)E.M¤.B£n3B 2 6 1 8 5 7 3 4 2 6 1 8 7 4 5 3 1 8 6 2 5 3 7 4 2 6 8 1 5 7 4 3 Order Crossover on First Sequence of Parent2 (based on the two cut-points on Parent1) First Sequence of Offspring Original First Sequence from Parent2 Two-Point Cut on First Sequence of Parent102)E.M¤.B£n Q cI*G! T$#`4k)OR < )ZXd4k$6 Q R-r •"[Z•"‰*" A3Žb‰/b[vJ"ŽK–Š‰"1HvJZL3,sPbŠgc*3AvJ–3b.g* -„4*4k).n{34**.— EG.E.nn/)gX4k$, )Gy. Q R-41U$B-Œr Q R!4k$MRE* = 'G4k$$ $(4J{$nyOH)E)4*n/H5[({33)'E.) =O> .)J > n/) = '. n)())(M)JK57)ˆ.4*$O"*XcE2‡.$k4.6X3E*h_$.dfE.Un d./#`4k)OyU. < )gXH4k$Z‰Mr-MFF = F.$Ung $y4)F. ))*F5P.„)E.)4*n/ =O> 4)(….„57y5C33E = *O4Š(57). 4*$OP'XcE'f„.F$+4U.A*XcEBF-.FMr-’4k$†Er‡*) ¤Km

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d./#`4k)O < )ZXF4k$(4Š$)—.H4*$OJ*X3'Er'Ki{E = O4*6 .Z f,G02)EM¤.B¤.BCut at Position 2 in First Sequence of Parent1 A C D B A D C Parent1 (CABD ABCD) B Sub-Floorplan11 (CA AC) Sub-Floorplan12 (BD BD) A D C B Parent2 (BACD ACBD) A C D B Sub-Floorplan21 (AC AC) Sub-Floorplan22 (BD BD)02)E.M¤.B¤ : E = #&0234*,.U$)AGRE.'nrd./#`4k)Of. < )gXM4k$ -Pn/)gXr4k$r'REAHF$P > Xc)$)*R. : N3E.n/ ? 57e.fidE = #`*O4ŠB < 4k)'.fE = #`O4*Ž5[)nJ4Š$Ke*XcE)$-n/)†# 4*$6r f*nP4*$O ™ –E = O4* > Ž. = –$ME$Be-T TrE = 34* fF. = !$†E$$.Hn/4*yOPR$+4'.C*X3'E ™ enU.)())JB–-. E = O4*Mn = Fn/) = .—¤„kOPn/).I)E$)P6.g fƒ…02)EF¤.B£¨3B„-. n/).I)E$), R,. = = )E*. = A$‡5[.P4.#&XL34*,'fn)„5[. $+4†'XcE`B ¤Oj

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A C D B A C D B D B A C D B A C D B A C Offspring1 (ACBD ACBD) Offspring2 (BDAC ACBD) Offspring3 (ACBD BDAC) Offspring4 (BDAC BDAC) Sub-Floorplan12 Sub-Floorplan2102)E.¤.B£¨M0)E."R+4'. < ).I)E.$)–.$F5[)dOc : E = #&0LO4ŠL†fE.Un d./#`4k)Of. < )ZXM4k$ •"[Z•" €•gZ7Š"“v(VOb.gŠb -VPE$)C4k$L• > E =O> .'nVJ+4cEn/–X > 'M. 4k4*E$)+BŽ-R6E.$)y4k$"4*V'FX)'.6NOE'n^Jn/)OXn/M†3n*4JcB ; .M441)‡nd34**.PG_.6E.$),'T4k57(y),G'XcE$ L)J > n.)(5[)"nE.KL4k4*E$)+B ; 65Š6E.$R.!*XcE$.25 JnU.)())JPE'.(JPE$),4 = = > _.J6E.$)G$6!.I*,E6CPE$) 4 = = > *F.R4k4*E$)F¦B–@f*.)*XcE2$.yn/ynn/P6. 6E.$),U$C57)’.C414ŠE$)G,).C52.C6E.$)A4k$f'-)J > $4*4* J.Pn/A'XcE`B ¤K§

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•"[Z•"+"h €xg.Z7Š"vJ–Ob.gŠJC€GuJvJJ -yI*(PE$)4k$J57(.G34**.AU4*n^3Ji„*.)(cE 57)’.PXcE*Š,/cnU..-4k))! = G_ ` *G.z_ NOEn/f5 .r*XcEhBŽ-E!G( $4,52.rcn$)-5Ž.C& "F(cE!y.CO4* f.g fG'G0L)E.M¤.B£m3B A C D B A D C B After applying Mutated Individual (CABD ABCD) Selected Individual (BACD ACBD) MUTOP1(B C)02)E.M¤.B£m Q E.$){4k$# QW ? Ÿ •"[Z•"+"' €xg.Z7Š"vJ–Ob.gŠJC€GuJvJP -6n/)*„6E.$)„4k$d57P34*'.J 4*n^3d‡.)”(cE 57).r*XcEŠ,n*.f-O$)A-.g fAG02)E.M¤.BjOB •"[Z•"+" €xg.Z7Š"vJ–Ob.gŠJC€GuJvJC -,6E.$)4k$‡ = ) ; OX)•B'.) E = F5dJ3E*( n).(41))6—.GR#CcR#&NOE.*n/(5RHNOE.*n/G4*J$GXU+B : *n/TOX)6Ž > 4*n > EP4*)(!.^$$ = T((cE–)E.4*'.)_$."41)) 52.C(cE"' = G.CN3E.n/f$rXAJ*$-.r'$Xr4k))*5Ln/ E = !5LJ3E*!!'+JO.+B ¤K

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A D C B Mutated Individual (CABD ABCD, 1011) After applying MUTOP2(C) C Selected Individual (CABD ABCD 0011) A B D 02)E.M¤.Bj Q E.$){4k$# QW ? i •"[Z•" fŠLL7.Z7Š"H–L.g -J$k4.A4cEn/ =3> .‡n/)gX†4k$)*r4*'n/‡*X3'E.ynE.O .$) ™ M4k4*E$)AG57”.(./cd.$) ™ r414ŠE$)+Brf.(XcE*&‰UT57) .nE.KG$)$,*XX > Z ~I.HX$E.A$n/ = {4Šn/ X > .$)•BP-'R*E.dE.X3X$Ž5T*X3'E f3c{I.dX$E.BP0.rX > $+4._16 "M*XcE•'A.(nE.Kd4k4*E'$)''.KI+B ; 5–.†I.d5T. $+4-XcE*g = Žr."n/PXcE* ™ *I*._Z.r.V$k4*.!4Šn/ $6XcE*Ž.F4k4*E'$)+B‡fM43n/PM4k$ƒ5[PX > $+4AX3*E 4cEn/G'G > .$)•B •") ‚+a(l(…g ; 'Cn*$4_–,n‡ = …Fn/$#&n/TO4*.C "P4Oƒ$ C.F = > A43E*n/ = & "$#&()–…./#&'()*2O4*B ¡ ZX n/)gX-4k$" "M.n/ = F$" T^‡4Š$K > )‡6E#&' > 34*V 4cEn/d4'J•6E#& > !34*B ¨$l

PAGE 62

s6AtHru6qd1 qGrqdFr€qdwAuJ‚tHwp‡qC‚•G}1uJ‚ -ƒ441)›.'nƒ*O4Š {)D& "4*E = 'n > gXb' = Jn/$#&n/' = *nJ$^AEBC-.†IM5 = nF$^AnnE*d$†4gXc. =3> Q # n/3n/)'n < Of5 ¡ < $)'G Q„<¡M< /¨b`BT-.rn/)A-5 = nF$^‡nUnE $4ZX3 =3> .rd)n : > F"@f$nU < KC` : @ < /icŸ/`BV-f5‰En/)'–5 k.PnnE!' = HC-5 = n*J$^c-$rE.^c.Z f+B 1k"h pH3Kb7ŽZ7Š"*-Zx{œ63"Ž$](…qs67ZKL[Z Q„ 4/#`4*n/ = cn^cB -G : @ < = n*J$^Eyn/)(4*P5fc—nnEB-.HnnE*Cn*$n/'n 57 = *nJ$^3$64gXc.„„Ž = †¨3B£i3Brf.† : @ < = nUJ$^AnnER$(X$# = y) > —. ¢= cn^cUb.„57J$B ¡ ).H5f, : @ < = nUJ$^ƒnnE†gX, > .57J$)H)G.r4k))"5Ž.C4*B ¨cŸ

PAGE 63

L = C¨3BŸ < $n/Un!5L. Q{<¡M< "n*J$^ < nE* < nE* ¡ ( ¡ E = !52cn^c ¡ E = !5 ¡ ¡ E = !5 ? $4* )j j$n c Ÿl i$l)n i .4 ŸŸ §n ¤K¨ J'nn nn Ÿin ¤Ki J¤K ¤K ¤)l)§ ii Ž = C¨3B£i < $n/Un!52.P : @ < "nF$^ < nE < nE* ¡ ( ¡ E = !52cn^c ¡ E = !5 ¡ ¡ E = !5 ? •Ÿl Ÿl ŸŸ§ m xŸl = Ÿl Ÿnn §m xŸln Ÿl ŸŸ m§ *n$l n$l nb¤Kn icŸi Šn$l = n$l n¨$l ii)j Šn$ln n$l n$l i)j3Ÿ *¨$l ¨$l ¤K§¨ i$l) Š¨$l = ¨$l ¨cŸŸ im Š¨$ln ¨$l ¨cŸ¨ ib¤Kn •Ÿll Ÿll §§¨ nnb¤ •Ÿll = Ÿll §$l)m n)jZ¤ •Ÿlln Ÿll §¨¨ nin *i$ll i$ll Ÿ¨§¨ ¨mb¤ *i$ll = i$ll Ÿgj3Ÿ/¤ mib¤ *i$lln i$ll Ÿ¨ni ¨nn *n$ll n$ll Ÿ§n ¨m 1k"' rC(2[5(c"1g.b[1"pHOg*‰‰ -r.nM*O4Š.! fn/c.A' <ŽJ E*. : *$,Ž(4*$ 9 = $UB ; .4*E. ? $‡ f 9 S–cV <-< ƒ.„'.4*E.(I*‡O$ f .634**.(3)hB02Rn/)J4*E.$)„57R.†*X3'E"N3E57& $J(cE $Fn'nE$.,")E*."R57FN3E.n/,4*JE.„. 9 ). < )F() : E = NOEn/((.c.n/ = {nnbV*.J5'# ? '(rŒ.*d5"2J. H.r0234*'+Be-.M5‰d(7•Ž",nn$•$fEf@-c#&n^y 57 9L & ".y5CK$)#†*44kx7$ =3> $l.UFG.H*4*41•B ¨i

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5'# ? '(rŒ.{J$) rE5[rn/)J4*E..G( f‡N3E(Kd5 {34*•B…-.Gn/OJ5. = )E(cE65R.,.( ",En/)(4ŠE.G. 5[#`4k(C f.BH0P./#&()e34*'.._x.F" f.…'nE. > )+)E.'.‡.52. = )EJ(3*E-5–y.dA$Yn/O' > d. gXU$4•B 1k" q:\•VO$(c"1g*f‚kOZŽ -(44k).'n(34*rn…* = ƒi$%ƒn$%34*'..B(S–34k# (OJ ",UE.U$ = i$%*n$%~34**†5[y!.AnnEJ' = . = n*J$^HE!E.(.rJCf5L4*$JRX$E.B–L = 6¨3B£n(!'+.CJ41K 4*$JfH-X$E.-EGH.r441)Ad-# = ,34*'.B Ž = C¨3B£n 8 E.-5[? $( W AG.Pnr0234* ? $J 8 E. ? 4*E$) : ¦ i$ll ¡ E* = !5–.$)* Ÿlll < )gX ? = = > lcB£§ Q E.$) ? = = > lcBal)¨ 1k" q:\•VO$(c"1g*FcL[Z -‡.'n‡*O4Š.6nn/4J($)E(O†.H.—3E = 65R > (ƒ. 34*•Br-.(.5‰EdOE = d5" > M{H34*„dMŸ$B†-3E.†.n†3# 4**.P R–4*3*En/‡ T$#&*()"O4* =O> .5‰EB… > nU.)„H3E = 65 > _!./#&*()!34**(n = ,43E*n/ f)E.J > /#&n/)(4*$)+B : n/ .J*O4Š.r6d-# = +_L.J34**.d "CEŸŸF(M57CnU = nUJ$^„I*B L = „¨3B¤.Z fJ = JEF5[ = )E = g$c_-R f+_!E*c#`( = G)G. Q{<¡M< = n*J$^c5[- T$#&*()k34**..B ¨n

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L = C¨3B¤‡! T$#&%dJ)+0234*'.6@-E*!)G. Q„<¡M< "nUJ$^ < UnE < nE ¡ ( fA7GA xxŒ.7G @REK'(Jq;g $4 ¤Km3B£i¨ icŸŸ$Bjj$i i¨ 3g Ÿ3B£§ncŸ i)j$m3BŸ¨)j n§$l .4 3BŸ¨ jblcB£§§ ¨)j$i F'nn Ÿ$B£i$ll ncŸ$B£nn §$l)i F¤K n)jOB£§cŸi m)jjOB£b¤Kn Ÿ§icŸ L = C¨3B£¨J! T$#&%dJ)+0234*'.†@-E),P : @ < "n*J$^ < nE* < UnE ¡ J R Ž•Œ. @REO(F7; •Ÿl innn¨i Ÿn¨)j$i ¨cŸ •Ÿl = inicŸmi Ÿnni$l n§ •Ÿln in)j$m¨ ŸmcŸi n¨ *n$l iib¤KcŸl ¤KicŸmb¤ Ÿ§$l *n$l = icŸll)$l n)jj$§ Ÿ§cŸ *n$ln in¨n$l$¤ ¤K¨$ll)¨ Ÿ¨ *¨$l icŸgjblll mni$l nib¤ *¨$l = icŸgjj$m¨ §mmnn ni)j *¨$ln icŸgjZ¤Knb¤ ni§ ni§ •Ÿll icŸl.Ÿmm Ÿm¨§cŸ §ncŸ •Ÿll = Ÿ§m$l)¨ Ÿ¨cŸŸnb¤ j$¨ •Ÿlln i$l.Ÿm$l.Ÿ ŸmicŸ¨m §cŸl *i$ll incŸ§)j$m n)j$§)j ŸmncŸ *i$ll = inb¤K¨cŸ¨ n¨b¤)l)¨§ Ÿgj$¨m *i$lln ii§b¤Kn¨ n§)j$n)jZ¤ Ÿ§$l.Ÿ *n$ll nmim§ mmn$l.Ÿ i)j$§cŸ L = ¨3B£¨‡ = yE*y = .57G$c_dM f.+_fE*KJ57 & "$#&J)2*O4ŠF57P2.‡ : @ < = n*J$^nnEB(L = F¨3B£mA.g RM. = xEx5[L. : @ < = nUJ$^MnnE*•57Lf./#&%d())0234**. fC. 3E = Ž5 > 2Lf57)E.B ; C)rR. = ŽE•57LŽORc_)Ž3Œ.+_ …Ec#`J_x.‡ = F.Z fr = rEM = '.57P0.34'K6fc_e…. 3E = !5 ; K#`Œ$57 8 B ¨b¤

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Ž = C¨3B£m(-./#&%dJ)+0234*'.6@-E*),.P : @ < "nF$^ < nE < nE 0.34O-R xŽf xxŒ 9 ¡ .BT5 8 @REK'(Jq;g •Ÿl m¨)j$§$l ii§cŸgj3Ÿ ¤Km)j3Ÿ ¨)j j$i •Ÿl = mnb¤¤)l ii§¨b¤K§ ¤)l)ncŸ ¤K¨ ¨§ •Ÿln jbl)¨m in§§§n ¨cŸgj$ ¨)j ¨m *n$l ¨§cŸi iin¨i Ÿm§$l)m Ÿn)j i)j$§ *n$l = ¨mcŸŸ¨ icŸl)¨$l)n Ÿ/¤Kn$l Ÿnm i)j *n$ln mib¤¤ ib¤Ÿl$¤Ki Ÿgj$n§b¤ Ÿ/¤K§ imcŸ *¨$l ¨m§b¤)l ii$l)¨m n$l$¤)l nn$l ¤Km *¨$l = ¨)j$nn$l ii$l)in)j n¨§§m n$ll ¤Kn *¨$ln ¨)jZ¤Oj$ iii$l)ib¤ n§b¤ŸŸ ncŸŸ ¤K§¨ •Ÿll ¨nb¤Ÿl i$lKj$¨cŸi m§§¨§ ¨¨m ŸŸgj$m xŸll = ¤Km§b¤Ki Ÿgj$n¨b¤ mb¤)l)m¨ ¨nn Ÿl)n§ xŸlln ¨cŸl)i)j i$ll)¨b¤K§ m§i§§ ¨m$l ŸŸ§ *i$ll ¨¨i$ll icŸ§$llKj Ÿmi¨§n Ÿib¤Oj imin Ši$ll = ¨¨mim icŸmb¤K¨$l Ÿn§)j$mm ŸlKj$§ ib¤Ki§ Ši$lln ¨nb¤Ÿl icŸl)n§§ Ÿ¨¨$l)§ Ÿinb¤ ib¤Ÿi *n$ll cŸmb¤ n¨m)j$§§ imimb¤Kn Ÿ¨§¨ nb¤Ki 1k"21 sP(…Ž$‰Š"L -E = '.H5[ = H.M T$#&*()+H./#&*()**O4Š /c41U(OH Tn/)J4*$“$)*G/c'.34**.BnE)56.Xb$U)E n/)(4*$U)!-)X,H.C5[)g f†n/)B 1k"21+"‰ uPŽbOKUpG(c"Ž71"x*"r3$ŽFuJ/†.UpG(c"L7Š"Ž*-7+*bL7*"L"Ž‰"Ž = 6EC = .ƒ57) ŸŸFE*r5-‡./#&()–*O4Šy/c4k# (O† "An/)(4*$$)(. = (E6 = 5[).G& "$#&(*)"3# 4**.†/c41U(O-4kn/X > Bf.Cn/)(4*$U)f T6J.C',Jf5 = A$y f.…JnB{Ž = H¨3Bjg fP.y41Un/K$,J4gXJK6 = =3> E'.n$% 34**JgX„i$%34*'B@RJB‹&inbd4*n/d R.gX3)‡5 = )E.(¨$lK‘ f.—E.{nZ#&% ;< P fƒ¤.X3'n/y > _V)n/.„.yXn" f.B -.M• fHE = .H57).M/c4k(O!.J.-nn/)EOf57-.MXn fBfŒ†) > 41f.6eOE* = f5 ; O#`Œ$57 8 d.A57Mn/)(4*‡Ž. ¨¨

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On/).n/)C{‡nZ#&%’ > )E.BG-.(/c41U(OeEd5[PV f.gX3'.) .Z ›GXU$P*En/)H5LmcŸNal$¤O’ f'nG = -GM4n/GXc.)B Q gX .(.{5T.().d f6'nU5V†nnEE*n/ =3> gXOXU$F5"¨I¤K¨) .Z f…'Ž = F¨3BjOB,R'e5.F R.…Xc.)P$Fn*X… R.)E.C > n/F .4*n/‡$cBG-*Mr'E$ =3> .‡gX$GXc.)C5-iI£i)~4kƒ.F $JE*+B L = ¨3Bj < )J4*$)F5Žn$%D0LO4Šd*yi$%D02O4*'.r@-E*–57. ? 4k) .'nr02O4*.)G6 : @ < "nUJ$^ < UnE < nE* ? n/O$ : Xc.)-' 0.O4*O-f xxŒ 9 x•R 9 ).-Œ 9 xŸl j3Ÿ$B£§cŸ m¨3B£¨§ i3B£ii mn3B£§cŸ xŸl = j$i3B£m)j m3BjZ¤ Ÿ$B£¨m mcŸ$B¤Ki xŸln jblcB£nn m)jOB£§ #&lcB£n mm3B£i§ Šn$l j$n3B£§cŸ m$lcBŸ/¤ lcB£mcŸ ¨§3Bal.Ÿ Šn$l = j$n3B£i m$lcB¤K #&lcB£i$l ¨3B¤Ÿ Šn$ln j$n3Bj$ mcŸ$B£n)j #&lcB£n¨ mcŸ$B£§n Š¨$l j$n3B£§cŸ ¨3B¤Oj #Ÿ$B£mm ¨m3B£mcŸ Š¨$l = j$n3B£¨ ¨§3B£¨§ #&lcBalKj ¨b¤.B£§b¤ Š¨$ln j$n3B£¨m ¨3BŸŸ #i3BŸŸ ¨)jOB£nn •Ÿll jZ¤.B£¨ ¨§3B¤Oj Ÿ$B£im mi3B£n •Ÿll = jZ¤.B£§n ¨)jOB£mcŸ n3B£mi ¨§3BŸl •Ÿlln jZ¤.B£m ¨)jOB£§ lcB£¨i ¨§3B£¨§ *i$ll j$m3BŸ ¨3B£nn ¨3B£§ ¨)jOBal.Ÿ *i$ll = j$m3B£i§ m$lcB£§cŸ jOBjbl ¨3B£ni *i$lln j$m3B£mi ¨3Bj$¨ jOB£$l ¨¨3B£n *n$ll j$m3Bj$ m$lcB£n 3B£m m$lcB£§b¤ fX3 : gX3) jZ¤.BŸ mcŸ$Bal$¤ i3B£i ¨3B¤K¨ 1k"21+" uPŽbOKUpG(c"Ž71"x*!f[+ŠZ27*"L"Ž‰"Ž -(E = '.57)”.(./#&*()LO4*'.F/c4k(Od TJn/)†# 4*$‡$)T.fEe5+ : 6E$FR. = ynZ#&%*O4Š.Zi)j`B–-f0.3¢# 4'KeRc_Ofx*Œ.+_OJ.ROE = e5 ; O#`Œ$57 8 –Ee57–.d : @ < = n*J$^,nnE*R).† T†4k„i)jb`B < )J4*$)*"(J.(J5 = 57O4UKr$AT f.+BFL = F¨3B£§A.Z fr.FEr5 = Fn/)(4*$') ¨m

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'G4kM.(4kn/O$‡Xc.)r = .$ f. =3> (44k) $4)n+Bˆ-.„44k).n„34**.‡ = HX$…En/)5P¤8£)j 57O4UK-$J,,gX$6En/)H5!ŸŸNal))H• R.•B L = ¨3B£§60.34'K"f6yx1Œ < )(4Š$)VŒF. : f# = Hn$%›023# 4**. < nE dD0LO4Š. : 0234*'.Zi)j : Xc.) R xxŒ 9 R Ž•Œ 9 f Ž+Œ 9 xŸl m¨)j$§$l ¤Km)j3Ÿ mm)jZ¤)l §n¨ Ÿ$B¤¤ ¤¤.B£nm •Ÿl = mnb¤¤)l ¤)l)ncŸ jZ¤¤Km Ÿl.Ÿ§ Ÿ/¤.B£§cŸ m$lcB¤Oj •Ÿln jbl)¨m ¨cŸgj$ j3Ÿgj$m$l ŸŸmb¤)l Ÿ$B£mi ¨¨3B£¨cŸ Šn$l ¨§cŸi Ÿm§$l)m m§b¤Ki$l n§cŸl)m Ÿn3B£$l ¨¨3B£$l *n$l = ¨mcŸŸ¨ Ÿ/¤Kn$l m$l)§b¤ nb¤K§¨$l jOB£§ ¨)jOBŸm *n$ln mib¤¤ Ÿgj$n§b¤ mcŸ¨n nnn¨n §3B£§ ¤OjOB£§§ Š¨$l ¨m§b¤)l n$l$¤)l m$l))j$n ¤¤OjZ¤K m3Bj$§ Ÿi3Bj$m *¨$l = ¨)j$nn$l n¨§§m mcŸm¨$l nb¤)l.Ÿ jOBal.Ÿ #¨3B¤K *¨$ln ¨)jZ¤Oj$ n§b¤ŸŸ m$l)m$l ¤KmmcŸ ¨3Bj3Ÿ ŸgjOB£mcŸ •Ÿll ¨nb¤Ÿl m§§¨§ ¨mcŸmm ¨b¤Knb¤Oj ¤.B£cŸ #im3Bjbl •Ÿll = ¤Km§b¤Ki mb¤)l)m¨ ¨$l$¤)ll ¨§i)jbl jOBal)m #3B£¨ •Ÿlln ¨cŸl)i)j m§i§§ ¨n)j$m$l ¨mi)j$§ ¨3Bal)§ #icŸ$B£nb¤ *i$ll ¨¨i$ll Ÿmi¨§n ¨m)jj Ÿin)j$m¨ n3BŸi #ncŸ$B£nm *i$ll = ¨¨mim Ÿn§)j$mm ¨mmn¨ ŸŸ§b¤K Ÿ$Bj$§ #Ÿ¨3Bj$§ *i$lln ¨nb¤Ÿl Ÿ¨¨$l)§ ¨nnb¤K¨ Ÿ/¤K§mnb¤ #&lcBŸi #`¤.B£§ *n$ll cŸmb¤ imimb¤Kn §nini Ÿm¨b¤Knn #ŸlcB¤K #¨§3Bj$m RX$ : Xc.) ¤.B£)j ŸŸ$Bal) -AE*n/)F' f$5[)E*J* > '. = *nJ$^nnEJ$ gXP-Ÿll‡(3*EBe-.MnM34**.415[F Tr, : -# = 34**.f57d. = nUJ$^nnEf f—Ÿllc_Ži$llHn$llH(3*EBd-RR4J$U > E.(.d5‰n/"*$!.d414ŠE$)‡¦Mn.)H5[!.d/c4k(O!i$llcB–ŒH.M.4*E. nnE*•gXT(TC¨$l(cE_g.V$4k4*E$)MOŽ.xn/)OPE8-FnO•OE* = 5rXUA*X3'EBf.A.'n,34**.FFƒ "^ f…F‡5M. n/) = $)*R.n/†.3R.4k57 = A : 'PE'$A.J$44)nU+B 0. = T414ŠE$)_.dnf* fc4k57 = = E.–.n/)KXn/R† 33,)E.)H f' = rg "BV02)E.C¨3BŸr.Z f!.CJ¦HI*.-n/)OXn/P4*!57 Šn$ll = n*J$^PnnE257V4k4*E$)6¦e5+i$llc_O¤)llc_.m$llc_c§$llc_c,ŸlllcB ; –V ¨)j

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$†.H6(4ZX(O6….HI.P f—n/.,4k4*E*$)…¦y64n/+B 02)E.…¨3B£¨3B£i.Z f,›'(4ZX(K. f.H5†.$ = nF$^nUnE fƒn/.,4k4*E'$)¦B„R'–.yI.PX$E.C'.yI)E.P "‡ = .…E*. .y(FX$E.r5[†e.64*$JBGE.C.‡4J–4*$(6Xb'E.r57P1O 4k4*E$)…¦† R = HkOBfn/GH'(4ZX(K† = '.—.‡I*.†X$E. n = Mn/H57E.. =O> n/)(4*E.6M4J14*$J-Xb'E.!H.HE*.P. /c41U(OBJ-.(n/)(4*E$)5".J4'J24*$(PXb'E.rM.CXc2 f' = /c4*„4*$5–57EE.C "^1B ; d.)E' = P.„$M‡En/)AI.dA.64* *n$P'(4ZX(K(6.HI.6'P‡ ")OE5-.G.F¦—$ f.G('nB 02)E.C¨3BŸ ¡ J'¦,02. < )KXn/ ? !5[fxn$llJ"nF$^ < nE ¨§

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02)E.C¨3B£iy$4* ; 'E$ ; (4ZX(Of,Ž•Œ.GŒ ; n/C' ? 4ŠEb# ) : ¦ 1k"21+" uJ/†.UpG(…3"L7Š"Ž*!-7+*b2[Š"Ž"L‰"x -eEk = .M57).e T$#&*()$34**."/34kJKk "Vn/)(4Š$ $)V. = TF.gX$dE–5+.MdE.$'n ? UJJ. = y0LO4Š. E'. 9 J02/. = > 0264*n4Šg ¤`B-, ? = 0234**.†4k = ($c_ XU$F$c_x{gX$J f.ER57 T,'$(Jn/$#&n/ Q{<¡d< = nUJ$^c_ ( > J'nnd*(J¤K3Be-.!$r*† f6n/)J4*$)*e$-.Z f((L = -¨3B£3BTd —X$_T.‡4*4k).'nF34*'.r = '‡ŸiIal)m)Xc.)6 f. 57fJJ'•iIŸŸgn/CG$cB L = ¨3B£6R6JŒ < )J4*$)*–ŒF 9 020Ž# = ,dE*.$n ? FJ. i$%0234* < UnE ? 4k),0234*'. ? 0234*'.Z ¤Z : Xc.) R Œ 9 R Œ 9 R Œ 9 RXO RXO fX3 RXO RXO RXO J'nn Ÿ$B£i$ll Ÿ$B£i¨ n3B£n§ Ÿ$BŸgjj Ÿ$B£i$ll ¤K¨3B£n #i3B£mm #`¤.B£¨ Ÿn3Bal)n J¤K n)jOB£§cŸi n§3B£§§ j$§i3B£i§i nm3B£m n3BŸ§ §)j$3B£ #n3B£ncŸ lcBj$i ŸŸ$Bal) fXU$ : gX3'.) #i3BŸŸ Ÿi3Bal)m ¨

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-VE*• = '.C57).V T$#&*())34*'.!/c4k(O• "n/)†# 4*$„$)R.6& "$#&J)Ž34**.(E-5V. : -# = 0234**.Zi)j`B -. : = 0234*f4kd. = ER57r$c_x*– fA57M. : @ < Jn/$#&n/' = nUJ$^nnEBR-.†$H f.n/)J4*$)*R$(g f„ L = G¨3BŸlcB—d——gX$_".H44k)ƒ.ny34*C = *‡Ÿl5£mn) Xc.)† • R.G).( fG$JgX3)!5!ŸN£n$lKyB Ž = C¨3BŸlFRJGŒ. < )(4*$U)ŒG. : -# = Ai$%0234* < nE dD0LO4Š. : D02O4*.bi)j : gX3) R Ž+Œ 9 R xxŒ 9 R xxŒ 9 •Ÿl innn¨i Ÿn¨)j$i i¨§cŸ¨i Ÿ§cŸmb¤ 3B£mcŸ i¨3B£i§ •Ÿl = inicŸmi Ÿnni$l i¨cŸŸgj$§ Ÿ¨cŸi§ jOB£¨)j ŸŸ$B£¨ •Ÿln in)j$m¨ ŸmcŸi im§§m¨ Ÿ§§$l ŸŸ$B¤K Ÿ§3B£§)j *n$l iib¤KcŸl ¤KicŸmb¤ ib¤K¨cŸŸ¨ ¨b¤K¨§m §3B£ib¤ ii3Bj$m *n$l = icŸll)$l n)jj$§ inb¤K¨)jZ¤ ¤K¨ncŸ ŸlcB¤¤ ŸgjOBj$n *n$ln in¨n$l$¤ ¤K¨$ll)¨ inn§m)j ¨¨)j$ #&lcB£mcŸ Ÿ3B£m$l *¨$l icŸgjblll mni$l incŸ/¤KncŸ Ÿl$¤Kn¨ m3B£ib¤ jOBjZ¤ *¨$l = icŸgjj$m¨ §mmnn in)j$imm b¤Oj$$l §3B£ii §3B£mcŸ *¨$ln icŸgjZ¤Knb¤ ni§ inb¤K¨m)j Ÿl)m¨mi jOB£n$l ŸŸ$B£§m •Ÿll icŸl.Ÿmm Ÿm¨§cŸ icŸl)n)j$§ Ÿ§$l$¤Ÿn lcBŸl §3Bal) •Ÿll = Ÿ§m$l)¨ Ÿ¨cŸŸnb¤ Ÿ§¨§m§ Ÿm)j$m)j #&lcBŸi ŸlcB£§ •Ÿlln i$l.Ÿm$l.Ÿ ŸmicŸ¨m i$l)§mcŸm Ÿ§¨icŸ¨ n3B£nm Ÿi3B¤K¨ *i$ll incŸ§)j$m n)j$§)j icŸ/¤Knb¤K nnmb¤¤ #§3BŸ§ #Ÿ$B£¨m *i$ll = inb¤K¨cŸ¨ n¨b¤)l)¨§ i$l)§m$l nnminm #Ÿi3B£in #¨3B£n$l *i$lln ii§b¤Kn¨ n§)j$n)jZ¤ i$l)m¨b¤ nb¤Kn¨§ #ŸlcB£n§ Ÿ$Bjj *n$ll nmim§ mmn$l.Ÿ ni¨§ m¨§cŸmi #i$lcB£in #&lcBjZ¤ RX$ : Xc.) Ÿ$B£n$l ŸlcB£mn m$l

PAGE 72

s6AtHru6qdZ sFvJws6}"‚krbvFw{‚ƒtHwp-GuPGyq |”vF‡z .'neRU = CJn/$#&n/KO4*.k$ŽnM4cEn/ = M& "$#&J) „./#&*()•34*'f = „.X4k+B ¡ ZX–n/)#`gXr4k$ "(./# I*.6$ = E*r*O4Š =O> n/) = '.Oc†E = #`*O4ŠBx.E.'nVn/)gXT4k$ $r/c4*'n > 4'J¦d.J*O4Š{$A = X4k+B Q E$)4k$r$ "^{). : N3E.n/ ? rn/c.G5& "$#&J)e*./#&'()*2O4* gX = G.X4k+B -HX4kƒ*O4Š.†.†J > 4*$U(JX$E.6 = yJEn(.H4k4.# E$)¦_Ln/)ZX†*PE$)4 = = _+FOE* = M5.$)*Byf. X$E.-.UJ.M.Mr-‡nn > 52.M34*-GPE* = r = G),)(P > E'.(n*NOE-57)%)A5eSec41U(OBTS–34*'n-(.c!*$f4F¦r f. $M = M.X4kGy.M5‰E.E.B–R$4*XM4 = = V5[f.rn/)ZXf4k$f$M = r.XJ$R. = -n/)gXd4k$R'fn)AE.)F$n >H=3> r.nC4# J¦gBCŒ{.(*n/(O_•.(441)n†34*R f' = n/)(JH = E ,*) > r-‡nKfO4*'.C3)hB mcŸ

PAGE 73

‡qd-qdyqdw{s6qC‚ Ÿš : Jn/)E*n/ ; E > cn$)+B ; O$)ŠxnU.) > @-)J$4H57 : Fn/)c# *En/BVi$ll)¨FSV)+B iZ : BK%d_3PB < *.$^$+_K*F@rBO@-5B1%)FŽO)–5[nZ#&% ; O$ < UnEB4Š$ ¨ng3¨m3B ; SVSVSR'( : )E. ? nI*nr%),E.)J$) < ).57n/_Ši$ll)n3B nZzc†BT%.—ŒDB ? B Q > B ; Kn/)*.n/ < $n/nJ5Ci3B£¨Z#&% : > ; K$) : n.(B"i$ll.Ÿ$B ¤$ : B-%R)._ + BcV.._MPB-R).._rc†B-ŒE+B Q 3*E ? n/JK = )dE*.$n ? JF.JG@fn/.) ? n^3FE 9 f02/. = > 0L ? 'n4*B24*$mcŸU mb¤.B ; STSVS ; O ™ : > (4k)E ) < nE : > F_*i$ll$¤.B ¨Z Q{<¡M< SVn/)nM ; .57J$)GxnU.))6 )/`BL f rBaJnn$BGB mZ6%6BaSfBŽ) = .B6d.n†RJd : $Un+_Ž4*J¦$)•_k* Q n*. 9 $U..B Ÿ§3B ajg6%6BaSfBŽ) = .B6-.(%)5 ; gX$$)+\ 9 )d5[)~{5[ < )(4kKPn JB–i$ll)i3B §Z6]JBxR$c_ : B+Œ$^$ = > h_eƒMB•]M).B : )Xc.H.F@fn/.)E$ ? n^c.A4* = =3> R*$4X‡d = ) : NOEn/ ? B†4*$FŸ§cŸUŠŸ§¨3B2G : )E ? nI*n %),RE)J$) < ).5[n/_•Ÿ3B Z )GPB*f)'+Be$4$) ¡ $E•,RIŠn : > JB-Ÿi3B ŸlbPŒDB # 9 B–E.._!6B 9 '.^Š_c6Bed_ ¡ B 8 Y > ^3*+_– Q B B ; f•B ; On/)n/F f.J#&g "$„*O4Š5[,n$% Q 'n/4cn/B ; O$) : > (4k)E*) ME > 5eSVn/)nd%)+_Ši$ll)m3B ŸŸšPŒDB # 9 B–E.._c†Bed_ ¡ B 8 Y > ^OU•_ < BL.$#dE* > _TrB2f.3nU$_– Q B B ; f'+Bx-.UJ#& $d34**.CE*.P.nMJBŽ4*$-mnb¤b3mn3B ; Ob# ) : > (4k)Eˆ)dE* > 5eSVn/)*nM%)+_ Q $n„i$ll)¨3B ŸiZ Q $ : J'n/)En/ ; n$Be f rBaJ$.J`Ban/)‡Zn) > b'./kBaKJ`B ŸnZ ; B]r > c_ Q Bkd = 'n+_cGS-B$^B"nZ#&% ? n/(Ofn/). 8 'n ; On/)n/B 4Š$Ri¨)j3i¨§3B ; STSVS ; O ™ : << )5[*n/_Ši$ll)n3B Ÿ/¤$ : B*]r^34*$'n^1_ < Ba%6B+d$_1* Q B ? B 8 nn*hB4'J¦$) =3> : 6E$AR..B Ÿ§n3B mi

PAGE 74

Ÿ¨Z B Q B 9 .GEc†BŒB < +B† < 6\• x*X < )E.J$4*c# = @-4*O$) 57 ¡ )c# : 'n.†0LO4ŠB–i$ll.Ÿ$B ŸmZ6@CBa](B Q ._eCBLŽ == $c_L*…@rBa]JBŽ" > )+B,ˆ57n//#&n/—Jn/$#&n/'V4*'n/B‡4Š$ ŸgjjŠŸ§$lcB ? 3n/*.)5 ; STSVS ; OhB < ).5B.) < %6_*i$lllcB Ÿgjg6PB Q E.$c_c](B30EbY > )h_ : B ¡ $^b$$^_Š%c†BO]rZY`B 8d9L:c; J3E*!4*n/(O = )—n/)/#`4*n^c. =3> .HN3E.n/y4*B4*$GŸ¨cŸ§gŠŸ¨ib¤.B ; SVSTSDŽn/)6) < )(4*E.-.,%)G5 ; O$ < nE : > J_•Ÿm3B Ÿ§Z : B ¡ $^$$$^_L](B+0E$Y > )h_+CB Q E.$c_ŽEc6B+]rZY`B Q cE ? n/(OM) : R# : En/E.M ;<9 > )E.f4*4*n$)*B"Ÿm3B ŸZ : BaMBV = E†MBaPB : ¦ > F^chBUXc > \G0 ? n/(OJ5[FnZ#&% 8d9L:3; B…4Š$ i§g3ncŸ¨3B+ J_ E > i$ll)n3B i$lb Q B*d6E.cBx ; ? n/(O5[-nZ#&% 8d9L:3; Bx4*$MŸ¨gŠŸ§3B ; STSVS : > (4k)E*) < nE : > J_•Ÿ§3B icŸš( : @ < "3^3.5hif0234**. : " )'./`BO f rBanBaEnn$BEŠZ$UnŠbE5h : @ < B iiZ Ba](BŽdE.)E._L†BxRFnh_L@rB ¡ B Q > ._2ŒB : B : n/_2ƒ6B : B•L > B‡-. Q $)n 8d9L:c;"9 > )E. : > ,B E†Ÿ§b¤.B inZ6PB*@RJ,A@rB*@f5B : > 9 X ? 5[Fn/PSVXbE*$)H5e-./#&%d(*) ; O$ < nEB64*$6m)j3ŸU3m)j$§3B ; SVSTS“Žn/)*M) 8d9L:3;r: > J_x%n/ = i$lllcB ib¤$6@CBZ@f5_PBb0*+_)](B # ¡ B < +_b* : Bb%dB30* = n$)6nU.))L57Ž/#&(*) 'K$nnEB ;: MSV%6_*i$ll)i3B i¨Z(†B)@-3)_KBKROrF'._ Q B : n3E = _K(@CB + ..B Q 3E.57n/E = > 5+n$%4*b.# '$#`gXg <-Q : nnE*fA.Pn^n*.B Q n/3n/)*nPST.)# .._•ŸcŸ$B imZ ¡ X : "`B2J57 892:3;? > 'n+%R),E.)J$)+B : 4# 8 $ ? E = '. < )(4* > _xŸ3B i)jg ? BaPB : E+_Š@rBk@fXcnU.•_ : B1SV $_+ : Ba](B 9 ,B Q E*#& > 0234**.(57 @f = : > (#`)c# ? n^$$B+4*$Tmgcj$i3B ; STSVS : > J41)E) < nE*eR* : > J_ i$ll$¤.B i§Z : OE.^3 B : )E.`_1]rE*X„"‰Y¢_ŽRJ Q .c_•*„]r* : $ "$BPnZ#&%R¢# .)E ;< \"nU.) > 57R ¡ /3%Rn6" > )+Bf¨b ; STSVSŒ^3.4 ) : ) ? 4*$)$)A) ; On/)n/_Ši$ll.Ÿ$B iZ Q B : UOXbd 9 B Q B ? $^1BHnJF\r : E.X > BJ4*$‡Ÿgj3im3B ; SVSTS < )(4*E._ E._+Ÿb¤.B n$lb6rBKŽ4B+F > nŠnZ#&% ? n/JKT$VXV)E..C4*n/Bk4*$"mgcj$i3B ; SVSTS : > (4k)E*) < nE : > J_*i$lllcB mn

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ncŸš < .'. 8 ¦E.H ? B c6BxŒ..B 892:3;f? 'n/(KPfA4J¦$)E*. ….n = ¡ F¦ ? )'Sec4)B4*$yn$lZK¤)l.Ÿ$B ; SVSTS Žn/)!),SVX)E.)*$ > < )(4*E.$)•_cE.)ERi$ll)i3B niZ ¡ RCBaSfBTŒ%dXcR$UB J ? 41n/X_ŠnbG)+BeR*)c#`Œ > ? $U)ASTEn$) ; n$B_Ši$ll)¨3B nnZ6%6Ba0"B$Œ).._)6BbL.._)†-'P@CB302SVXb'E$)P5 : N3E.n/ ? 2'Pcn^ ? n/(O =3> 9 ). < )F() : E = N3E.n/ < )(4ŠE.$)+Br4Š$JŸl)mgŠŸŸŸ$BŽ%)ŽM STE.4k_i$lllcB nb¤$6@CB + .._](B!@> < Ba](B!]M)•_R%6BaB .B : cn'n ; On/).n/ Q 3.._ ? Z T{x_d ? 57Jn/ < $n/¦$)5JnZ#&% < nE*B4*$mn§g3m¨i3B ; SVSTSŽn/)!),STn/),%Xcn/_*R4•i$ll.Ÿ$B mb¤


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datafield ind1 8 ind2 024
subfield code a E14-SFE0001549
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c FHM
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(OCoLC)148053257
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FHMM
090
TK7885 (ONLINE)
1 100
Fernando, Pradeep R.
0 245
Genetic algorithm based two-dimensional and three-dimensional floorplanning for VLSI ASICs
h [electronic resource] /
by Pradeep R. Fernando.
260
[Tampa, Fla] :
b University of South Florida,
2006.
3 520
ABSTRACT: Dramatic improvements in circuit integration technologies have resulted in a huge increase in the complexity of circuits that can be fabricated on a single integrated circuit (IC). The significance of the performance and reliablity issues of interconnects has increased greatly demanding radically different solutions such as Three-Dimensional Integrated Circuits (3D IC) and Optical Interconnects.Three-Dimensional ICs are an elegant solution to the interconnect and device density issues in the current and future technology generations as they provide an additional dimension for packing the devices. This results in a direct reduction in the chip package area and the total wiring required to complete all the interconnections. More importantly, the number and the length of long, global wires are reduced significantlydue to the availability of the third dimension for routing purposes. But to fully exploit all the advantages associated with three-dimensional ICs, a good three-dim ensional packing of devices is needed. This greatly increases the importance of Floorplanning and Placement stages ofthe VLSI Physical Design process. There have been many initial attempts to develop a physical design framework for three-dimensional ICs but only a few of them focus on physical design for three-dimensional macro-cell based circuit designs. This work develops a novel genetic algorithm for performing both two-dimensional and three-dimensional macro-cell floorplanning. The genetic floorplanner employs two novel crossover operators. The first crossover operator (MTOX) is an unbiased stochastic search operator, while the second crossover operator (HOOX) is a heuristic operator that searches for floorplans with good area usage. Both the crossover operators can be applied transparently for both 2D and 3D floorplanning.Three mutation operators have been developed to work with the chosen floorplan representation scheme, namely Sequence Pairs. Despite the use of a comparatively s mall population size of 200, the genetic floorplanner achieves reduction in footprint area and wirelength for both 2D and 3D floorplanning as compared to some of the recent works in the literature. For 2D floorplanning, the genetic floorplanner achieves a 12 percent average reduction in total wirelength as compared to a Quadratic Programming based Floorplanner for a small 2 percent increase in area. For 3D floorplanning,the proposed floorplanner achieves a 11 percent average reduction in total wirelength and a 5 percent decrease in footprint area as compared to a Simulated Annealing based 3D floorplanner.
502
Thesis (M.A.)--University of South Florida, 2006.
504
Includes bibliographical references.
516
Text (Electronic thesis) in PDF format.
538
System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
500
Title from PDF of title page.
Document formatted into pages; contains 64 pages.
590
Adviser: Srinivas Katkoori, Ph.D.
653
Physical Design
3D Integrated Circuits
Evolutionary Search
Placement
Sequence Pair
3D integrated circuits.
Evolutionary search.
Placement.
Sequence pair.
690
Dissertations, Academic
z USF
x Computer Engineering
Masters.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.1549