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Distributed Optimization using Virtual and Real Game Strategies for Aerodynamic Design

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(1)Distributed Optimization using Virtual and Real Game Strategies for Aerodynamic Design Zhili Tang, Jean-Antoine Desideri, Jacques Périaux. To cite this version: Zhili Tang, Jean-Antoine Desideri, Jacques Périaux. Distributed Optimization using Virtual and Real Game Strategies for Aerodynamic Design. [Research Report] RR-4543, INRIA. 2002. �inria-00072045�. HAL Id: inria-00072045 https://hal.inria.fr/inria-00072045 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Distributed Optimization using Virtual and Real Game Strategies for Aerodynamic Design Zhili Tang — Jean-Antoine Désidéri — Jacques Périaux. N° 4543 September 2002. ISSN 0249-6399. ISRN INRIA/RR--4543--FR+ENG. THÈME 4. apport de recherche.

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(50)    . Ô p\Ö E. . É tu¢vl{n‡Ÿ Œ@x „z„tyx wW»Otun º | ® o°CzˆO€HnmrnVƒ‰i ||_®Ž€‚z„z„tuÉ¡ilm9|nr—x Šw z{|\†ilƒnVn‡zFƒ‰®´ÕPtuvl¢|6~ ~¡º ŠS€lz{xt}{|_„|~|_žlvl· wun ~ m † ~¸ z„¢i¡n"n~ln x ˜tux „®´wf|¹¡tuz{wil|nFŠ º|_ƒ‰t}~lze¢P®´¹lvlz{~PilŠSnz„tu|x~Ån {|tuƒ † †ˆ\n ~Pã¡x ~lmon tu† Š"ƒ—xŠ˜ƒei¡®´x|{wux_w}|6ŠSº—z„n"ƒe„tyt}ƒ‰~Äz„tyz{Š ilƒjno¢tux »n n{| z{†ilˆOn)~¡»6x xmow}vltynŠ Ô V›Ö.       ºŸl¹Mi¡ºtuŠ˜ili‡n"ty„ƒ@n x³®´vltu~PƒoŠSz„xYtu|®´~vl~¡| Š®‚z„z{tuil|n`~/ÕP||6®—º¶z„i¡»Øxn „ty€¡x „ž¡nVw}ƒ„nVƒ„ƒvlx{~n † z„¹Çi¡|nǍžHz„|ilvln ~ †€lx {n"{ˆƒ{ƒ‰| vl®l{nžH| † † #t "Wˆ‡n x{ƒn ~¡ºÇŠ nÇn!mržHn"n~\zºz„tu|n n"~l~Èn † z{iltu~)nă‰xnVŠSŠSz{z{t}v¡|_x ~ w €¡x„z{nV{ƒ„xƒ„~¡vlƒ‰{|_n’~lxty~Še† |_—xƒ‰z˜vlx €H{n ¢˜nƒ„z|€l~l{tyŠn"ƒ{x ƒ„tuvl‰„®´|_n’t}tuw¼~ tu~ tu~O† »{n"x{¢ƒ„n {n† † n"v¡ƒ„t}ŠS¢_z{~!t}|_€l~!{|€lž¡{|w}n"ž¡m w}n"¹‚m |_·M“ z„iln3»6x€l„{tyx6n"z{ƒ{t}ƒ„|_vl~„n tu~!† ˜z{x il¢9n‡Šx |Otu„n ®´ä9|tuŠ wt}n"ƒ‰i¡~\zjx€P|n ® €¡„| † v¡Š n"ƒxr»6x {tux z„tu|~!t}~ z„i¡n‡Š|_ƒ‰zj®´vl~¡Šz„tu|~ Ô _Ö    "!      '#           ºƒ„i¡i¡xtu€PŠ˜i¶n_·±tyƒ“Fxăo®´t¯vlz9~¡i¡ŠSz{x_t}ƒ9|_~Èx wu„| nV®jx z{† ilˆ*nžH»6n x n {~³tyx6z„motu|n ~¶~\z{tut}~¶|_~lz{n il† nžOÕ¡ˆ$|6º xã¡mrn"w nV† ƒ‰|_»6~ x „"ty x  ¹`žlwuz„n"ilƒnÄx |~ z„† iln"z{rilnz„n »6{xm9„ƒ9tyx6z{Š t}x|_~/~¬žH|nÄ®ex n"tux‰ƒ„®´tu|_w}t}ˆ w z{m9† {nxxz„†~\n"„t}ˆoz„motuz{|tut}~¡~lmoxtunnVw†ƒmoxn nƒÇ‹lz{Šz„iln il| €ln† z ~O|vl!®Mm㡺žP~liln"t}tuz„Š˜n i!|®† ºÇt† "W|_nVn vlƒ‰{tuw n ¢† ~¡~!„Š nV»6n"«\x ƒ"vl¹¼{tut}žPx{n—nVžlŠ w}z{nVx ilƒÇvPn’ƒ‰x n¢z{z„n n"il»x6n"n"z{~„n ˆo¹Wz„Št}z„i¡|n"nmo{x ÕP€lz„|6vltu|ºÊz„~tu~l·ŽºÇ¢‡Ã—|_z{vl|6t}mow º† nn i¡»_t¯n xØ®V»_ºÇ¹_n‡nFžOz„ˆ9ºÇ| v¡n"žH„ƒ„nrnFtu~lv¡ƒ„¢r|ƒ‰wutuŠ »~l|n¢~\† z„z„{ilx|nƒ w z{ƒ„il|wun »|_nF„ˆ_z„¹‚i¡z„ni¡Õ¡n‡|6Õ¡ºK|6º nV«_n"vP«\x6v¡z„tux |z„~Ptu|ƒj~¡|ƒ—~¡xŠ „n’n3n"tu»~\n"z„„{ˆ9| † t}z„v¡n"Š{n x † z„tu|x~ƒ—· Š |~¡ƒ‰z„˜x tu~\z—t}~¸ƒ„v¡Š˜i¸x9ºjx؈9z{i¡x6z’ºÇn3|_~lw}ˆ ~ln"n † z„| 6. E. E@O. 5Y.

(51) )à CÒSà Þ Î . CàÁÍrà VÌ fàBÑ6á¬Þ SàÁá àÁÒ CÞ¡Ì ßÌ6á FÎ{Ì ßM˗Ì6Í9Î CÒ{Ì Î àBÎ.   

(52) .  . . . . . .  . . E E. “z㡍˜ƒ‰z"¹lºn † nã¡~¡n‡ƒ‰|_mrn _xŠ |žltyx ~m9x z„{tuŠ n"ƒ®´|—Š |~O»n"~ltun ~¡Š nFtu~ z„iln®´|_w}wu|6ºt}~¡¢ † n {t}»6x6z{t}|_~¡ƒ.                  

(53)   '         

(54)   '    Ô Ö Ãen {nºÇn3Š|_~¡ƒ„t †  n"jz„iln‡ƒ‰z„nVx  † ˆ!ƒz˜x6z„n’Õ¡ |6º3¹lx~ † z„iln3»6x {tyx6z„tu|~ | ®z„iln‡•Mvlw}n"—n"«\v¡x z„tu|~¡ƒx„n. Ô Ö 

(55)   ' 

(56)  465     x_ƒz„iln3{n"ƒ„vlw}z| ®        ‡¹       ‡¹¡iln ~¡Š n Ô Ö       (' 

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(62)      »6“Fxƒ„tyºx6z{n’t}|_mo~¡n"x ~_wHz{®´t}||_{~lmn † |€l®'{z„n i¡»On‡tu|•Žv¡vlƒ„wuwun ˆ—¹‚~lnV«_|6ºvPx6t}z„~\tu|z„{~P| ƒj† ºv¡t¯Š z{nilt}z„~ iln‡z{il”n x ¢† ˜|x m9~¡x¢t}ty~ x ~/ m vlw¯z{t}€¡w}tun  ¹Px ~ † tu~_z{n ¢_{x z„n’z„iln.

(63) !  

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(65)      5 Ô Ÿ  _Ö   #     h¢_j„i¡t † nÇwutun~¸®ÁzŽz{i¡ilxtuƒ’~ †€¡xƒ„€Pt † n"nǍ"¹W|t}®¡z’z{tyilƒ’n€Pxn"žP„|6tu| »_†n`tynVŠ‡«_tuvP~ x6z„tu|† ~rtu{Š n"xŠS~)z{t}|_žH~n ¹H† z„t}il»On"t † „n n ®´† |{t}~\n‡z{z{|eilzn)ºãP|F{€Pƒ‰zFx „tuz{~\ƒ"z„·n ¢_“e{ƒ xwº€PnÇx vP„ƒ‰zFn| z„®Çi¡nn"«\ Fv¡°fx6zz{ˆOt}|_€P~ n  Ô Ÿ  \Ö`tyƒ. !        !    Ô Ÿ VÖ          x~ † z„iln‡ƒ„n"Š |~ † t}~\z{n ¢˜x wW€¡x‰z|® nV«_vPx6z„tu|~ Ô Ÿ _Ö. !       

(66)  !     !     !    Ô ŸŸÖ            À®`z„ilnr®Bx Fã¡n"w † žP|_vl~ † x„ˆ-tyƒFm9xt}~\z{xt}~¡n †¸† v¡„tu~l¢!z„iln † n"ƒ„tu¢~¹Wz{iln ~  5®´|tu~‚Õ¡|6ºÊºjxØ»n_¹ z{tu~\i¡z„x6n"z¢˜tyx6ƒoz„z{tu||/~ ƒ„Š xØxˆ ~! !žHn3 º „t}z‰z{n ~ 5¡ ·Kt}®ºn¸Š x~³moxân !   85Å®´|9z{iln¸|vl z‰Õ¡|6º ºxØ»_n¹Çz„iln¸xžP|6»_n.

(67) !          !      !    Ô Ÿ œ_Ö          x~ † n"«\v¡x6z{t}|_~ Ô Ÿ  \Ö`žHn"Š |mon"ƒ.   !  '  !        !   Ô Ÿ6p\Ö         ÆÇ|_~¡ƒ„n"«\vln ~\z{w}ˆ_¹Oz„iln»6x {tux z„tu|~ | ®@Š|_ƒ‰zj®´vl~¡Šz„tu|~¸Š x~!žHn3º{t¯z„z„n ~.      !      '          '

(68)   !   '  !        '   !     Ô Ÿ›Ö EKH. E V. E X. E. . Y Y[Z\2]^_]`. . . .

(69) ؟. 'Ð_à @àÏ¡Ì á. E. lΘÌ6á Fá ÀÑ àÁáHÎ Sà ÒSà ‚Ì Þ¡Î ÒSàBÌ Þ. . . . -. .  .

(70)  . . . . Úe|6º³„nVx {{x~l¢njz{iln—z{ilt} † x~ † ®´|v¡‰z{i9z„n"„m9ƒÇt}~z„ilnF„tu¢i\z`i¡x~ † ƒ„t † ne|®'x žH|6»nn"«\v¡x z„tu|~¹\ºnei¡xØ»_n.   !  '  !       !   '  !      '         #   Ô Ÿ _Ö.   !  

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(76)       . . . #. . . . O. . .  . ‘F~z„ilnx tu„®´|tuwWƒ„vl„®BxŠ n! 6¹‚xŠ"Š|_ † tu~l¢)z„ilnFÕ¡|6º­ã¡n"w † žP|_vl! ~ † x„ˆŠ |~ † t¯z{t}|_~  5¡¹OºÇn’i¡xØ»n        5

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(82)    5 ¹Pƒ‰|rz„i¡n®´|vl„z„i!z„n"„m žPVn Š|monVƒ Ô Ÿ Ö   !      

(83) '

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(86)               ~\z{„| † v¡Š n Ô \Ö Ô ÖÇt}~\z„| Ô V›_ÖS¹Oz„|o¢_nz.     !      '          '

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