Scaling of Probability-Based Optimization Algorithms J. L. Shapiro ...

Download PDF
4 downloads 2723 Views 268KB Size Report
Comment
Department of Computer Science University of Manchester ... landscape. In this case all vectors are equally fi t, so the " best " vector Hx* is a random vector and ...
      !#"%$ &(') * +,-.  /0 1 2.3* ! 4658795;:=@?8ACBED FHGJILKNMPORQSGUTOWVYX6Z[VQ\I^]@O_GUM9`@acbdGJTeacG2fWTLbhgGJMjiPbhOlkVYXnmoKYTeajp^GUiPO_GUM moKYTLajpLGUiPO_GJMrq@mtsUu\vwyxf2z {\zE|~}€EW‚~Jƒd„†…E‡ˆƒ‰…‚UƒdŠ‹ Œ #ŽN@^‘6’ˆ wnVNI^]L“dKYO_bdVNT@”–•LKNi_GU—,˜™TLacMRGJQ\GUTOjKY“šx=GUKYMRT^bdT^›\bdi9iPp^VEœTžMRGUŸ]^bdM_G.gNGUM_k iPGUT@” iPbhO_bdgNGWiRaJKN“hbdT^›.VYX¡bhORi6“dGUKNM_T^bdT^›.MjKEO_Gz8¢£pLG“hGrKYMRT^bhTL›MRKYO_G£Q¤]LiPOyiRaJKY“dGœbhO_p O_p^Gi_k@ilORGJQ¥i_bh¦UGHbdT%K¤I^MRVN•L“hGUQ§”™—@GUIeGUTL—@GJTOœ£K¨kNzn¢£p^bdi£b©ii_p^VEœT,bdT,OlœV I^MRVN•^“dGJQ†iUª«O_p^G[T^GJGr—@“dGc”–bhT@”™KWpeK¨k iPORKaj¬¡qUbdT¤œp^b©ajp2ORp^G“hGrKYMRT^bhTL›WMRKYO_G[Q¤]LiPO gEKYT^b©iPp­GJ®@IeVT^GJTO_b©KY“d“dk bdT­O_pLG§i_k iPO_GUQ¯i_bd¦JGNq¡KYTe—%bhT°K,iPQ\V VYORp­X±]^TLacO_bdVNT bhT°œp^bdajpoO_p^GS“hGrKYMRT^bdT^›†MRKYO_G§Q¤]LiPOHgEKYTLbdi_po“dbh¬GO_p^G\iRŸ]eKYMRG2M_V VNO9VYX6ORp^G iPk@iPO_GUQ²i_bh¦UGNz6¢£œV2Q\GcO_pLV —Li[KNM_GWILM_VIeViPGr—¤X±VM[MRGJQ\VEg bdT^›.O_p^b©iiPGUTLiPbhO_bdg” b³Olkz6´µ“dGUKNM_TLbhT^›S—@k TLKYQ\b©aJi[œp^b©ajp,VN•ˆGJk@i£—@GJORKYbd“dGU—•eKY“©KYTLaJG9b©ii_p^VEœT†ORV ›NbdgNG9aJVNTLi_b©ilORGJTO[IˆGJM_X±VNMRQ†KYTLaJGWVEgNGUM6O_p^G#GJTORbhMRGWMjKYT^›GWVYXš“dGUKNM_T^bdT^›2MjKEORGUiUz ´WT1KNTLKY“dVN›%VYXQ§]@ORKYO_bdVNTbdi§iPpLVEœT°ORVoM_GrŸ]^bhMRGK%“dGUKYMRT^bdT^›%MRKYO_G†œp^b©ajp i_aUKY“dGUi£KNiORp^GbdTgGJMjiPG.i_k iPO_GUQ¶i_bh¦UGNq@•^]^OWbdiILM_V•^“hGUQ·bdTL—@GJIˆGJTe—@GJTOUz ¸ ¹º @^»¼9½9’ˆ^¾P» º ¢£p^GUM_G[pLKNi¿•eGUGJT§Q¤]Lajp§M_GracGJTO8œ[VM_¬#]Li_bhT^›HI^MRVN•LKN•^bh“dbhOlkHQ\V@—@GJ“©i¿O_V#iPGrKYMjajp2bhT¤VNI@ORbhQ\bd¦UKEORbhVT I^MRVN•^“dGJQ†iUz8¢£pLG9I^MRVN•LKN•^bd“hbhOlk§Q\V@—@GU“ˆ›GJT^GUMRKYO_Gri;aJKNTL—@b©—^KEORGHi_VN“d]@O_bdVNTLi;O_V¤O_p^GHVNI@ORbhQ\bd¦UKEORbhVT I^MRVN•^“dGJQ%z2˜–Ob©i#]^Iˆ—LKEO_Gr—-i_V O_pLKYO#ORp^G†iPV“h]^O_bdVNTLiH›NGUT^GJMjKEORGU—°i_p^V]^“d—°bhQ\I^MRVEgNG§VEgNGUM9ORbhQ\GNz f9i_]LKN“h“dkNq¿O_p^G†ILM_V•LKY•^bd“db³Olk-QSV@—@GU“;b©i2K%ILKYMjKYQ\GJO_GJMRbd¦JGU—-›NMjKYILp^bdaUKY“6Q\V@—@GJ“ÀqnKYTL—]^I¡—^KEORbhTL› O_pLG[Q\V@—@GJ“ bdT gNVN“dgNGri=ajpLKNT^›NbdT^›ORp^G£ILKYMjKYQ\GJO_GJMji=KNTL—IˆViRiPbd•^“dk.O_p^G£iPO_MR]La~OR]^M_G[VYX^ORp^GQSV@—@GU“Áz ¢£p^G›GJT^GUMRKN“¡iRajp^GUQSG.œVNMR¬@iKiX±VN“d“hVEœWiUq  ˜™T^bhO_b©KY“dbh¦UGHORp^GQ\V@—@GJ“«ORViPVQ\G#ILM_bdVNMñGz ›ez;KS]^T^bhX±VNMRQ¶—@b©ilORM_bd•^]@ORbhVTeÄ~Å ÂÆ GJIˆGUKYO Ç Q\:=>^V@Èt—@GJ?n“ÀÅ ÉCACÊ8˞ÌJÍrÎ?ª8›NGJTLGJMjKEO_GK2—LKEORKi_GcO[•kSi_KNQ\I^“hbdT^›X±MRVNQÏO_p^G9I^M_V•LKY•Lbh“db³Olk ÇÏÐ:=ÎÎÉÁÌUÎ ÍUÑYAÁÊ¿ÍUAÁËDeʲÌUÍUÎÌUÍU?Ϊn?[O_ªGUiPaJO£M_O_Grp^KEG2ORG —LKoKEORbdK†Q\KI^iMRVEiPVgN“hGU]^—tO_bd—LVNTLKEORi[K-O_V\iPGJOROSp^G• ktI^MRi_VNGJ•^“dGU“dGJa~Q%ORbhTLÅ ›oO_pLG •ˆGcO_O_GJM Ç i_VN“d]@O_bdVNTLiKNTL— M_GUQSVEg bdT^›§O_p^GœVNMjiPG#VNTLGUiUÅ Ç 7yKYTeÎ —\>@BEO_Ê8p^G#ACÊ8bdËÒQSILÌJM_ÍrVEÎg?[GUª—ac—^MRKYGUORKYK§O_G†iPGJK O.T^ÃCGNGJzœ²›Lz6I^KNMRiVN•LK2KNQ\•^bhbh“d®bhOlORk­]^MRQSG9V@VYX=—@GUO_“np^G#X±M_VNV“©Qӗ†Q\O_pLV@G†—@VNGJ“«“©—°KYTeQ\—†V@O_—@pLGJG “ Q\ViPO“hbd¬NGU“hkQ\V@—@GU“š›NbdgNGUT,ORp^GbhQ\I^MRVEgNGr—,—^KYORK\i_GcOjÄcÅ ] ^TO_bd“yÃCiPO_VI^I^bdT^›†acMRb³ORGJMRbhVT Q\GJOjÄ FHb³Ô¡GJMRGJTO KN“h›VNMRb³ORp^Q†i†KYMRGž“©KYMR›NGU“hk—@bdiPO_bdT^›]^bdi_p^Gr—• kO_p^G°aJ“dKi_iVYX.I^M_V•LKY•Lbh“db³OlkQSV@—@GU“di ]Li_GU—«z†ÕLVNM.M_GUg bhGUœWi.VYXyORp^GKYILI^M_VKNajpobdTLaJ“h]L—^bhT^›žORp^G—@bhԈGUM_GUTO›MRKNI^p^b©aJKY“nQ\V@—@GJ“©i.œp^b©ajp

pLK¨gGH•ˆGJGUTž]eiPGr—«q^iPGUG uLq–z;¢£p^GUi_GKY“d›NVNMRbhO_p^Q†ipLK¨gNG#•ˆGJGJT%aJKN“h“dGU—yiPO_bdQ†KEORbhVT VNX8FHbdiPO_MRb³” •^]@ORbhVT­´W“d›NVNMRbhO_p^Q†ià [FW´HÄcÅ^˜œbh“d“š]Li_G#O_pLKYOO_GJMRQ·p^GUM_Gz yF9´9i¤KNM_G,M_GU“dKYO_GU—ORV°›GJT^GJO_b©aKY“d›NVM_bhO_p^Q†iUÅ6bhTeilORGUKN—VNXWGJgVN“dgbdT^›oK­IˆVNIL]^“dKYO_bdVNTšq;Ko›NGJT^” GJMjKEORbhgGoQ\V@—@GJ“.œp^b©ajpI^MRV@—@]LacGriORp^GIeVI^]^“©KEO_bdVNTµKEO GrKNajp›GJT^GUMRKYO_bdVNTÒb©i,GUgNV“hgGU—«z²´ Q\VYORbhgEKEORbhVT,X±VM]Li_bhT^ › [FW´9i£bdTLiPO_GrKN— VY X .´9ib©iO_pLKYOWbdiORpLKEOWbd T yFW´HiO_p^G2iPO_MR]LacO_]^MRG.VYX O_pLG§›MRKNI^p^b©aJKY“¿Q\V —^GJ“6acVM_MRGUi_IeVTL—^iWO_V O_p^G§X±VNMRQ VYX;ORp^GSaJM_Vi_i_VEgNGUMVNIˆGJMjKEORVNM#bh T .´9i\ñbdT O_pLGiPGUTLiPG§O_peKEO¤Kž›NbdgNGUT°›NMjKYILp°œbd“h“6I^MRV@—@]LaJG\—LKEORKžœp^ViPGSI^MRVN•LKN•^bd“hbhOlkoœbd“h“6T^VNO2ajpLKYT^›G Q¤]eajp,]^TL—^GJM£K¤ILKNMPORbdaJ]^“©KYM[aJM_Vi_i_VEgNGUM6VNIˆGJMjKEORVNM~Ä~z8˜–XšO_p^G [FW´ aUKYT,“dGUKNM_TO_p^G.ilORM_]ea~O_]LM_GHVYX O_pLG†›NMjKYI^pšq«bhOM_GUQ\VEgNGUiHORp^G\T^GJGr—oORVoiPGJO#ORp^G†acMRViRiPVEgGJMHVNIˆGJMjKEO_VMH• kopeKYTL—ñ•L]@O¤iPGUG  X±VNMGUg bd—@GUTLacGKN›KYbdTLiPO£O_p^b©iRÄcz ˜™TSO_p^b©inILKNIeGUMUqKHgGJMRk2iPbdQ\I^“dG yFW´ b©i;acVTLiPb©—@GUM_Gr—2VNTSgNGUM_k§iPbdQ\I^“hG£I^MRVN•L“hGUQ\iUz8˜–Onb©i;i_p^VEœT O_peKEOyORp^GHKN“h›VNMRb³ORp^QÏb©i[Gc® O_MRGJQ\GJ“dk\iPGUTLiPbhO_bdgNGWO_VORp^G9gEKY“d]^GWVNXš“hGrKYMRT^bdT^›MRKYO_Gzn¢£pLGW“hGrKYMRT^bdT^› MjKEO_GSQ¤]eilOgEKYT^b©i_p°œbhO_pO_p^G†i_k@ilORGJQ i_bh¦UG§bdTKžI^MRVN•L“hGUQ —@GJIˆGJTL—^GJTOœK¨kqšKYTL—oX±VNM2i_VNQ\G I^MRVN•^“dGJQ†i£bhOWpLKNiO_V†gEKYT^b©i_p GJ® IˆVNTLGJTO_b©KY“d“hk,XCKNiPOUz;¢£œVacVM_MRGUacO_bdgNGUi[Q\GUKiP]^MRGUiKNM_GaJVNTLi_bd—@” GJMRGU—šªnK\TLGJœ “dGUKNM_TLbhT^›\MR]^“dG#œpLbdajpžVN•ˆGJk@i—@GJORKYbd“dGU—ž•LKY“©KYTeacG.bhT O_pLG2iPILKacG.VYXnILKNMRKNQSGJO_GUMRiUq KYTe— KNTžVIeGUMRKYO_VM£KNTLKY“dVN›VN]LiyO_V\Q§]@ORKYO_bdVNT%œp^b©ajp pLKi£•eGUGJT%I^MRVNIˆVi_GU— I^MRGJg bhV]Li_“hkz ¼  ¹  !Œ #";»yL¾™ $   @‘ º ¼W‘nL ¢£p^G2i_bhQ\I^“dGUiPO9GJ®@KNQ\I^“hG.VNXnK [FW´ bdi9wnVNI^]^“©KEORbhVT@”–•LKNi_GU—,˜™TLacMRGJQ\GJTOjKY“šxšGrKYMRT^bdT^›­ÃC&w %˜lx8Ä œp^b©ajpœKi\bhTO_MRV@—@]LaJGU— • 'k %£KY“d] (P)K ³s*Àzµ&w %˜lx)]LiPGriKI^MRVN•LKN•^bh“dbhOlk1Q\V —^GJ“9œpLbdajpb©i†K I^MRV@—@]La~O6VNXˆbdTL—@GUIeGUTL—@GJTO;I^MRVN•eKY•^bd“hbhO_bdGUi¿X±VM6GUKNajpSacVQSIˆVNTLGJTO6VYXˆO_p^G£•^bdTLKYMRk¤i_GUKNMRajpSiPILKacGz xšGJ,O +.-H—@GJTLVYO_GO_p^ G /ÀORp1acVNQ\IˆVNT^GUTO¤VY1X +=0 q6KN T 2;”–aJVNQ\IˆVNT^GUTO2•LbhTLKNM_k-gNGra~O_VM2œp^b©ajptbdi¤K iPORKEORG,VNXO_p^GžiPGrKYMjajpi_ILKacGNz-¢£p^G,I^MRVN•eKY•^bd“hbhOlkQSV@—@GU“[b©iS—@4G 3LTLGU—t• kO_p^G 26”™acVQSIˆVNTLGJTO gNGra~ORVNM9VNX6ILKYMjKYQ\GcORGJMji 5 7Ã0 6PÄJqeœp^GUM_G 5 -R7à 6PÄH—@GJTLVYO_GriORp^G¤I^MRVN•eKY•^bd“hbhOlk O_pLKY8O +.-&9 s§KEOHO_bdQ\G 6~z ¢£p^G2KN“h›VNMRb³ORp^Q œ[VM_¬@i£KNiX±V“h“dVEœWiUq  ˜™T^bhO_b©KY“dbh¦UG 5 -Rà : Ä 9 s ; z ilORM_bdT^›i\•k i_KNQ\I^“hbdT^›X±MRVNQ O_p^G­•^bdT^VQSb©KY“ Ç Õ8fWbhI¡Te—^—,KYORO_p^G.GO_pL•ˆGGUiPILO9KYilMjORKYM_Q\bdT^Gc›\ORGJbhMjTži ORp^-RGÃ76CIeBÒVI^s¨]^Ä “©KE9 ORbhV-PT Ã6P+=ÄD0 AYBFz EG + -8A H -RÃ76PÄI=X±VNMWKY“d“=/jz 5 5 5 Ç Â ]^TO_bd“yÃCiPO_VI^I^bdT^›†acMRb³ORGJMRbhVT Q\GJOjÄ ¢£p^GKY“d›NVM_bhO_p^Q pLKi,VT^“dkOlœVIeKYMjKYQ\GcORGJMjiJqORp^GiPbd¦JGVYXORp^GIeVI^]^“©KEO_bdVNJ T >(KYTe—ÒO_pLG “dGUKYMRT^bdT^›SILKYMjKYQ\GcORGJM E[z K  Ž =º Ž ¾™^M¾ LW¾™LÉC>^Ê8ÑNÎ6"  BEÎ*)UÎ ÑNÍUACDˆÊÒÌr>^Èt?nÉCACÊ8Ë  T^GVNX¿ORp^G2GUKiPbdGUiPOQ\GcO_pLV —LiX±VNMHi_KNQSIL“hbdT^›SX±M_VQ¶K†—@b©iPO_MRbh•^]^O_bdVNT%bdiWO_V†]Li_G.O_pLGM_fG (lGUa~ORbhVT Q\GcORp^V@—«z£˜™T ORp^b©iJqˆVNT^GpeKNi,+«7à +   +ˆÄWKNiWK\I^MRVNIˆViRKY“¿—@bdiPO_MRbd•^]@O_bdVNT=ÅLbhO9bdiO_p^G§I^M_V•LKY•Lbh“db³Olk,VYX I^MRVNIˆVi_bhTL›,ORp^G†gEKY“d]^\G +  X±MRVNQ +=z¢£p^GUTšq.-§7à +   +ˆÄ.b©i#O_pLG†I^M_V•LKY•Lbh“db³Olk­VNX£KaJaJGJI@ORbhT^›žORp^bdi ajpLKNT^›NGznFHGcOjKYbd“hGr—ž•LKY“©KYTLaJG#aJVNTL—^b³ORbhVTž•ˆGUaJVNQ\GUi +¡à +   +¡Ä-¤à +   +ˆÄ ;7à +ˆÄ 9 +«7à + +  Ä-¤à + +  Ä ;7à +  Ä) ÃPs  Ä Õ^VMGc®^KYQ\I^“dGNq ORp^GœGJ“d“³”–¬ T^VEœT m­GJO_MRVNIˆVN“dbdiP”$9KNiPO_bdT^›\KY“d›NVM_bhO_p^Q¥pLKNi ÃPs!VÄ -§7à +   +ˆ&Ä 9ÒQ\bhT BÒsÅ O_p^GILM_bdVNM•^b©KNi_GUiORp^GGUiPO_bdQ†KEORG.O_VEœ£KYMj—^i9s ; ^z ¢£p^b©iWaJKNT •ˆG2KYILI^“hbdGU—,O_VGw %˜lx-• k]eiPbdT^›SO_p^G.X±V“h“dVEœbdT^›\“hGrKYMRT^bhTL›§MR]^“dGNq - 7à 6PZÄ B E + -A H 5 - 7à 6PMÄ  B  ÃPsUvÄ 5 -PÃ6CBsrÄ 9 5 Gs BF

CÒbhO_p 9 :†bhOH›bhgGUi£ORp^G¤]eiP]LKN“¿Gw %[˜lxMR]^“dGNňœp^GJT°M_GUIeGrKEO_Gr—@“dkžKNI^I^“dbhGr—%VNTo\K [eKYO#i_ILKNaJG bhO9acVNT gGJMR›NGUiyO_V%s ; @z fWTL“hbd¬NGFHGcOjKYbd“hGr@— %KN“dKNTLacG†Gw %[˜lxyq«O_pLbdi2KNI^I^MRVKajp—@V GriM_GrŸ]^bhMRGU—i_IeGracb©KY“yiRaJKN“hbdT^›%VYX£O_pLG “dGUKYMRT^bdT^›MjKEO_Gq•L]@OyORp^GHiRaJKN“hbdT^›b©i;Q\VNMRGW•ˆGJT^bd›NT†ORpLKYT†bdT,iPORKNTL—^KYMj—\&w %˜lxoKNTL—\bdi[I^MRVN•^“dGJQ bdTL—@GJIˆGJTe—@GJTOUz ˜–O,b©i,—^GcO_GUM_Q\bdT^GU— X±MRVNQ O_p^MRGJG-acVNTeiPb©—@GJMjKEORbhVTLiUz Õ8bhMjilOrq£Q¤]@OjKEO_bdVNTÒQ§]LiPO •ˆG “©KYMR›NGGUT^VN]L›NpO_VacV]^TO_GUMRKa~O2ORp^G,GJԈGra~ORiSVNX9—@M_bhX‰OSO_VEœ£KYMj—^iMjKYTL—@Vc QacVNMRT^GUMRiVNXWO_pLG p k IeGUMRaJ]^•eGz6¢£p]eiJqO_pLG 3^®@Gr—†IeVbhTO£VYXšORp^G.K¨gNGJMjKY›G—@bdiPORKNTLacGHO_V s ;Ói_KNQSIL“hGr—\X±M_VQ²O_p^G 3^®@GU—†IˆVNbdTO —@b©ilORM_bd•^]@ORbhVT TLGUKYMORp^G.pk IˆGJMjac]^•ˆGacVM_T^GUMacVNTOjKYbdT^bhTL›2O_pLGVNI@ORbhQ§]^Q¥i_p^VN]^“©—žacVNTOjKYbdTO_pLG VNI^O_bdQ¤]^Q œbhO_pK M_GrKNi_VNTLKN•^“hG§I^MRVN•LKN•^bh“dbhOlkÃÁi_K¨k­›M_GrKEORGJMHO_pLKNTs H > 2 ÄczSwy]@OPORbhT^› O_pLGUi_G acVTLi_bd—@GUMRKYO_bdVNTLi[ORVN›NGJO_p^GUMk bhGU“d—^iUq “dVN›G>     E  à  :Ä 2 E 

5R  Î Ì 8ɱÍrÌ ¢¿ViRKEORbdiPX±kO_p^G­aJVNTL—@bhO_bdVNTei\bhTGUŸ]LKEORbhVT)-Ä ;29z6Õ^VNMORp^G.T^GJGr—@“hGJ”ÀbdT@”™KE”–pLK¨k@ilOjKNaj¬¡q O_pLG2KY“d›NVNMRbhO_p^Q •ˆGJpLK¨gGU—,“hbd¬NGFHGcORKNbh“dGU— %£KY“©KYTeacG.&w %˜lx;z@˜–OT^GUgNGJMXCKNbh“dGU— O_VV 3LTe—,ORp^G.VNI@ORb³” Q¤]LQ X±VNMHO_p^GST^GJGr—@“dGc”–bhT@”™KE”–pLK¨k@iPORKNaj¬,I^M_V•^“dGJQ†iWX±VM9ORp^G\iPbd¦JGri9›bhgGJToI^MRGJg bdVN]Li_“dkNz.Õ^VNMHO_pLG X±]^TLacO_bdVNTLi#VNX;]^T^bhORKEORbhVTšq¡T^V,bdQ\I^MRVEgNGJQ\GUTOHVEgNGJMHilOjKYTL—^KNMR—°&w %˜lxtb©i9GJ® IˆGUacO_Gr—«qšiPbdTLaJG2O_pLG iRaJKY“dbdT^›,]Li_bdT^› Q§]@ORKYO_bdVNT-bdi#œVNMjiPGqˆMRGUŸ]^bdMRbhT^› E²s ; 2MjKEO_pLGJMHO_pLKNT E²s ;  2z $9VEœ£” GJgGJMrq«œb³ORpO_]^T^bdT^›%VYX[O_p^G†Q§]@ORKYO_bdVNTMRKYO_Gq¡O_p^G†MjKYT^›G¤VNX EH& iœbhO_pœp^b©ajp°ORp^G†VNI^O_bdQ¤]^Q œ£KNiKY“dœ£K¨k iyX±VN]LTL—%acVN]L“d—ž•ˆGbhTLaJM_GrKNi_GU—,VEgNGJMiPORKNTL—^KYMj—,Gw %˜lx;z   » º =’ _½9Ž ¾l» º Ž ¢£p^G%“dGUKYMRT^bdT^›MRKYO_GžVYX&w %˜lxµpLKNiSORV•ˆG­gNGUM_k1i_Q†KY“d“£X±VNM\ORp^G­KY“d›NVNMRbhO_p^QORVœ[VM_¬¡qyKNTL— ]^T^ILM_Gr—@bdacORKN•^“hki_V\KNi[b³OW—@GUIeGUTL—^i£]^IˆVNT,O_p^G.I^MRVN•^“dGJQ·i_bd¦JG#bhTžK¤I^MRVN•L“hGUQ·—@GJIˆGJTL—^GJTOœK¨kz ¢£p^b©i#œKi9i_p^VEœTobdToOlœV,gNGUM_k­i_bhQ\I^“dGSGc®^KYQ\I^“dGUiUzF9GJORKYbd“dGU—o•eKY“©KYTLaJ?G 3^®@GU—­O_p^G\I^MRVN•^“dGJQ —@MjKYQ†KEORbdaUKY“d“hk¤bhT\ORp^G£Olœ[V2aUKNi_GUi6iPO_]L—^bhGr—«z6f9i_bhT^›2—^GcORKNbh“dGU—\•eKY“©KYTLaJGNqEORp^G9KY“d›NVM_bhO_pLQÏacVTLiPb©iP” O_GUTO_“dk 3LTL—^i8ORp^GVNI^O_bdQ¤]^Q VEgGJM¿O_p^G£GUTORbhMRG£MRKNT^›NG[VYXˆ“hGrKYMRT^bhTL›HMjKEORGUiUz¿m­]@OjKEORbhVTSKN“di_V 3L® Gr— O_pLGWI^MRVN•^“dGJQ²œp^GJT\ORp^G9IeKYMjKYQ\GcORGJMjinœ[GUM_GWajp^ViPGUT\O_V¤iRKEORbdiPX±k§K2I^M_V•^“dGJQS”ÀbdTL—@GUIeGUTL—@GUTOiPGJO VYXnbdT^GUŸ]LKN“hbhO_bdGUiUz ¢£p^G­I^pLGJT^VQSGUT^VNTÒiPO_]L—^bhGr—p^GJMRGoacV]^“d— p^V“d— bdTKYT Fk [FW´2q;•ˆGUaUKY]Li_G%X±VNM KYT k1Olk IˆG­VYX Q\V@—@GJ“ÀqO_p^GHI^M_V•LKY•Lbh“db³OlkSb©i;p^bd›NpVNXš›NGUT^GJMjKEORbhT^›2K¤IeVI^]^“©KEORbhVTœp^b©ajp†M_GUbhT@X±VMRaJGUi;O_p^GHQSVEgG (l]LiPO†Q\K—@GNz  T1O_p^G%VYORp^GJMSpLKNTL—«q;Q\VNMRG%acVNQ\I^“dGc®tQ\V@—@GJ“©iSpLK¨gNG Q†KYT kQSVM_GžILKNMRKNQSGJ” O_GUMRiUqeKNTL—%KY“©iPV†peK¨gNGQ\VNMRG2iPV]^MjacGUi£VNX6g¨KNM_b©KY•Lbh“db³OlkqLi_V\O_p^G2b©iRiP]^G¤Q\K¨k •eG¤“hGri_ibdQ\IeVMPOjKYTOUz ˜–O\œ[V]^“d—1•eGžbhTORGJMRGUiPO_bdT^›oORV-“dGUKNM_Ttp^VEœ bdQ\IeVMPOjKYTOSO_p^b©i§i_GJTeiPbhO_bdg b³Olktb©i¤bd'T [FW´9i§]Li_bhTL› acVQ\I^“hGJ®,›NMjKYILp^bdaUKY“¡Q\V@—@GJ“©iJz  X=ORp^GI^MRVNIˆVi_GU—žacVM_MRGUacO_bdgNGUiUq —@GcOjKYbd“hGr—,•LKN“dKNTLacG.œbd“h“«•ˆGQ\VNMRG—@b (aJ]^“³OORV\›NGJTLGJMjKY“dbh¦UG9ORV Q\V@—@GJ“©i=bdT¤œpLbdajpORp^G£ilORM_]LacO_]^MRG;b©i=“dGUKNM_TLGU—«z¿˜–O8MRGUŸ]^bdM_Gri=KNT2]^TL—@GUMRiPORKNTL—@bdT^›WVNXLKY“d›NVNMRbhO_p^Q & i —@k TLKNQSb©aJi#VT1K [eKEO2i_ILKNaJGNq«œp^b©ajpQ\K¨k­•ˆG†gNGUM_k­—@b (ac]^“hOO_V 3LTe—°bdT°ORp^Vi_G†aJKiPGriJz¤¢£pLG Q¤]^ORKEORbhVT@”ÀOlkIˆGoVIeGUMRKYO_VNM†œbd“d“9GUKiPbdGJMO_V1›GJT^GUMRKN“hbd¦JGq[•ˆGUaUKY]Li_G­b³OžVNT^“dkMRGUŸ]^bdMRGUiKt•LbdKi O_VEœ£KYMj—^i;K.MjKYTe—@VNQ —@b©ilORM_bd•^]@ORbhVTšz$WVEœGJgNGUMUqYO_p^G#KYI^I^MRVNILM_b©KEORG£i_GcO_O_bdT^›¤VNX¡O_p^GHILKYMjKYQ\GcORGJMji Q†K¨k•ˆG2—@b (aJ]^“³OORVKNiRacGUMPOjKYbdTšz   O   =º ’  Ž

  *,

+3 #1%06>/( *,+.-D@B &!0 #"%"%$$&A&')( "%*,$+.24-/$E.$!#& "%0 $1%+3&/24+3&&5-F"6#0 724+.8 1%&+ "%$&$GH9+C:8"%& $*,&d& 9&-41%$f "% >gh24 *3 ? l>_k)&d#mR$1%n o. ip6q6Iq,>rsu+Ut?$v24wP obxN1,yu"6z#qR&{03+NyuzT|@it*,y)+3qK+3n60Kt "%}#$!y~s&jot 24}€M+ 0Kh>o#t.&x.$qK*,n,24qKt *Mp6$& q^o- t $*",‚N1%$n6(y~s ƒ7"%p $s}& €  o € ? † ~ y  s  o  t ‚

Z # c  ‰ ? ‰    „ … U „  ‡ ˆ  Y#dx o in g„#…1,16o€ †?&_Š y~s9oAt }#nK&_–A-Fhf o ‹U;C—_ †?y˜gi}y~E.so#t & [ ™P„ 5w%šy~sB+ ‹y~s+Ko1%t*3Zl‚Uc€‰vH‰on6 sByuz?‹`w6‚’‘eqK“•” o.o€  Wd›M#0 061%œ>*,#*Ÿ16"%->+]gi*,$2403$+3 &+ 031,+ ".*3ZŸ:[ž ™P+ + 1%a& *Ÿ+ 1#&_;e-j Ÿ0 5! "6+3*3> + £ŸZ]so¤_&-¡p s˜qKQt p6#qK1%Z œ?{?H*T¥˜{;U¦K:( Y( W ".6 ¢§?Y{gic?ZJ9'˜c#& ‰‰1%2d ^- $*",1%$( "%$&*  {84¨C„… RoQª€ †?y~© s>ot_+3}&?n6( –D+3$h&i ¢o‹]I—_>†?y˜+D}y~+.s~«5ot#Zi"%{?$¥YH&¦K: @uY‰1 Y8§51%Y+3WH*, X?Z®& .*,V+FVH¯?"%  *,+ !+ 0 "%$&¬&-­$"%*j *,+A@u1j 1%+.-$0 "%$&  X# #Q/&_ N-Œ+ *,!$$&œ9ª&iZ^1%\°(_ Ÿ#›R($ U $±]*"%$!0A!-24( + ?1%-9 +3Z^*3 ¶&_-¡I+3²[0K N> &gi$0.( #U ³1%+3 ;´#1,".*,ZŸ1%S]GH+ &a­$GH+K1%@`*,$")aŒ "%$24@e$kbE.8$"%&$!&µ$!*j(5#a­"jSU(1%($!-&$& #9 '  ¯8d#fO[>9&_81%24"%$"%>_> #2¹&d$9gh&i ?Z ?k)+ 16>_!#$#& "%#$$1%1%*^*3C [±]º+ &_q,&-°p + y~;]"%†$n,0C-qe#;U2=‘e9o#M#y)qK1%1$wP ©"%9>sBtª+324')*Ÿh[ogJ+3‹]&#( &—+ †",16y)".8qK J"%neQ¤_1,a5p 8ZJs˜· qK3$t 2`Vp6VqKVZ 2¸ VV+3Y?&5:!", 1%W#§?5c#a°W Z®&3VVa{?*, $!*7@i9+ &+ "%$0