A Combined Nelder-Mead Simplex and Genetic Algorithm ... - Alliot

            !" #$%&'$(&)'* +,-.()/)0$()&1 23&%$3* 4*1('* +,5(6+*0 +* 3$ 7$8)9$()&1 : *;')*11* *3)1 ?@ABB C&63&60* 4*+*D E'$1F* $33)&(G'*FH*'FH*I*1$FIJ' (*3K L??M BNO @< P@ OP 1.5

1

0.5

-20

-10

00

10 x

20

-0.5

-1

E)96'* @K p Lq M Lr s @= q t uv OAwOAxMI y* `)33 f'0( F&10)+*' 2')*`$1a,0 F3$00)F$3 (*0( J61F()&1 L^19%*' $1+ z&0*1 @{{O|M K @ ~€ q„ v …~€ F&0L q ‚ M }Lq~ w    w q~€ M s PAAA ‚ ‚ƒ ~ †‡ ~ ‚ƒ ˆ ‡ t u@w @Axw q ‚ t uv @AAAw @AAAx #*(,0 9*1*'$3)b* (H)0 J61F()&1 (& $1_ +)/*10)&1 %_ +*f1)19 K ‰ ‰ p Lq~ w    w q‰ M s PAA@ r  q„‚ v … F&0L †‡q ‚ M ~ ~ ˆ ‡ t u@w‚ƒr xw q ‚ t‚ƒuv @AAAw @AAAx '*.'*0*1(*+ &1 f96'* @ J&' r s @ $1+ q t uv OAwOAxI : 3&F$3 &.()/)b$()&1 /*(H&+ /$_ f1+ (H* 93&%$3 /)1c )/6/ &J (H* J61F()&1 Lq€ s AM= &13_ )J (H* 0($'()19

.&)1( q€ %*3&190 (& x v Š w ŠuI ^J r ‹ @= (H* 93&%$3 /)1c )/6/ /$_ %* J&61+ &13_ )J (H* 0($'()19 .&)1( %*3&190 (& Œ ‚Ž~‰ x v †‡Š w †‡ŠuI 2*1*()F $39&')(H/= &1 (H* F&1('$'_ /$_ *$0)3_ f1+ .&)1(0 )1 (H)0 $'*$= %6( (H* f(1*00 &J (H*0* *3*/*1(0 F$1 %* H)9H $1+ (H*_ /$_ +)0$..*$' `)(H (H* 0*3*Fc ()&1 .'&F*00I CH)0 .'&%$%3_ *D.3$)10 `H_ 2:0 J$)3 &1 (H)0 .'&%3*/ `H*1 r *DF**+0 ?A L‘6'$1+ $1+ :33)&( @{{’MI ^1 (H)0 $'()F3*= 2:0 60* $ 7*3+*'ce*$+ 0)/.3*D*0 .&.6c 3$()&1 (& ($a* $+8$1($9* &J (H* 9&&+ .'&.*'()*0 &J 06FH 3&F$3 &.()/)b$()&1 /*(H&+0I CH* $)/ &J (H* 9*1*()F $3c 9&')(H/ )0 (& f1+ 9&&+ $'*$0 J&' (H* 0)/.3*D $39&')(H/ `H*'*$0 (H* 3$((*' `)33 f1+ (H* 3&F$3 /)1)/6/ )1 (H)0 $'*$I ^1 (H* f'0( .$'(= (H* 7*3+*'ce*$+ 0)/.3*D $39&')(H/ )0 .'*0*1(*+I “$'( O +*0F')%*0 H&` (H* 9*1*()F $39&')(H/ $1+ (H* 7*3+*'ce*$+ 0)/.3*D $39&')(H/ $'* F&/%)1*+I ^1 .$'( ? (H* $39&')(H/ )0 (*0(*+ &1 (H* 2')*`$1a,0 J61F()&1I z*063(0 &1 4&'$1$,0 J61F()&1 $'* $30& 9)8*1I ” •–— ˜—™l—[š›—\l \™œk[nZ– #*(,0 $006/* (H$( (H* .'&%3*/ (& %* 0&38*+ )0 (H* J&3c 3&`)19 K ž ‡r ‰ Ÿ L  M   t¡ E&' J61F()&10 &8*' ¡ ‰ = (H* 7*3+*'ce*$+ /*(H&+ &.*'c $(*0 `)(H $ 0)/.3*D ¢ )1 ¡ ‰ = `H)FH )0 0.*F)f*+ %_ )(0 L £ @M 8*'()F*0K L € w  ~ w    w  ‰ MI CH* %*0( 8*'(*D  € )0r +*0)91$(*+ (& %* (H* 8*'(*D J&' `H)FH Ÿ L € M ¤ Ÿ L ¥ M J&' ¦ s @w   w r I #*(,0 +*0F')%* $ F&/.3*(* )(*'$()&1 J'&/ 0)/.3*D ¢§ (& 0)/.3*D ¢§¨ ~ K E)'0(  ~ w    w  ‰ $'* '*©*F(*+ (H'&69H (H* %*0( 8*'(*D I E)96'* O 0H&`0 $1 *D$/.3* J&' r s OI CH* '*©*F(*+  €8*'()F*0 $'* 3$%*3*+ ª ~ w    wª ‰ I ^J $ '*©*F(*+ 8*'(*D 9)8*0 $ %*((*' J61F()&1 8$36* « (H$1 0(*. )0 06FF*00J63 $1+  € = (H*1 (H*(')*0¬­®$1­¯°±²³ (H* $39&')(H/ ­´µ¶³·±²³ 0(*.I CH* ­´¸ µ¶³·±²³ 0(*. F&10)0(0 &J *D.$1+)19 *$FH '*©*F(*+ *+9* Lª¥ v  € M (& (`)F* )(0 3*19(H (& 9)8* $ 1*` *D.$10)&1 8*'(*D ¹¥ I º ^J (H* ­´µ¶³·±²³ 0(*. )0 06FF*00J63K »¦ t u@w r xw Ÿ L¹¥ M ¼ Ÿ L € M (H*1 ¢§¨ ~ s ¢½ª¾L € w¹ ~ w   w¹ ‰ M `H*'* ¢½ª¾ 0&'(0 8*'()F*0 $FF&'+)19 (& (H*)' )1F'*$0)19 J61F()&1 8$36*0I

v2

c2

r1 v0

e1

c1

v1

r2

e2

E)96'* OK CH* ? .&00)%3* 0(*.0 9)8*1 (H* 0)/.3*D ¢ `)(H 8*'()F*0 L € w  ~ w   „ MI

º ^J (H* ­´µ¶³·±²³ (*0( )0 1&( 06FF*00J63K ˆ¦ t u@w r xw Ÿ L € M ¤ Ÿ L¹¥ M (H*1 ¢§¨ ~ s ¢½ª¾L € wª ~ w   wª ‰ MI « ^J (H* ¬­® ­¯°±²³ 0(*. )0 1&( 06FF*00J63K ˆ¦ t u@w r xw Ÿ L € M ¤ Ÿ Lª¥ M (H*1 ¢§¨ ~ s ¢½ª¾L € w¿ ~ w   w¿ ‰ M `H*'* (H* F&1c ('$F(*+ 8*'(*D ¿ )0 (H* /)++3* &J  € $1+  ¥ J&' ¦ s @w   w r I ¥ CH* $39&')(H/ )0 0(&..*+ `H*1 (H* 0)b* &J ¢§ )0 0/$33*' (H$1 (H* '*h6)'*+ .'*F)0)&1 ÀK  L  ‚ w  ¥ M ¤ À L‡ w¦MžÁq @w x tu r„ `H*'*  Lq wÃM )0 $ +)0($1F* /*$06'* %*(`**1 q $1+ ÃI 4&18*'9*1F* &J (H* $39&')(H/ F$1 %* J&61+ )1 L7*3+*' $1+ e*$+ @{NB= eFÄ)11&1 @{{NMI Å ÆkXnj\Znkj ÇnZ– œ—j—Zn] \™œk[nZ– ^1 (H)0 .$.*'= F3$00)F$3 2*1*()F :39&')(H/0 $1+ 58&c 36()&1$'_ 4&/.6($()&1 .')1F).3*0 06FH $0 +*0F')%*+ )1 (H* 3)(*'$(6'* L2&3+%*'9 @{’{= o&33$1+ @{7K AcOA@c@B