     "!# $  $ %'&)(*+,.-/(0*1324$576989:35;89<>=@?ACB5ED94=3FC576989G8HFI5EJIA'K =3FL=NMC89FC5769OH5;13PQ4C?RA
BS5;<>1TP>O9570*=NUV=TFW=T2X5 ? AC=TYHD[ZVP>=T28\0*=3]^=T5 ?
_a`+bcedIfgc^hjikl^mInNn$o@n$pgqsr3pEnLbjtuc^hjvwlyxzT{}|LnLhjn~rIvwWiybjxjvwhs|
nLxjm3vwd7c^ nLrItuc^l^mIvzk3c^|Wn$fgzL{}|WnLhjnX^'eQL^CLzgLc^7cerWyN3yT­¯® °y± CLNfI$@tacer3Rq3rI pEn$3bjyta¡'c^hjvwn$Tr²¢TkNlyLvwiy£r3¤lyRi}¥3@³¦§ceg´'¦¨nLNb¥cehj¢TnLbjWvw© iy+x ¦sNªg¦« ¬µ  µ  µ vwCcebjv¶dgc^vzHkiyvwIc^ClQym3Tn'¹Rz9NkIn$$b¤Nc^R¢WfI  ·$¦§ªLfIgr7¦zW«R{}¬ |Wn$hjnaL$¸^  µ L$zgWc^gc^rimgc§Wixjhjf3dIvwiydÄcxjhjbjvwrI·bjiyÅbjvwhjv¶r3·\xj|xjhjiytÆhjnav¶tÃIbjnRWihjmIig´ºc^»gxjvw¼ l½y¾RdI¿Ii>ÀLxjv¶½y·$ÁÃr\Â n$p ° vwiybjbc$ÇÉÈ+fIbVxj|xjhjiytÊm7cexVhjmIbji>iÃpEiNc^hjfIbji>xÇ'Ë7vwbjxjhzIhjm3i ° vwiybjbc
vwrIxjhjbjf3lyhjvwnLr*xjiyhÉvwx lynLrWiybjhji>dÃvwrhjn¯c+xjiyhÉnLp'xjhjbjvwrI·}bji>Åbjv¶hjvwr3·}bjfIowiyxÉfIxjvwrI·}bji>·LfIoc^b@iyÌIbjiyxjxjvwnLr3xÇWki>lynLr3d7zQiyLiybj|*ce·Liyrh@vwxlynLt'n$xjiydnLpcgxjhjbjvwrI·Sc^xghjm3iÉ·Liyr3nLti
cerId\cÍxji>h+nLpHxjhjbjvwrI·bjiyÅbjvwhjvwrI·bjfIowiyxcex+vwhjxÎnRÅr¯v¶r3xjhjbjfIlyhjvwn$rxjiyhÇ ° mIvwbjd7z'c·Liy
r3iyhjvwlnL'iybcehjvwnLrÏcerIdxjiyowiylyhjvwnLrÐnLp+bji>Åbjv¶hjvwr3·XbjfIowiyx¯cebjivwrhjbjnNdIfIl>iyd\hjnÑc^owownRÅ
hjm3iuc^·$iyrhjxÒhjnÅ+iyiydnLf3hÒhjmIiSÅ+n$bjxjhÒbjfIowiyxÇ Â iSlc^bjbjvwiydnLf3hÒiyÌ'iybjvwtiyrhjxÒn$rm3nÅÓc^·$iyrhjxÍiyWnLowWi}hjm3bjnLf3·Lmxji>o¶p; bjiyIowvwlc^hjvwn$r7Ç ° mIi}bji>xjfIowhjxÍm7c§Wi}xjmInRÅrXhjmgc^hn$fIbgxj|xjhjiytÔlc^riyWn$owWi r3nLhnLrIow|Òhjm3iÒce·LiyrhjxÕy·Li>rInLtÃiyxg´If3hceo¶xjnÖhjmIi bjiyÅbjvwhjvwrI·
bjf3o¶i}xji>hjxÇ× 3Ø ÙVÚCÛ9ÜÒÝSÞß7ÚCàeÜÍÙ
á <>]^5Eâ9ã5E=TäIå 5Eæ¨4Ãç á å 5Eæ¨4Iè9<Q4$PQ4$=T<>ã O=T]^]Q42Xé9]QP ]Q1Y913]É1TY9äEM5;YCê34P>]^5E:T=T]Q4ã132éHä;4$ëSé9OH4Y9132ì4Y9=1Tæ ä;5Eæ¨4í989]Ò=TäEPQ1]^14Y9:35;YH44<Ò=3<Q]Q5;â9ã$5;=3ägPQMCP>]^42XPÒU}5E]^OÐä;5Eæ¨4ìsä;5EFT4Ãé9<>1Té@4<>]^5E4PÒP>89ã O=3P=T89]Q1TY9132Mî=3Y9Dï4êT13ä;êW=3í95;äE5E]jMIð á ã$ã13<QD95EY9:3ä;MCA+5;]u5EPaY94$ã4P>P>=T<>MÏ]^1ÏD94$PQ5E:TYï]^OH4 é9<Q1Cã$4P>Pæ¨1T<ã$1TY9P>]^<>89ã$]^5EY9: ]^O94\PQMCP>]^4$2ñ<>=T]QO94<¯]QO9=TYÔ]^1²D94$PQ5E:TY[]QO94P>MCPQ]Q42#5;]QPQ4$ä;æ^ð òS4$PQ5E:TYH4<>P
O9=NêT4]^1Ðé9<Q4$é9=T<>4]jUV1Ð2=35;Yóã132é@1TYH4YC]^PNô=\P>4]Ã1TæÍ13íCõ^4ã$]^Paç¨P>MC2í@1TäEPaö;÷Rø§Aã O9=3<Q=3ã]^4$<
PQ4$ùI8H4Y9ã$4P*ö ú3ûüTøjA3í95;YH=T<>MuPQ]Q<Q5EY9:TP*ö ýTøjAHþIìs]^4<>2XPö ÿTøjè PQ]Q=TY9D95EY9:æ¨1T<Ò=T:34YC]^PV=TYHD4YCêC5E<Q13Y9ì
24$YC]^P=TY9D =P>4]Ã1Tæ<>4=Tã$]^5E1TY <>89äE4Puç¨<>4U}<>5;]Q5;Y9:\<Q8Hä;4$PXöE÷ ûý3ø§A þIìã$=TäEã89äE89Puö ÿ3ø§èÖD94âHY95;YH:]^O94*5EYC]^4<>=Tã$]^5E1TYÐ=T2X1TYH:13íCõ^4ã$]^PNðK}O94\4$êT13ä;êW=TíH5;äE5;]jM[13æ=TY á å 5Eæ¨4ÑPQMCP>]^4$2 D94é@4Y9DHPOH4=NêC5;äEM[1TYÄ]^O95EPuí9=TP>5EãD94$PQ5E:TY ð
B4YHã4IA9]^O94$PQ41TíCõ^4$ã]^PS=TY9D <>4=3ã]Q5;13Y\<>89äE4P289P>]í4<Q13í989P>]]^1uã O9=3Y9:T4$P=TYHD ã=TéH=Tí9äE4
1Tæ+1Té@4Y9ìs4Y9DH4DÑ4ê31TäE89]^5E1TY ð 4ê34<>]^O94$ä;4$PQPNAIé9<>4êC5E1T89P}P>]^89DH5;4$PO9=NêT4æ¨1Cã8HPQ4$DÐ2X=35;Y9äEM13Y]^O94¯4$êT13ä;89]Q5;13Y\13æ =3:T4$YI]QP}89P>5;Y9:uâHëI4$DÑ<Q4$=Tã]Q5;13Y\<>89äE4PNð ²=TYHì2X=TDH4*<Q89äE4PNAIO91NUV4ê34<NATDH1
Y91T]}=3ä;UV=NMCPO9=Nê34]^O94*ã$=Té9=3í95;äE5E]jMa1Tæ 1Té@4Y9ìs4Y9DH4DÑ4ê31TäE89]^5E1TY ð
6989G8HFI5O9=TP<Q4$é13<Q]Q4D[]^O94\1Té9]Q5;2X5EG=3]^5E1TY[1TæÒP>]^<>5;Y9: <Q4$U}<Q5E]^5EY9:Ñ:T<>=T2X2X=T<ö TøjA7=3Y9D
²=T]QPQ89G$=TFC5TéH<Q13é13PQ4$D*=UV=NMS]Q1]^<>=TYHPQäE=T]Q4Í]^O94VK}5E4<><Q=ö  øI5;YHPQ]Q<Q89ã$]^5E1TY¯P>4]Òö 3ø§ðB1NUV4ê34<NA
Y91*é9<>4êC5;1389P<>4P>4=T<>ã OO9=TP<>4=3ä;5EG4$D=*K}5E4<><>=Tìsä;5EFT4 á å 5;æ¨4P>MCPQ]Q42Ê=TP=*P>]^<>5;Y9:*<>4U}<>5E]^5EY9:PQMCP>]^42Y91T<}4$êT1TäEêT4$D=uP>4]Ò1Tæ+P>]^<>5;Y9:X<>4U}<>5;]Q5;YH:<>89äE4PNðjYÄ]QO95;PuéH=Té@4<NA+U4Ñé9<>1Té@1TP>4\=3Y á å 5Eæ¨4 PQMCP>]^4$2 5;YïU}O95Eã OÄí@1T]QOï]^O94Ñ=T:34YC]^PX=3Y9D]^O94uP>4]1Tæ<Q4$=Tã$]^5E1TY <>89äE4P*ã$=TY 4êT13ä;ê34]Q1T:34]^OH4<íCM²é9<>1NêI5ED95EY9:Ð]^O94uP>MCPQ]Q42 U}5E]^O[]^OH4=Tí95Eä;5E]jM²]Q1 5;2Xé9<>1NêT4]^O94u<>89äE4XPQ4$]*íIM 5;]QPQ4$ä;æ^ð jY[13<QD94$<]^1 <>4=TäE5EG4]^O95EPWA7U4X]^=3FT4X]^OH<Q4$4
PQ]Q4é9P}]Q1D94$êT4$ä;13é=PQ]Q<Q5EY9:<Q4$U}<Q5E]^5EY9:PQMCP>]^42í9=TP>4D\1TYK}5E4<><>=@ð Î5;<>PQ]WA3U4ã13YCêT4<>] 3ú
K}5;4$<Q<>=TY[5EY9PQ]Q<Q8Hã]^5E1TYHP5EYC]^1²=óPQ4$]¯1Tæ÷Rü  5EY9D94é@4YHD94YC]<Q4$U}<Q5E]^5EY9:²<>89äE4PÐç 5;YH5;]Q5;=3ä<>89äE4PQ4$]Lè^ð =Tã Oó<Q89äE45;P*<>4é9<>4P>4YC]Q4D²=3PÃ=ÑP>4ùC894$Y9ã41Tæ]^O94X2X=T]Qã O95;YH:\13<ÃP>89í9P>]^5E]^8H]^5E1TY 1Tæ
<Q4$:T89äE=T<}4$ëIéH<Q4$PQP>5;13Y9PNAIU}O95;ã OÑ2X=TF34P]QO94¯<>89äE4*<Q13í989P>]}=T:T=35;YHPQ]Òã O9=3Y9:T4$P]^1u5E]Lð9694ã$1TY9D A
U4ó4ùC895Eé 4ê34<>MÄ=3:T4$YI]\U}5;]QO í@1T]QO =ÔP>]^<>5EY9:Ô=3P\]QO94ó:34Y9132X4 =TYHD=ÄP>4]\1Tæ¯P>]^<>5EY9:<Q4$U}<Q5E]^5EY9: <Q89äE4Pu=3Y9DÔ]QO94Yï2X=TF34\]QO94 =T:34YC]PQ4$ä;æ¨ìs<Q4$é9äE5;ã$=T]^4Ð89P>5;YH: 5E]^Pu1NU}YÄ<Q8Hä;4ÑP>4]Lð
å =TP>]^äEMIAIUV45;YC]Q<Q1CD989ã$4=:34Y94$]^5Eã1Té@4<>=T]^5E1TY\=TY9DÑP>4äE4ã$]^5E1TY13æ <>4U}<>5E]^5EY9:<>89äE4P}P>1X]^O9=3]]^O94*=3:T4YC]QPVã$=TYÑUV44DÐ1T8H]}]^O94*UV1T<>PQ]V<>89ä;4$PWð
SÚIÛHàeÙ Ý óà!ÉÛ9Û"



#%$'&

(*)+,.-"/10'2)354*0'687:9;0'</1/1-=2>?2@68<A+#%$'#

QB<A6R)SUTWVCXY<AZ682

jY ]^O95EPP>MCPQ]Q42²A4$êT4<>MîK}5E4<><Q=3YÄ5EY9P>]^<>89ã]Q5;13Y 5;P\D94YH1T]^4$DïíIM =Ïã O9=3<Q=3ã]^4$<WA+=3Y9D ]^OH4
4ëC4ã$89]^5E1TYX1Tæg=3Yu5;Y9P>]^<>89ã$]^5E1TYX5;P<Q4$é9<>4P>4YC]^4$D=3PÖ]^OH4=Té9éHä;5Eã=3]^5E1TYX1Tæg=*P>]^<>5;Y9:*<>4U}<>5E]^5EY9:<Q89äE4IðB=Tã Oî=3:T4$YI]5EPuã1T2Xé@1TP>4DÄ1Tæ= P>]^<>5;Y9: =TPX]QO94 :T4$Y91T2X4Ð=TY9DÄ= <>4U}<>5E]^5EY9: <>89äE4PQ4$]Lð á Yî=3:T4YC]¯<>4éHä;5Eã=3]^4P5;]QP:34Y91324íIM[89P>5EY9:²5E]^P1NU}YÏ<Q4$U}<Q5E]^5EY9: <>89ä;4$PWCð jYÏ1T<>D94$<]^1u5E2éH<Q1Nê34Ã]QO94¯<>4U}<>5;]Q5;YH:<>89äE4*PQ4$]LA9U45EYI]Q<Q1CD98Hã4*=u:T4$Y94]Q5;ã*13é4$<Q=3]^5E1TYÑ=TYHDÐYH=T]^8H<Q=3ä
PQ4$ä;4$ã]^5E1TYÑ5EYC]^1u]^OH4¯PQMCP>]^4$2 ð'K =3í9ä;4÷Ãã$1T2Xé9=3<Q4$P}1T89<P>MCPQ]Q42ÆU}5;]QO K}5;4$<Q<>=X5;Y ]Q4<>2P1Tæ
1TíCõ^4$ã]LAI:34Y9132X4IAI=TYHDÐ<>4=3ã]Q5;13Y<>89ä;4Cð
D ¿3» EGF*HCÁCI n$t7cebjv¶xjn$runLp73bjnL'nLxji>dXxj|xjhjiyt)c^r3d ° vwiybjbc° vwiybjbc
J bjnL'n$xjiydXxj|xjhjiyt
È+L´ KEiyl>hmI 7cebc^lyhji>b
Muc^l^mIvwr3i}lynNdIi`+iyrIn$tikRhjbjv¶r3·
kROi NfIiyr3lyiVn$p7tac^l^mIvwrIi}l>nNdIi± ic^l>hjv¶n$rXbjfIowi kRhjbjvwrI·Ãbji>Åbjv¶hjvwr3·*bjfIowi P Ìiylyf3hjv¶n$rn$p7v¶r3xjhjbjfIlyhjvwn$r

jY 1T8H<SP>MCPQ]Q42²A9]QO941TíCõ^4$ã]^PÃO9=Nê34]^OH<Q4$4FC5;YHD9P1TæÍã O9=3<Q=3ã]Q4<>PWôC5EY9P>]^<>89ã]Q5;13Y AH<Q4$:T5EPQ]Q4<NA=TY9DÐ2X42íH<Q=3Y94Ið
[ 3.2@68/1\BZ60])3^(*7.-L/@-LZ68<A/12 =Tã O 5EY9P>]^<>89ã]Q5;13Yã OH=T<>=Tã]Q4<Ðã13<Q<>4P>é13Y9D9PÑ]^1ï13Y94[1Tæ]^O95E<Q]jMCìs]jU1K}5E4<><Q=3Y\5EY9P>]^<>89ã]Q5;13Y9PWð 1T<}4$ëI=32Xé9ä;4CôX`Z _ badc e fEAA X`Z _Ãg÷ ahc i?f;A _kj69B á adc l fEAÉð$ððRACmò onjòmdapc q?f

r <As%0'26<A/U(*7.-"/1-"Z 68<A/12Wt 4:35;P>]^4$< ã OH=T<>=Tã]Q4<>PÉ<>4é9<>4P>4YC] =3Y¯5EY9PQ]Q<Q8Hã]^5E1TYé135;YC]Q4<NAR<>4:3ì
5;P>]^4$<QPaç¨=3PWAHíCëÉAHã$ëÉAHDHë7èQA@=TY9Dó=]Q4Y9ìsU13<QD PQ]Q=Tã F ã13YC]^=T5EY94$D²íCM =\K}5E4<><Q==uB_ jð%=Tã O=T:T4$YC]*O9=TP¯]QO94P>4aã O9=3<Q=3ã]Q4<>P*5;YÏ5E]^P:T4YH1T2X4u=TP¯UV4äEäÖ=3P¯5EY9PQ]Q<Q8Hã]^5E1TYÏã OH=T<>=Tã]Q4<>PW%ð jY9ìPQ]Q4=TD1Tæ9P>]^13<Q5EY9:S=TY=3D9D9<>4P>P 5EY t á ÄAL=Ã<Q4$:T5EPQ]Q4< ã O9=T<>=Tã$]^4< 5;2Xé9äE5E4P]^OH=T]+5;]ÎP>]^1T<>4P+]^OH4
YI8H2í@4<Í13æ5EY9P>]^<>89ã]Q5;13Yuã O9=T<>=Tã$]^4<>PÎí4$]jU4$4YX]^OH4í4$:T5EY9Y95EY9:*1Tæ@]^OH4:T4$Y91T2X4Ò=TY9Du5E]^P>4äEæ=TY9Du=3ä;P>1¯5EY9D95Eã=T]Q4P]^O94SY94ëC]Í5EY9P>]^<>89ã]Q5;13Yuã O9=T<>=Tã$]^4<N"ð u+13YI]Q=T5EY95EY9:*]^O94$PQ4Sã O9=T<>=Tã$]^4$<QP5EY=:34Y9132X4ÃOH=TP}]jUV1=3D9êW=TYC]^=3:T4$PWôv j]Î2=3FT4$P+5E]Îé13PQP>5Eí9ä;4V]^1<>4é9<>4P>4YC]+]^O94Ò2X1NêT4$2X4YC] 13æ9=é135;YC]Q4<NA4$]^ãCð;AL=3P+<>4U}<>5E]^5EY9:=XPQ]Q<Q5EY9:@AI=3Y9D
v 5;]Ò4$Y9=Tí9äE4P}=3:T4$YI]QPÒ]^1O9=NêT4Ã289äE]^5Eé9äE4é135;YC]^4$<QPNAI4]QãIðEAIU}O95Eã O\2X4=3Y9PÒ]^O944$ëI4$ã89]Q5;13Y
1Tæ+]^O94*5EY9P>]^<>89ã]Q5;13Y\ã$=TYÐí4*2X=3D94*5;YÑé9=3<Q=3ä;äE4äjð
w <A+xVB/@-L3.<y(*7B-"/1-"Z6<A/@2 K}O94P>4Xã O9=T<>=Tã$]^4$<QPÃ=T<>45EYC]^<>1CD989ã4$Dó]Q1ÑPQO91NUÊ]^O94Xí@4:35;Y9ì
Y95;YH:=TYHDa]^O94Ã4YHDa1TæÉ=:T4YH1T2X4IðTK}O94<>4:35;P>]^4$<Öã O9=3<Q=3ã]Q4<>PÍ1Tæ7=3Ya=T:34YC]Í=T<>4ã$1TYC]^=35;YH4D
1TY9äEMa5EY9PQ5ED94*5E]^P2X4$2í9<>=TY94Cð
K =3í9ä;4úXP>O91NU}P}]^O94*ã OH=T<>=Tã]Q4<>P8HPQ4$D\5EYÑ1T89<}P>MCPQ]Q42²ð
D ¿I» EGFgzCÁ.I m7c^bcelyhjiybjxÖfIxjiydvwrXIbjn$'nLxjiydXxj|xjhjiyt° vwiybjbc
J bjnL'n$xjiydXxj|xjhjiyt
qsr3xjhjbjfIlyhjvwnLrlQmgc^bcelyhjiybjx ¢Ég {gR |É¦W¦L¦$* }gÉR ~É¥7¹ qrIxjhjbjf3lyhjvwnLrÅ nLbjd3x
qrIxjhjbjf3lyhjvwnLr'n$vwrThji>mb Eq¬± iy·$v¶xjhji>bÖl^m7cebc^lyhji>bjx± iy·Lvwxjhjiybjx jceÌ@zN´ÌzNl>Ì@zNdIJ.Ì  
@  aª ° iyrI Å nLbjdxjhcelQ ' ¦W¦W¦  W
MÃi>tS´3bc^rIi}l^m7cebc^lyhji>bjx

g

#%$'

r <4*/10]60]3Bs r \.'<A2R20'3.s r <As%\B]-"/m?,B/@<A2@20')%3B2

ó4Ð<Q4$é9<>4P>4YC]¯]^OH4\4$ëI4$ã89]Q5;13Yî1Tæ= K}5E4<><Q=3YÏ5;Y9P>]^<>89ã$]^5E1TYî=3PP>]^<>5;YH: <>4U}<>5;]Q5;Y9:gð?=Tã OK}5;4$<Q<>=TYî5EY9P>]^<>89ã]Q5;13YÔ5EPXã1TYCê34<>]^4DÔ5;YC]^1 1TYH4\13<2X13<Q4\PQ]Q<Q5EY9: <Q4$U}<Q5E]^5EY9: <>89äE4PNð K}O95;P=Té9é9<>1T=3ã OO9=3P}]^O94*æ¨13ä;äE1NU}5EY9:]QO9<>44*=TDHêL=3YC]^=T:34PV1NêT4$<` =T]^P>89G$=TFC5f P}é9<>1Té@1TP>=TäÍö Tøjô÷TðWOGb'¡!¢1£@O¤G¥ Ló4U}<>5;]Q4P>]^<>5;Y9:\<Q4$U}<Q5E]^5EY9:a<>89äE4PÃU}5;]Qx
O _4$<Qä <Q4$:T89äE=T<4$ëCé9<Q4$PQP>5E1TY9PXö ¦3ø§AHU}O95Eã O²4Y9ì
=Tí9äE4PÎ89PÎ]Q1Sã$=T<><QMÃ1T89]+ã132Xé9ä;5Eã=3]^4$D<>4U}<>5;]Q5;Y9:gð3ZVY]^O94Ò13]^O94$< O9=3Y9D A$]^OH4V<>4U}<>5E]^5EY9:<Q8Hä;4$P}é9<Q13é13PQ4$D\íC§M  =T]^P>89G$=TFC5789P>4Ã]QO945E<1NU}YÐæ¨1T<>2²ðú@ð ¨LO©@%ª¤R¥¬«*­g®¬ª@¯G@°O±@O®'G®¬®'G¥ á PQ]Q<Q5EY9:X<>4U}<>5;]Q5;Y9:<>89ä;4*5EP}<>4é9<>4P>4YC]^4$D=3P}=P>4ùC894$Y9ã413æ ]QO94*2X=T]^ã OH5;Y9:X13<VP>89í9ì
PQ]Q5;]Q89]^5E1TY 13æ =u<>4:389ä;=3<Ò4ëCé9<>4P>PQ5E1TY\ã1T2í95EY94DÑíC³M ² ´µ 1Té@4<>=T]Q1T<>PWð3K}O95EP}2X4]QO91CD
PQ5E2Xé9äE5;â94$P]^OH4*<Q89äE4P}=3Y9DÐé9<Q1NêC5ED94PÒ]QO942 U}5;]QOÑ<Q13í989P>]^Y94$PQPÒ=T:3=T5EY9P>]Vã OH=TY9:34PNð

@ð

 `¶@%·!£A@L· %ª¸§ ­R¥ b¹¡@g

ó4 <>4éH<Q4$PQ4$YI] Tú[K}5E4<><Q=3YÔ5EY9P>]^<>89ã]Q5;13Y9PX=TP ÷ ü óP>]^<>5EY9:[<Q4$U}<Q5E]^5EY9: <Q89äE4PNA+U}O95Eã O=T<>4*5;YHD94é@4Y9DH4YC]æ¨<>1T2 4=Tã OÐ1T]QO94<NðCK}O95EP<>89äE4*PQ4$]O9=3P=TYÑ=TDHêL=3YC]^=T:34*1NêT4$<` =T]^ì
PQ8HG=TFC5of PNA U}O94<>4\= é9<>5;13<Q5E]jM[1T<>D94<5EPYH44DH4DÔ1NU}5EY9:ó]^1 ]^O94ÑY913Y9ì5EY9D94$é4$Y9D94$Y9ãM=T2X1TYH:\<>4U}<>5;]Q5;YH:Ð<>89äE4PNð jYó1389<*P>MIP>]^4$2²A@<Q89äE4P*=3<Q4=TéHé9ä;5E4D æ¨<>1T2 ]Q1Té[D91NU}Y PQ4$ì
ùC894YC]^5E=TäEäEMIA'íH89]]^OH41T<>D94$<}5;PSã O9=TY9:34=3í9ä;4CðIK}O95EP2X4=3Y9P]QO9=T]1389<P>MCPQ]Q42 O9=TPYH1
é9<>5;13<Q5E]jMu1T<>D94<}=32X1TY9:<Q4$U}<Q5E]^5EY9:X<>89ä;4$PWð
K}O94Ñæ¨1TäEä;1NU}5EY9:[]jU1[4$ëI=32Xé9ä;4$PuPQOH1NUO91NUÆ1T89<u<>4U}<>5;]Q5;YH: <>89äE4Pu=3<Q4Ñ=TéHé9ä;5E4Dïæ¨13<c o*u á fC=3Y9y
D c oUº»fEð ?-"+,B]<b& o*u á ç¨5EY9ã<>42X4$YI]Ò=3ë7è+5EP}<>4é9<>4P>4YC]^4$D=3P}æ¨1TäEä;1NU}PNôU}O94<>4Iô¼½A¾A¿A½¿A¾A½AÀÂÁÁÃ¼½ÄkÅÆ»ÇAÈ8½AÆ»ÉÄA½Àô}5EY9P>]^<>89ã]Q5;13Y\ã OH=T<>=Tã]Q4<Òã13<Q<>4P>é@1TY9D95EY9:]^1ogu á¿
a Ê'GO®'@Ìª¯  ª®¬¹'ÍAÆ ¿ Ë
Æ Ç a ÆA¿»Î ÊGLO®'¹ª@®¬G¥Ïª¯  ª®¬@¹]Í ÆA¿»Î»5;P]QO94Òã O9=T<>=Tã$]^4<+ãäE=TP>P<>4é9<>4P>4YC]^5EY9:S<Q4$:T5EPQ]Q4<Îã O9=T<>=Tã$]^4$<QPNAR=3Y9D <>4é9<>4P>4YC]QP+G$4<>1
T1Æ<¿ 2X1T<>4 ÆA¿ ð'K}O94<>4æ¨13<Q4CA Æ»Ç 2X=T]^ã OH4P13Y94*=T<>í95E]^<>=T<>Ma5;YHPQ]Q<Q89ã$]^5E1TYÑÆã ¿»O9Î =3<Q=3ã]^4$<}]^O9=3]O9=3P
G4<>1X1T<Ò2X1T<>4 Æ¿ í4$æ¨1T<>4Ã=3Y9DÑ=Tæ¨]Q4<Nð+5E:@ðÒ÷PQOH1NU}P]QO94Ñ4ëC4ã$89]^5E1TYÄ1Tæo*u á =TPPQ]Q<Q5EY9: <Q4$U}<Q5E]^5EY9:@ð.Î5E<QP>]LA ]^OH4Ðæ¨13<Q2X4$<
PQ89íHPQ]Q5;]Q89]^5E1TYó2=3FT4$P ¾ 2X1NêT4<>5E:TOC]æ¨1T<Ã1TYH45EY9PQ]Q<Q8Hã]^5E1TY ã O9=T<>=Tã$]^4<Nð S4ëC]LA]QO94äE=T]Q]^4<
PQ89íHPQ]Q5;]Q89]^5E1TY 2X=TF34P Ä 2X1Nê34Ð<>5E:TOC]uæ¨1T<u13Y94 5;YHPQ]Q<Q89ã$]^5E1TYïã O9=3<Q=3ã]^4$<X=TPuUV4äEä§ðÎK}OH4P>4
1Té@4<>=T]^5E1TYHPÍã13<Q<>4P>é13Y9Du]^1]^O94Sæ¨=Tã]]^O9=3]Ö]QO94 o_Ä=TY9Du<>4:35;P>]^4$<Í=Të=T<>45EY9ã<>42X4YC]Q4Da5EYK}5;4$<Q<>=@ð
s/pN/Np/gs/a($J)/$1a/g[pNABCAaBC]Ð ÑOÒBÓÔÖÕ]Õ]ÑO×
[NpABCABaC]Á CÁ P ÌiylyfIhjvwn$rnLp7q'Û I ® c^xÍxjhjbjvwrI·bjiyÅbjvwhjvwrI·ØÙGÚ @Hë aaÂé@4<>æ¨1T<>2)Y94$ëC]V5EY9P>]^<>89ã]Q5;13Y AI1T]QO94<>U}5EPQ4ÃPQFC5Eé5E]Lè+Y94$4D9P
 ?-"+,B]<b# oUºóç 5;æ+ã=
289äE]^5Eé9äE4*<Q89äE4PNðoUº\5;P}<>4é9<>4P>4YC]Q4DÐ=TP}æ¨1TäEäE1NU}PWô½ Ü Ê ÆA¿»ÎAÝ8½mÁAÁ¼½A¾AÞ½AÞA¾A½AÀ
ß ½ Ü Ê ÆA¿»ÎAÝ8½mÁAÁ¼½A¾AÞ ÅÆ»ÇAÈ½ÞAÆ»É¾A½À
*oUº
goUº
%«@¡O

U}O94<>4§c Þ fI5EP]^O94*5EY9P>]^<>89ã]Q5;13Y\ã OH=T<>=Tã]Q4<Òã13<Q<>4P>é@1TY9D95EY9:]^1 Éð+5E:@ðVú P>O91NU}P ]QO94Ï4ëC4ã$89]^5E1TYÓ1Tæ =TP P>]^<>5;Y9:ï<>4U}<>5;]Q5;YH:@ðVK}O94Ï13é4$<Q=3]^5E1TYÓ1Tæà ½ Ü Ê ÆA¿»ÎÝ½á <Q4$]^89<>Y9P$A5jð 4IðEA]QO94Ö<>4:389äE=T< 4$ëCé9<Q4$PQP>5E1TY*D91C4P+Y913] 2X=T]Qã O¯]^O94V:T4$Y91T2X4Cð
B4YHã4IAH]^OH4P>89í9P>]^5E]^89]Q5;13Y²1Tæ]QO9489éHé4$<S<>89äE4¯5;PSY91T]S4ëC4ã$89]^4$D AH=TPP>O91NU}Y 5EY²]^OH4äE4æ¨]^ì
O9=TY9D\â9:T8H<Q4CðZVY\]^O94Ã1T]QO94<ÒO9=3Y9D A3]^O94Ã1Té@4<>=T]Q5;13Ya1Tæ à ß ½ Ü Ê ÆA¿»ÎAÝ½ á <>4]Q89<QYHP ®¬¹A3P>1]^O9=3]Ã]QO94XPQ8Hí9PQ]Q5;]Q89]^5E1TY 1TæÖ]^O94XäE1NU4$<S<>89äE45EP4ëC4ã$89]^4$D A@=TPP>O91NU}Y²5EYó]QO94X<Q5E:TOC]QìO9=3Y9D
â9:T89<>4Ið
ù/\[$N c/â»ã!äåæ¹äèç¬é@êë

[AcBC

pUABC]! /\[$N c/ùs/pU($J)/U$1p/g[AcBC

pUABC]

ìê!íî¬ï äGäèêð
ñUò@ó?ô¤õö`ô¤÷óóõø

[AcBC

UApBC]

Á CÁ ÌTi>lyfIhjvwnLrnLpgqË úÐc^xÍxjhjbjvwrI·ÃbjiyÅbjvwhjv¶r3·

Ø ÙGÚ 1z P#%$'ûQB<A]<AZ60])35)S r <A4*/10]60]3Bs r \.'<2

jY1T8H<VP>MCPQ]Q42²AT4=Tã O\=T:34YC]ÖO9=3P5E]^P}1NU}Y<Q4$U}<Q5E]^5EY9:<>89äE4SP>4]r A3=3Y9D5E]P>4äEæ¨ìs<Q4$é9ä;5Eã=3]^4$P
89PQ5EY9:*r²ðWB4$<Q4CAN4$êT4<>M<>4U}<>5E]^5EY9:*<Q8Hä;4}5EYrÊ5EPÖ4ëC4$ã89]Q4Duæ¨<>1T2 ]Q1TéuD91NU}YuP>4ùC894$YC]^5E=TäEä;MCð
K}O94}YC892í@4<Í13æ=3é9é9äE5;4$DX<Q89äE4PÖé4$<Í5;]Q4<>=T]Q5;13Y AL]^O94$<Q4$æ¨1T<>4IALD94$é4$Y9D9P1TY]^O9413<QDH4<1Tæ@]^OH4<Q89äE4PN%ð Öê34Y²5EæÖ=\ã1T8Hé9ä;41TæÖ=T:T4$YC]^PÃO9=NêT4]^O94XP>=T2X4:34Y91324CA]^O942X1T<>4]QO9413<QDH4<Ã1Tæ
5;]QPS1NU}Y <>89äE4P5EP=3D9=TéH]^4D ]^1a]QO94:34Y91324CA']QO94æ¨4$U4$<5E]^4<>=T]Q5;13Y9P]QO94=3:T4$YI]QPY94$4D²]Q1
PQ4$ä;æ¨ìs<Q4$é9äE5;ã$=T]^4Cðó4u5EYC]^<>1IDH89ã4X]^OH4uPQ4$ä;4$ã]^5E1TY 1Tæ<Q8Hä;4$P¯5;Y 1T<>D94$<*]^1Ñ5;2Xé9<>1NêT4<>4U}<>5;]Q5;Y9:Ñ<>89äE4P>4]QPWð
B4<>4IAÉ]^O94â9]^Y94$PQPêW=TäE894a1TæÒ=²<>4U}<>5E]^5EY9: <Q8Hä;4a5EPDH4â9Y94$DÏ=TP]^O94aYC892í4$<13æV=3é9é9äE5;4$D]^5E24$PWð Î5E:@ð P>O91NU}PÖP>ã O94$2=3]^5Eã=3ä;äEMX]^O94ÃPQ4$ä;4$ã]Q5;13Ya1Tæ7<>4U}<>5;]Q5;YH:<>89ä;4$PWðT694$ä;4$ã]^5E1TY5;üY r
5;P4$ëC4ã8H]^4DÐ=TP}æ¨13ä;äE1NU}PNô÷TðPQ13<Q]Ò=3ä;ä713æ ]QO94*<Q8Hä;4$P}=Tãã$1T<>D95EY9:]Q1X]^O94*YC892í4$<}1Tæ+=Té9é9äE5E4DÑ]^5E2X4PNA
ú@ðD94äE4]Q³4 T<Q89äE4P}æ¨<>1T2]^O94*í@1T]Q]^1T2²A
@ð:T4$Y94<>=T]Q4SY94$Ë
U T<>89äE4P}íCMa:T5EêC5;YHü: T4$ä;5E]^4*<>89äE4P}:T4$Y94]Q5;ã13é4$<Q=3]^5E1TY A
ü@ð5;YHPQ4$<Q]ÒY94$U<>89äE4P}5EYÐ]QO94*2X5;DHD9ä;4*13æ r²ð
K}O95;P1Té@4<>=T]^5E1TYÄ5;P4ëC4ã$89]^4$D U}5E]^O éH<Q13í9=Tí95EäE5;]jýM £[é@4<5;]Q4<>=T]^5E1TY+ðÎK}O9<>1T89:3OÄ]QO95;P
1Té@4<>=T]^5E1TYÔé9<Q1Cã$4P>PWAÉ<Q89äE4PXU}5E]^OÄæ¨4UV4<=Té9é9äE5E4DÔ]Q5;2X4$P=3<Q4\<Q4$2X1NêT4DÏ=3Y9Dî<>89äE4PU}5;]QO
2=3YCMa=Té9éHä;5E4DÑ]^5E2X4P}=3<Q4P>4äE4ã]Q4D ð

Initial Rule Set R 1

Randomly
Rearrangei th Rule Set R i

i+1 th Rule Set R i+1
Duplication& Genetic Operation

Sort(Probability = p )Deleted(Probability = 1-p )Á CÁ kRiyowiylyhjvwnLrun$pgbjiyÅbjvwhjvwrI·*bjf3o¶i>xØÙGÚ 1þ#%$'ÿ

QB<A]<AZ60])35)S [ 3.0?0B\.-L]2

#%$

w

jY 1T89<SPQMCP>]^42²A9=a:T4$Y91T2X4*5EP<>4é9<>4P>4YC]^4$DÑ=TP=aP>]^<>5EY9:@A9PQ1u]QO9=T]S5;]QPäE4Y9:3]^O 5EP4äE=TP>]^5EãIð
K 1a=Nê31T5ED\]QO945EY9â9YH5;]Q4¯<Q4$é9<>1IDH89ã]Q5;13Y 1TæÎ=T:34YC]^PNAI]^O942X=TëC5;2892 é13é989äE=T]^5E1TY 5;P5;YC]^<>1CD989ã$4D ð%jæÍ]QO94é@1TéH89ä;=3]^5E1TY²13æÍ=T:34YC]^PS4ëCã4$4D9P 9A<Q=3Y9D91T2XäEM\ã OH1TP>4Y²=3:T4YC]QP=T<>4ÃDH4äE4]^4$D ð
ZV89<¯P>MIP>]^4$2 =3ä;P>1 D94äE4]Q4P=T:T4$YC]^P¯]QO9=T]¯=3<Q4uYH1T]¯=3í9ä;4u]Q1²P>4äEæ¨ì<>4é9äE5Eã=T]Q4Iðg6H89é9é@1TP>4]^O9=3]Ã=3Yó=3:T4$YI]Ãã=3Y9Y913]S=3é9é9äEM²=TYCM <>89ä;4D9894X]Q1Ð=ÐD95EPQ=3D9êW=TYC]^=3:T4$1T89PÃ289]Q=T]Q5;13Yó5EYó5E]^P:T4YH1T2X4IðCK+1u<>42X1NêT4ÃPQ8Hã OÐ=3:T4$YI]QPWA']^O94¯P>MCPQ]Q42Æã O94ã FCP}]^OH4¯YC892í@4<13æ =3é9é9äE5;4$D <Q8Hä;4$P
é4$<}5;]Q4<>=T]^5E1TY\=TY9DÐUV44DHP}1T89]Ò4ê34<>MX=T:T4$YC]U}5E]^O91389]}=TY\=Té9éHä;5E4DÐ<Q8Hä;4$P}5;YÐ5;]QP}<Q8Hä;4P>4]Lð
\B68-L680])3

ZV89<XPQMCP>]^42 O9=TPX]^OH4Ðæ¨13ä;äE1NU}5EY9:ó]jUV1 289]Q=T]^5E1TYHPuæ¨1T<Xí13]^O :T4$Y91T2X4PX=3Y9DÄ<>4U}<>5E]^5EY9:<Q89äE4PNAIU}O95Eä;4*]QO94*K}5E4<><Q=PQMCP>]^4$2)O9=TP}13Y9äEM28H]^=T]Q5;13Y\æ¨13<}:T4$Y91T2X4PNð <3B)+< w \B68-"60])3 K}O95;PPQ]Q<Q5EY9:Tìsí9=3PQ4$D\P>MCPQ]Q42OH=TP]jUV1u1T]QO94<289]^=3]^5E1TY9PNAC5EY9P>4<>ì
]^5E1TYÑ=TY9DÐD94$ä;4$]^5E1TY AC5EYÑ=TD9DH5;]Q5;13Y\]Q1uPQ89íHPQ]Q5;]Q89]^5E1TY A'U}O95;ã OÐ5EP89P>4DÐ5;YÑK}5E4<><Q=gð
r \B]< w \B68-"60])3 K}O94X<>89äE428H]^=T]Q5;13Y ã$1TYC]^=35;Y9PÃ]^OH<Q4$4FC5EY9D9P1TæÍ13é4$<Q=3]^5E1TY9PNôHD989é9äE5;ì
ã=T]Q5;13Y ACD94$ä;4$]^5E1TY A9=TY9DÑ2X1CD95Eâ9ã=3]^5E1TY ð á P=3YÐ4$ëC=T2Xé9äE4IAC]QO94¯2X1CD95;âHã=T]Q5;13Y 1Tæ+=u<Q8Hä;4 
5;P<>4éH<Q4$PQ4$YI]Q4D\=TP}æ¨1TäEäE1NU}PWô a ?   J    a!" ?   J  #  $
jY 13<QDH4<u]^1Ïã OH=TY9:3%4   5EYI]Q&1  # AUV4Ð5EYC]^<>1CD989ã4 ]QO9<>44 FC5;YHD9Pu1TæÃ1Té@4<>=T]Q5;13Y9Pu=TPu<>89äE4289]Q=T]^5E1TY+ôC5;YHPQ4$<Q]Q5;13Y AID94äE4]Q5;13Y AI=TYHDÐP>89í9P>]^5E]^8H]^5E1TY ðCÞ ^Ú ÎÙÝ,+àCß7Þ CàeÜÖÙ
jY 1T8H<ÃP>MCPQ]Q42²A]^O94=TYHã4P>]^13<SP>4äEæ¨ìs<Q4$é9ä;5Eã=3]^4$PS89P>5EY9:]QO94X5;Y95E]^5E=TäÎ5EY9P>]^<>89ã]Q5;13Y P>4]uç^÷ ü <Q89äE4PNè^AU}O95Eã Oa5;PV4ùC895EêW=TäE4YC]Í]Q1]^OH4K}5E4<><Q=3Y5EY9P>]^<>89ã]Q5;13YuPQ4$]LðTK}O94=3Y9ã4$PQ]Q1T< f PÖ:T4YH1T2X4
5;YÑ1T8H<}PQMCP>]^425;P=XP>]^<>5;YH:ã$1TYCêT4$<Q]Q4D\æ¨<Q132)]^O94*:34Y9132X4Ã13æ ]QO94*K}5;4$<Q<>==TY9ã$4P>]^1T<Nð  4PQ]Q=T<>]^4Dó]^O94u4$ëCé4$<Q5E2X4YC]S8HY9D94<*]QO94Xã13Y9D95E]^5E1TY 1TæÖ]QO9=T]]QO94XYI8H2í@4<*1Tæ=TY9ã$4P>]^13<QPÃ5;P  ðCK}OH4*é9=T<>=T2X4]Q4<>PÒU489P>4=T<>4Ã=3P}æ¨1TäEä;1NU}PNô aÔ2X=TëC5E2892)YC892í4$<}1Tæ+=T:34YC]^P-/. aÔ:T4$Y91T2X4Ã289]Q=T]Q5;13YÐ<>=T]Q4-10 aÔ<>89ä;4289]^=3]^5E1TYÐ<Q=3]^4
2 aÔé9<>1Tí9=3í95Eä;5E]jMu1Tæ+<Q8Hä;4P>4äE4ã]Q5;13Y\é@4<5;]Q4<>=T]^5E1TY
3 aÔYC892í@4<}13æ <>89äE4P}UV44DH4DÑ1T89]Òé@4<<>89äE4PQ4$ä;4$ã]^5E1TYó4Í13í9]^=35;YH4D]^O94Ö213PQ]7<>42X=3<QFW=TíHä;4Î<>4P>89ä;]78HY9D94< ]^O94Íã$1TY9DH5;]Q5;13YÃ134æ   a36ú 5 a
67 @÷ 5 - 0 a67 ¦65 2 aý67 T6
ú 5 3 a÷Rü@ð j]}]Q1I13Fa=Tí@1T8H]Væ¨1389<}O91389<QP}æ¨13<}=uPQ4$<Qê34<VU}5;- ]QOÑ. =ú@ð T9ì 8VB§G uB_ j ]^1uã$=T<><QMu1389]¯¹÷  @A 5;]Q4<>=T]Q5;13Y9PWð
jYÎ5E:@ð9ü@AC]QO94¯YC892í@4<1TæÎ=Té9éHä;5E4D <>89äE4P5EPé9äE1T]Q]^4D =3:T=35;Y9P>]}]^OH4¯YC892í@4<13æ 5E]^4$<Qì=T]^5E1TYHPWðCK}OH4YC892í@4<1TæÎ=Té9éHä;5E4D <>89äE4P5EPDH4â9Y94$D =TP]QO94YC892í4$<13æ+<>4U}<>5E]^5EY9:u<Q8Hä;4$P]^O9=3]Ã=3<Q4=TéHé9ä;5E4D æ¨<>1T2 ]QO94XPQ4$]Ã13æÃ÷Rü Ð<Q89äE4P*U}5E]^OH5;Y 1TY94X5EY9D95EêC5;D98H=Täjð jYó]QO94uâ9:T8H<Q4CA]^O94 P>1TäE5;D+A+D91T]Q]^4D+A=TYHDÄí9<>1TF34Y ä;5EY94$PuPQO91NUÆ]^O94 2X=3ëI5E28H2 YC892í@4< ç í4$PQ]Wè1TæÃ=TéHìé9ä;5E4D <>89äE4PNAC]^OH4¯2X5;Y95E28H2ÆYC892í4$<WAC=3Y9D ]^OH4*=NêT4<>=T:34SYC892í4$<WA'<Q4$PQé@4ã$]^5EêT4äEMIð +5E:@ð'ü
PQO91NU}P]^O9=3]]QO942X=TëC5E2892 YC892í4$<13æ}=Té9é9äE5E4Dî<>89äE4P5EY9ã$<Q4$=TP>4P¯U}5E]^OÄ]^O94\5;Y9ã$<Q4$=TP>4
5;Y[5E]^4<>=T]Q5;13Y9PNðH6Hé4$ã5Eâ9ã=3ä;äEMIAg]QO94X2X=TëC5;2892 YC892í4$<*5;P*=3é9é9<>1NëC5;2X=T]Q4äEMÔ¹÷ Ðæ¨1T<*5E]^4$<Q=3ì
]^5E1TY9P*í@4]jUV44$Y ¹÷ gA  \]^1Ðÿ @A  =3Y9D 5EY9ã<>4=3PQ4$P]^1ÐúTýÐæ¨1T<5;]Q4<>=T]Q5;13Y9P1TæÖ2X13<Q4]^O9=3Y
@A  @ðTK}O95EPV<>4P>89äE]Ò24$=TY9PÒ]QO9=T]Ò]^OH4*=T:T4$YC]^PV1Tí9]Q=T5EY\5E2Xé13<Q]Q=TYC]<>89äE4P}U}O95EäE4ÃUV44$D95EY9:
1T89]}89YHY94ã$4P>PQ=3<QMu<>89äE4PNð(Â» *) 5

30

best
worst
average25

Number of applied rules

'

20

15

10

5

0
0

20000

40000

60000

Á IÁ cebjvscehjvwnLrXn$pÖc^I3owv¶i>dbjfIowiyx
IterationØÙGÚ ;: =<80000

100000jYÎ5E:@ðCýgAC]^OH4¯5;YC]Q4<>êL=3äÉ1Tæ+ã4$ä;ä D95;êC5EPQ5E1TYÑ5EPé9äE1T]Q]^4D =3:T=35;Y9P>]Ò]^O94YI8H2í@4<13æ 5E]^4$<Q=3ì
]^5E1TY9PNðWK}O945EYC]^4$<QêW=TäH1Tæ@ã4äEäHDH5;êC5EPQ5E1TYX5EPÍD94âHY94Du=3PÍ]^O94YI8H2í@4<Í13æ@5E]^4$<Q=3]^5E1TY9Pæ¨<>1T2 ]^OH4
ä;=3]^4P>]]Q1a]^O94PQ4$ã13Y9DÑä;=3]^4P>]ã$4äEä D95EêC5;P>5E1TY Að Î5E:@ð9ýaPQOH1NU}P]^O9=3]]QO94¯í@4P>]5EYI]Q4<>êW=TäjA']^OH4=NêT4<>=T:34Ö5EYC]^4<>êW=TäjA$=TY9DX]^OH4VUV1T<>P>]+5EYC]^4$<QêW=TäjA$=TäEä9D9<>=TP>]^5Eã=3ä;äEM*D94ã$<Q4$=TP>4U}5E]^O]^OH4}5;Y9ã$<Q4$=TP>4
5;Ya5E]^4$<Q=3]^5E1TY9PNðN6Hé4$ã5Eâ9ã=3ä;äEMIA3]^OH4=NêT4$<Q=3:T4Ò5EYI]Q4<>êW=Tä@5;PV=Té9éH<Q1NëC5E2=3]^4$ä;Mý *=3]ÃY÷ *5E]^4$<Qì=T]^5E1TYHPí98H]D94$ã<>4=3PQ4$PÖ]^R1 =T]ÃY÷ gA  *5E]^4<>=T]Q5;13Y9PNðNK}O95EPÒ<Q4$PQ89äE]Öã$=TYaí@4Ã4ëCé9äE=T5EY94DaíCM]^O94¯æ¨=3ã]]QO9=T]]^O94=T:T4$YC]^P}=Tæ¨]Q4<X¹÷ gA  5;]Q4<>=T]Q5;13Y9PO9=Nê34*=uí4$]^]^4$<<>89äE4¯PQ4$]]^OH=TY ]^OH4=TY9ã$4P>]^1T<>PNð
500

best
worst
average

450
400
350

Interval

300
250
200
150
100
50
0
0

20000

40000

60000

80000

100000Á CÁ cebjvc^hjvwnLrXn$pgvwrhjiybjCceon$pglyiyowodIvwv¶xjvwn$r
IterationØÙGÚ > ?<ó4Í=3ä;P>1}P>]^89D95E4D*]QO94ÖêW=3<Q5E=T]Q5;13YÃ13æC]^O94Í:34Y9132X4Íä;4$Y9:T]QO ð K}OH4Íä;4$Y9:T]QO*1TæC]^OH4Í=TY9ã$4P>]^13<
U=3P 3AU}OH5;äE4]QO94äE4Y9:3]^O\1Tæ7]^OH4D94$PQã$4Y9D9=3YC]^PV=Tæ¨]^4$<÷YgA  5;]Q4<>=T]Q5;13Y9PÖUV=TP<Q4$D989ã4$D]^1uÿ ¦gð3K}O95;P5;Y9DH5;ã$=T]^4$P}]^O9=3]}]^O94*:34Y9132X4ÃUV=TPÒ5E2Xé9<Q1Nê34DÐ]^O9<>1T8H:TOÐ]^O94*5E]^4$<Q=3]^5E1TY9PNð
K}OI8HP¯U4u13í9]^=35;YH4D[]^O9<>44æ¨89Y9D9=324$YC]^=TäÖ<Q4$PQ89äE]^PNôg=3YÏ5;Y9ã$<Q4$=TP>4X5;YÏ]QO94aYC892í@4<1Tæ=Té9é9äE5E4DÑ<Q8Hä;4$P}é4$<}5;]Q4<>=T]^5E1TY+AI=uD94ã$<Q4$=TP>4S5EYÑ]^O94*=Nê34<>=T:T4S5;YC]Q4<>êL=3ä§AI=3Y9DÐ=uD94ã$<Q4$=TP>4S5EY]^O94:34Y9132X4}ä;4$Y9:T]QO ðNK}O94$PQ4}<>4P>89äE]^PÍã$ä;4$=T<>ä;M5;YHD95;ã$=T]Q4]^O9=3]Íí@1T]^Ou=3:T4$YI]Q1P fN:T4YH1T2X4P=3Y9D<Q4$U}<Q5E]^5EY9:X<Q8Hä;4$P}PQ4$]^P}4ê31TäEêT4$D5EYÐ1389<}P>MIP>]^4$2²ð
+5EY9=3ä;äEMIARU4í9<Q5E4 @HMSD94$PQã$<Q5Eí@4Ö=TY*4$ëC=T2Xé9äE4Ö1Tæ'YH4U}äEMS:34Y94$<Q=3]^4D*<>89äE4PNðRK}OH4Í=TY9ã$4P>]^13<<Q4$é9ä;5Eã=3]^4$PÃ5E]^P:34Y91324íCM 4ëC4ã$89]^5EY9:Ð]^O94X<>4é9<>1CD989ã$]^5E1TY äE1C1TéóD91TG$4Y9P1TæÖ]^5E24$PWð@K}OH4<Q4$U}<Q5E]^5EY9:*<>89ä;4$PÍ=T<>4}é@4<>æ¨1T<>24$D²¹÷ *]^5E2X4P5;Yu13Y94}ä;1C13é ð  4O9=Nê34Væ¨1389Y9Du]QO9=T]Í=3Yu=T:34YC]=Tæ¨]^4$<}ü gA  5;]Q4<>=T]^5E1TYHPV:34Y94$<Q=3]^4$PV=uYH4U <>89äE4Iô¼½¾ e ¿A½ e ¿A¾A½AÀ5ÁAÁÃ¼8½AÄkÅÆ»ÇÈ½AÆ»ÉÄ½AÀ

K}O95;PÖ<Q89äE4Òã=3Y4$ëC4ã8H]^4}]^OH4}PQ4$ùI8H4Y9ã$4V13æ5EY9P>]^<>89ã]Q5;13Y9P c e ¿ f'ç Z`_kÃ=3Y9D*ogu á è@5;YX1TYH4
PQ89íHPQ]Q5;]Q89]^5E1TY ð S=T2X4äEMIA35E]Ö<>4D989ã$4PV]^O94ÃYC892í@4<V1Tæ <Q89äE4PVY94$ã4P>P>=T<>Mæ¨1T<V]^OH4SäE1C1Téa]Q1 ¦@ðK}O95;PÃ<>4P>89ä;]=TäEPQ1aP>89é9é@1T<>]^PÃ]^OH4æ¨=Tã$]]QO9=T]Sí13]^O²]QO94=3:T4$YI1] f P:T4YH1T2X4PS=TY9D²<>4U}<>5E]^5EY9:<Q89äE4PQ4$]^Pã$=TYÐ4ê31TäEêT4Ã5;YÑ1T8H<}PQMCP>]^42²ðîÜÖÙß!)eÞ Ià^ÜÍÙjYa]^O95EPVé9=Té@4<NAUV4P>]^89DH5;4$Da]^O94Ã4ê31TäE89]^5E1TYX13æ7<Q4$U}<Q5E]^5EY9:¯<>89äE4P>4]^P5;Y1T<>D94<]^1¯5E2Xé9<Q1Nê34]^O94aíH=TP>5;ãaDH4P>5;:3Y 13æÒK}5;4$<Q<>=@ð jYî13<QDH4<*]^1 <Q4$=TäE5;G$4u]^O95EPWAÉU4]^1C1TFó]^O9<>44aP>]^4$é9P¯]Q1²D94ìêT4äE1TéÐ=XPQ]Q<Q5EY9:<Q4$U}<Q5E]^5EY9:XP>MIP>]^4$2)í9=3PQ4$D\13Y\K}5E4<><Q=gð +5E<>PQ]WACU4ã$1TYCêT4$<Q]Q4WD 3úK}5E4<><>=TY
5;Y9P>]^<>89ã$]^5E1TY9PÒ5EYI]Q1=XP>4]V1TæÒ÷ ü 5;YHD94é@4Y9DH4YC]Ò<Q4$U}<Q5E]^5EY9:<Q89äE4P¯ç 5;Y95E]^5E=Tä7<>89äE4SP>4]Wè^ð =Tã O<Q89äE4¯5EPS<>4éH<Q4$PQ4$YI]Q4D =3P=aP>4ùC894$Y9ã4¯13æ]^O942X=T]^ã OH5;Y9:1T<P>89í9P>]^5E]^8H]^5E1TY²13æ<Q4$:T89äE=T<4$ëCì
é9<Q4$PQP>5E1TY9Pã132í95EY94$D íC=M ²´µ/13é4$<Q=3]^13<QPNð96H4ã13Y9D AgUV4u4ùC895Eé9é@4D[4ê34<>M²=T:34YC]ÃU}5;]QO
í13]^Oî= P>]^<>5;YH:²=TP¯]QO94a:34Y91324=TY9D[=²P>4]¯13æÒPQ]Q<Q5EY9:²<>4U}<>5;]Q5;YH: <Q89äE4P=TP¯5E]^P1NU}Y[5;Y9ì
PQ]Q<Q89ã$]^5E1TY P>4]WA'=TYHD²U42=3D94¯]QO94=3:T4YC]QPPQ4$ä;æ¨ìs<>4é9äE5;ã$=T]Q4*íIMÐP>]^<>5;Y9:<Q4$U}<Q5E]^5EY9:@ð'å =TP>]^äEMIA
U4a5EYC]^<>1CD989ã4$D[=²:T4$Y94]Q5;ãa13é4$<Q=3]^5E1TY[=TYHDÏPQ4$ä;4$ã]^5E1TY[13æV<>4U}<>5E]^5EY9: <Q8Hä;4$PP>1 ]^O9=3]]^OH4=T:T4$YC]^P*ã1389äED UV44$D[1T89]*]QO94aUV1T<>PQ]<>89ä;4$PWð@K}OH4u=TY9ã$4P>]^1T<*13æ1389<¯P>MCPQ]Q42 ã$1TY9P>5EPQ]QP*1Tæ
í13]^O²]QO94:34Y913244ùC895EêL=3ä;4$YC]]^1a]QO94K}5E4<><>=u=TY9ã$4P>]^1T<=TY9D²]QO945EY95E]^5E=Tä <Q89äE4P>4]WA'=3Y9D
5;]}P>4äEæ¨ì<>4éHä;5Eã=3]^4PÒíCMP>]^<>5EY9:X<Q4$U}<Q5E]^5EY9:@ðó4Òã=3<Q<>5E4D¯1389]Î4ëCé4$<Q5E2X4YC]^P=3Y9D13í9]^=35;YH4D]^O9<>44ÒFT4$M*<Q4$PQ8Hä;]QPWô$=TY5EY9ã<>4=3PQ45;YX]^OH4
YI8H2í@4<Ã1TæÎ=Té9éHä;5E4D²<>89äE4PSé4$<S5E]^4$<Q=3]^5E1TY A9=D94$ã<>4=TP>4*5EY²]^O94=NêT4$<Q=3:T45;YC]Q4<>êL=3ä§AH=TYHD =D94ã$<Q4$=TP>45EYu]^O94}:34Y9132X4VäE4YH:T]^O+ðWK}O94P>4Ò<Q4$PQ8Hä;]QPÍ5;YHD95;ã$=T]Q4V]QO9=T]1389<ÍP>MCPQ]Q42 ã$=TYX4ê31TäEêT4
Y91T]}13Y9ä;M]^O94*=3:T4YC]Q1P f3:T4$Y91T2X4$P}í989]}=TäEP>1]QO94*<>4U}<>5;]Q5;Y9:<>89ä;4P>4]QPWð
( DC¤ "Û ÉÙ?ß C$ÇÃkRFf Eyf3Tvz  Ç¶z ° cer7ceCc$zÉHÇ G I mIi>tvwlc^oÖiyWn$o¶f3hjvwnLr cetnLr3·îc^bjhjJv I3lyvc^oÖIbjnLhjn$ lyiyowowxÇóqsLr Kiy
dgc^f7%z MuÇ ® Çwz MÃl I cexjv¶owoz7WÇwkIÇwz J celQIc^bjdgz ÛÇ *Çwz ± c^xjtfIxjxjiyrgz@k3Ç¶ziydIxJÇ G ® bjhjJv IIlyvceo@³@vwp;i < qj9q G
z MÃq ° J bjiyxjx
J bjnNlyiyiyd3vwrI·Lxn$p hjm3iuki>Wiyrhjmuqsrhjiybjrgc^hjvwnLrgc^o I nLr3pEiybji>rIlyin$r ® bjhjJv IIlyvc^o7³vwpEiC µ LL  N MPOCP Qµ ÇÃ3kRbjFf nLEyhjf3iyTvwrXvz3iyÌJÇiyG l>fIP hjWvwnLnLrgowfIÇ hj®vwn$bjr\hjJv n$IIp lyvxjceiyo@owp;³@bjvwi>p;SiIbjRWnNdI f3Lly$vwrI ·I^Tbjn$Q·LO'bec^'tÃ xÒvwr[cÒlyn$bjiÃIbjn$'iyowowiyd\´|7c^bceowo¶i>oµ Q$ÇÃkRFf Eyf3Tvz*JÇ GÒkhjbjvwr3·*bjiyÅbjvwhjv¶r3·¯·Lbc^tÃtac^bnLIhjvwtJv Eyi>dufIxjvwrI·\c^rui>WnLowIc^´Ivwowvwhs|tic^xjf3bjiÇ+qsr{}iyowiytÃiyr7zÉWÇwzÉkn$xjv¶z J ÇwzIiydIxJÇ G ® d3CcerIlyi>xVvwr ® bjhjJv IIlyvc^o7³vwpE§i jehjWm P fIbjn$'ic^r I nLr3pEiybjiyr3lyi
n$r ® bjhjJv IIl>vsceo³vwpEi J bjnNl>iyiydIvwr3·Lx  z@kRIbjvwrI·$iybj < i>bjosce·'6z Kiybjowvwxr  µ $'  M'$ OM'LMCÇÃkRFf Eyf3Tvz *ÇwzIÈ+r3n'Yz Û*JÇ GT~rIvwWiybjxceoIbjiy3o¶vwlcehjvwnLr¯vwrac+xjhjbjvwrI·}bjiyÅbjvwhjvwrI·xj|xjhjiytaÇ3q!r G J bjnNl>iyiydI
vwrI·$x}nLp hjmIiË7vwpEhjmqsrhjiybjr7cehjvwnLr7ceo I nLr3pEiybjiyr3lyin$r\fItacerIx*cerId I nLtÃIfIhji>bjx E I  µ $ µ  Ç LUL¸NO'LNM
$WÇ V µ vwhjhjbjµ vwl^m7z J ÇwXz K+c^Fr E>m7c^p§z Â HÇ GîkRiyowpE iyWn$o¶f3hjvwnLr v¶r cl>nLrIxjhjbjf3lyhjvwWi´3vwr7c^bj| xjhjbjvwr3·\xj|xjhjiytaÇ
® bjhjHv I3lyvc^o³@vwpEi j$¸L¸L = QNO 
$ÇÖËCn$rhc^r7c$z Â JÇ G : ® ow·Ln$bjv¶hjm3 tµ vwll^µLmIµ iytvwxjhjbj|TÇqra³c^r3·Lhjn$r7z I Çw`}Ç¶z ° c§|ownLbz I ÇwzCËÉc^bjti>bz LHÇ VVÇ¶z± c^xjtfIxjxjiyrgzNkIÇwz>iyd3xHÇ G ® bjhjJv IIlyvc^oN³vwpEi+qjYq G bjnNlyiyiyd3v¶r3·Lx7n$pIhjmIiVki>lynLr3d ® bjhjJv IIlyvc^oN³vwpEi Â nLbj
xjm3nL7z ® d3dIvwxjnLr3 Â iyxjowiy|³jL¸$¸ µ  $L¸O µ C¸ J
U$Ç ± c§|Tz ° ÇwkIJÇ G ® rceI3bjn'c^l^mhjnÍhjmIi xj|Trhjm3iyxjvwx@nLpTowvwpEiÇ$qr³c^r3·Lhjn$r7z I Çw`}Çwz ° c§|Town$bz I Ç¶z>Ë7c^bjtiybzWJÇ VÒÇwz ± c^xjtfIxjxji>r7zCk3Ç¶zRiydIxJÇ G ® bjhjJv IIlyvc^oI³@vwpEiÖqj9q G J bjnNlyi>iydIvwrI·$xÎnLp9hjm3ikiylyn$rId ® bjhjHv I3lyvc^oC³vwpEi
nLbjxjmIn$7z ® dId3vwxjnLrI iyxjowiyW| jL¸$¸ QPU$ OML'Â$mÇ MucehjxjFf EceTvz9kIÇwzCkRFf Eyf3Â vsz*ÇwzCÈ+xc^r3n'µ z  MuJÇ G ° v¶i>bjbcÖvwrIxjhjbjf3lyhjvwnLrIx+v¶tÃIowiytiyrhjiyd¯f3xjv¶r3·xjhjbjv¶r3·
bjiyÅbjvwhjvwrI·bjfIowiyxÇÒqsZr G J bjnNlyi>iydIvwrI·$xnLp+hjm3iÃË7vwpEhjm\qsrhjiybjrgc^hjvwnLrgc^o I nLr3pEiybjiyr3lyin$r\fItacerIx
cerId n$tIf3hjiybjx E  $ %Ç  $ L UOCP U¸$ÇÖËCbjvwiyd3I ozWÇ PVÇ ËÖÇHGkMuc^xjIhjiybjµ vwr3· µ ± iy·$µ fIoc^µb P ÌIbjiyxjxjvwµ nLr3xÇÍÈ}Õ ± iyvwowow|Ïj$¸L¸PU
AB