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F = (F1, & , Fgmax), S = (S1, & , Sgmax), M = (M1, & , Mgmax),  EMBED Equation.DSMT4 c, c ( [a, b]: Ft(c, c ) d" Ft+1(c, c ), Fgmax (c, c ) ! min(c, c ).  EMBED Equation.DSMT4 c, c ( [a, b]: St(c, c ) e" St+1(c, c ), Sgmax (c, c ) ! max(c, c ).  EMBED Equation.DSMT4 c, c ( [a, b]: Mt(c, c ) e" Mt+1(c, c ),  EMBED Equation.DSMT4 t, Mgmax (c, c ) ! Mlim(c, c ). "0:CN DC=:F8N 1C45< =07K20BL M+.  EMBED Equation.DSMT4 c, c ( [a, b]: Mt(c, c ) d" Mt+1(c, c ),  EMBED Equation.DSMT4 t, Mgmax (c, c ) ! Mlim(c, c ). "0:CN DC=:F8N 1C45< =07K20BL M (A<. @8A.3). Mlim  ?@545; DC=:F88 M,  EMBED Equation.DSMT4 .  SHAPE \* MERGEFORMAT  8A. 3. 0?@02;5=85 DC=:F89 F, S, M+, M !5<59AB2> DC=:F89 F 8 S <>3CB 1KBL >?@545;5=K A 8A?>;L7>20=85< ?0@0<5B@878@>20==>9 B@5C3>;L=>9 =>@<K Tq, AE>4OI59AO : <8=8<C<C, 8 ?0@0<5B@878@>20==>9 B@5C3>;L=>9 :>=>@<K Gq, AE>4OI59AO : <0:A8<C<C, A>>B25BAB25==>. !5<59AB2> DC=:F89 M >?@545;ONBAO =0 >A=>25 ?0@0<5B@878@>20==>3> >?5@0B>@0 >A@54=5=8O. CABL 5ABL 425 E@><>A><K C1t = (c11t, c21t .. cn1t) 8 C2t = (c12t, c22t .. cn2t), 2K1@0==K5 =0 ?>:>;5=88 t 4;O >?5@0F88 :@>AA8=3>25@0, 8 E@><>A><0 C1t >1;0405B ;CGH59 DC=:F859 ?@83>4=>AB8 ?> A@02=5=8N A C2t. ">340, 5A;8 Ot O2;O5BAO t-9 DC=:F859, ?@8=04;560I59 A5<59AB2C DC=:F859 F, S 8;8 M, B> 35=5@0F8N ?>B><:0 Ht = (h1t, h2t .. hnt) <>6=> 2K@078BL D>@<C;>9: hit = Ot(ci1t, ci2t), i =1,& ,n. A;8 8A?>;L7>20BL 2 :0G5AB25 DC=:F88 Ot DC=:F8N 87 A5<59AB20 F, S 8;8 M, B> ?>;CG8< A>>B25BAB25==> F-, S- 8;8 M- :@>AA8=3>25@. @8<5=OO @07;8G=K5 284K B@5C3>;L=KE =>@< 8 :>=>@<, <K <>65< ?>;CG0BL @07;8G=K5 284K >?5@0B>@0 :@>AA8=3>25@0. 0AA<>B@8< A;54CNICN ?@54?>AK;:C: 8AA;54>20=85 >1;0AB8 2>:@C3 ;CGH59 E@><>A><K ?>72>;O5B ?>;CG8BL ?5@A?5:B82=K9 35=5B8G5A:89 <0B5@80;. ;O 55 @50;870F88 ?@54;0305BAO =5G5B:89 M2@8AB8G5A:89 :@>AA8=3>25@. 2545< >1>7=0G5=85:  EMBED Equation.DSMT4 , 345 f1 8 f2  7=0G5=8O $ E@><>A>< C1t 8 C2t. 5=K ?>B><:>2, A>740205<K5 =5G5B:8< M2@8AB8G5A:8< :@>AA8=3>25@><, O2;ONBAO =5G5B:8<8 25;8G8=0<8 A DC=:F859 ?@8=04;56=>AB8, >?8AK205<K<8 :@82K<8 0CAA0 (@8A.4), 8 8<5NI8<8 A;54CNI85 ?0@0<5B@K: ?5@2K9 ?>B><>: i1 = ci1t; d i1 = *| ci1t  ci2t|, 2B>@>9 ?>B><>: i1 = c21t; d i2 = (1  )*| ci1t  ci2t|.  8A. 4. $C=:F88 ?@8=04;56=>AB8 ?>B><:>2 =5G5B:>3> M2@8AB8G5A:>3> :@>AA8=3>25@0 "0:0O @50;870F8O :@>AA8=3>25@0 ?>72>;O5B A>74020BL >4=>3> ?>B><:0 @O4>< A E@><>A><>9 A ;CGH59 $, 0 4@C3>3>  2 1>;55 H8@>:>9 >1;0AB8 >?@545;5=8O, GB> ?@82>48B : ?>445@6:5 @07=>>1@078O 8 ?>72>;O5B 8AA;54>20BL ?5@A?5:B82=K5 >1;0AB8 ?>8A:0. ?5@0B>@ <CB0F88 A>2<5AB=> A :@>AA8=3>25@>< >15A?5G820NB @07=>>1@0785 2 ?>?C;OF88. ;0AA8G5A:0O 18B>20O <CB0F8O =5 ?>4E>48B 4;O .  @01>B5 ?@54;030NBAO 25I5AB25==0O <CB0F8O A M;5<5=B0<8 8<8B0F88 >B6830 8 =5G5B:0O <CB0F8O. CABL ! = (A1, c2 .. cn)  <CB8@C5<0O E@><>A><0, Ai ([a, b]  <CB8@C5<K9 35= =0 ?>:>;5=88 t, 0 ci' ( [a, b]  MB>B 65 35= ?>A;5 <CB0F88. ">340 25I5AB25==0O <CB0F8O A M;5<5=B0<8 8<8B0F88 >B6830 >?@545;O5BAO A;54CNI59 D>@<C;>9: Ai' = ci + r(bi  Ai),5A;8  = +1 8;8 Ai' = ci + r(Ai  ai), 5A;8  =  1, 345  ( { 1, +1}  A;CG09=0O 25;8G8=0, 2K18@05<0O ?@8 :064>9 <CB0F88, >?@545;ONI0O =0?@02;5=85 <CB0F88; r = r0exp(1/s), r([0, 1]  25;8G8=0, >?@545;ONI0O A8;C <CB0F88; r0([0, 1]  <0:A8<0;L=> 2>7<>6=0O 25;8G8=0 <CB0F88, >?@545;O5<0O ?5@54 70?CA:>< 0;3>@8B<0; s  <=>68B5;L, >?@545;ONI89 AB5?5=L 87<5=5=8O <CB0F88 2 7028A8<>AB8 >B ?>:>;5=8O. 5G5B:0O <CB0F8O >?@545;O5BAO A;54CNI8< >1@07><: Ai' = ci + r(bi  Ai), 345 r([0, 1]  7=0G5=85 =5G5B:>9 ?5@5<5==>9, >?@545;ONI55 A8;C <CB0F88 8 2KG8A;O5<>5 A ?><>ILN ?@028; 107K 7=0=89. 0@0<5B@K , B0:85 :0: 25@>OB=>ABL 8 B8? <CB0F88, 25@>OB=>ABL 8 B8? :@>AA8=3>25@0, @07<5@ ?>?C;OF88, :>;8G5AB2> ?>:>;5=89 O2;ONBAO :;NG52K<8 2 ?>445@60=88 10;0=A0 :0G5AB2>/@07=>>1@0785 ?>?C;OF88. 5=5B8G5A:89 0;3>@8B<, @01>B0NI89 A ?;>E8<8 ?0@0<5B@0<8, ?>:07K205B 7=0G8B5;L=> EC4H85 @57C;LB0BK. >41>@ ?0@0<5B@>2 ?>4 :>=:@5B=CN @5H05<CN ?@>1;5<C O2;O5BAO =5B@8280;L=>9 7040G59. !;54C5B >B<5B8BL, GB> 4;O ?>2KH5=8O :0G5AB20 @01>BK  =5>1E>48<> 8A?>;L7>20BL @07=K9 =01>@ ?0@0<5B@>2 =0 @07;8G=KE MB0?0E 687=5==>3> F8:;0 ?>?C;OF88. -B> >1CA;>2;5=> =5>1E>48<>ABLN A>740=8O @07=>>1@078O =0 ?5@2KE H030E 8 ?>2KH5=8O :0G5AB20 @5H5=8O =0 70:;NG8B5;L=KE. >MB><C ?@8<5=5=85 040?B82=>3> , 48=0<8G5A:8 87<5=ONI53> A2>8 ?0@0<5B@K 8 35=5B8G5A:85 >?5@0B>@K, ?>72>;O5B 7=0G8B5;L=> ?>2KA8BL :0G5AB2> @5H5=8O. > 2B>@>9 3;025 48AA5@B0F88 ?@54;0305BAO 8A?>;L7>20BL 107C 7=0=89 =0 >A=>25 2@5<5==KE ?@>4C:F8>==KE ?@028;, @50;87CNI59 ?>41>@  8 8E <>48D8:0F8N 2 7028A8<>AB8 >B B5:CI53> A>AB>O=8O ?>?C;OF88 8 65;05<KE F5;59 35=5B8G5A:>3> ?>8A:0. !B@C:BC@0 A0<>=0AB@0820NI53>AO  ?@82545=0 =0 @8A.5.  EMBED Word.Document.8 \s  8A.5. !B@C:BC@0 A0<>=0AB@0820NI53>AO   @01>B5 ?@54;0305BAO A;54CNI89 =01>@ ?0@0<5B@>2 , E0@0:B5@87CNI8E B5:CI55 A>AB>O=85 ?>?C;OF88: 07=>>1@0785 35=>B8?0 (GD): 0) EM<<8=3>2> @0AAB>O=85 (?@8 18B>2>< :>48@>20=88); 1) 52:;84>2> @0AAB>O=85 (?@8 25I5AB25==>< :>48@>20=88); 2) =0 >A=>25 38AB>3@0<<K G0AB>B=>AB8 7=0G5=89 35=>2; 3) 48A?5@A8O 7=0G5=89 35=>2. 07=>>1@0785 D5=>B8?0. 7<5=5=85 ;CGH59 E@><>A><K. !@54=55 87<5=5=85 DC=:F88 ?@83>4=>AB8 ($) ?>?C;OF88. 064K9 2E>4=>9 8;8 2KE>4=>9 ?0@0<5B@ <>65B ?@54AB02;OBLAO ;81> A ?><>ILN G5B:>3> 7=0G5=8O (B8? :@>AA8=3>25@0, B8? <CB0F88 8 B.4.), ;81> 2 2845 =5G5B:>9 ?5@5<5==>9.  :0G5AB25 ?@028;  ?@54;0305BAO 8A?>;L7>20BL <>48D8F8@>20==K5 ?@>4C:F8>==K5 ?@028;0. >48D8F8@>20==>5 ?@>4C:F8>==>5 ?@028;> <>65B 1KBL ?@54AB02;5=> 2 2845: IF(CA;>285) THEN(A>1KB851)WAITtTHEN(A>1KB852). !>1KB851 8 A>1KB852 ?@54AB02;ONB A>1>9 A>1KB8O =0G0;0 8 >:>=G0=8O =5:>B>@>3> 459AB28O, 8<5NI53> 2@5<5==CN ?@>BO65==>ABL t. 59AB285 <>65B ?@5@K20BLAO 4@C38<8 459AB28O<8 8 A>1KB8O<8. @8<5@K >1KG=>3> 8 <>48D8F8@>20==>3> ?@>4C:F8>==>3> ?@028;0: IF ("Fbest 5 = =5 87<5=8;>AL) THEN (@8B5@89 >AB0=>20=AB8=0,1) IF("Fav=<0;>)and(GD=<0;>)THEN(5@>OB=>ABL <CB0F88=C25;8G8BL,1) WAIT 5 ?>:>;5=89 THEN (5@>OB=>ABL <CB0F88=C<5=LH8BL,1) A?>;L7>20=85 <>48D8F8@>20==KE ?@>4C:F8>==KE ?@028; 405B 2>7<>6=>ABL A>:@0B8BL :>;8G5AB2> 70?CA:>2  70 AG5B CAB0=>2:8 2@5<5=8 459AB28O  8 ?>72>;O5B ?;0=8@>20BL ?>A;54>20B5;L=>ABL 459AB289 35=5B8G5A:>3> ?>8A:0, C?@>I0O A>740=85 107K ?@028;.  >1I5< A;CG05 ACI5AB2C5B 3 C@>2=O, 345 2>7<>6=0 040?B0F8O ?0@0<5B@>2 : 1) C@>25=L ?>?C;OF88  040?B0F8O ?0@0<5B@>2, ?@8<5=O5<KE 4;O 2A59 ?>?C;OF88; 2) 8=48284C0;L=K9 C@>25=L  >@85=B8@C5BAO =0 040?B0F8N ?0@0<5B@>2 ?>4 :>=:@5B=K5 E@><>A><K; 3) :><?>=5=B=K9 C@>25=L  48=0<8G5A:0O 040?B0F8O >B45;L=KE >?5@0B>@>2 :064KE E@><>A><. 5E0=87<K 8=48284C0;L=>9 040?B0F88 <>3CB 1KBL 8=B5@5A=K 4;O :>=B@>;O ?0@0<5B@>2, A2O70==KE A 35=5B8G5A:8<8 >?5@0B>@0<8.  MB>< A;CG05 ?0@0<5B@K 1C4CB >?@545;5=K 4;O 548=8G=>9 E@><>A><K, 0 =5 4;O 2A59 ?>?C;OF88 2 F5;><. @58<CI5AB2> 40==>3> <5E0=87<0 A>AB>8B 2 B><, GB> >= ?>72>;O5B ?@8<5=OBL A?5F8D8G=K5 AB@0B5388 2 @07;8G=KE G0ABOE ?@>AB@0=AB20 ?>8A:0.  B@5BL59 3;025 =AB@C<5=B0;L=0O A@540 ?>445@6:8 M2>;NF8>==>3> ?@>5:B8@>20=8O GenSearch >?8AK205BAO AB@C:BC@0 8 ?@8=F8?K @01>BK @07@01>B0==>9 8=AB@C<5=B0;L=>9 A@54K (!) GenSearch. 0 @8A.6 ?@54AB02;5=0 >1I0O AB@C:BC@0 ! 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