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Global Optimization and Multi Knapsack : a Percolation Algorithm

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(1)Global Optimization and Multi Knapsack : a Percolation Algorithm Dominique Fortin, Ider Tsevendorj. To cite this version: Dominique Fortin, Ider Tsevendorj. Global Optimization and Multi Knapsack : a Percolation Algorithm. [Research Report] RR-3912, INRIA. 2000. �inria-00072741�. HAL Id: inria-00072741 https://hal.inria.fr/inria-00072741 Submitted on 24 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. Global Optimization and Multi Knapsack : a percolation algorithm Dominique Fortin, Ider Tsevendorj. N ˚ 3912. ISSN 0249-6399. ISRN INRIA/RR--3912--FR. ` THEME 4. apport de recherche.

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(195) 2 KNR B 5P: I U S/K J UNONKM I Q J UNONK/U TVK B KM/W UXOK/U B QN[ TZK B K PW PP3K  4

(196) 2 KN[ B 5P: I U S/K J ULS/O I L J ULS/O KW UNLXSYQ B PM TZK B K/LNW M[  4

(197) 2 P3K B 5P: I U UNK J OMNM[ I Q J OMNM[ KW ONM/QNK B QN[ TZK B S/[W S/[NM  4

(198) 2 PNP B 5P: I U UNK J UNOXS/M I M J UNOXS/M KW UXONSNS TZK B K PW PQXR  4

(199) 2 PL B 5P: I U UNK J OMNM[ I M J OMNM[ KW ONM/UQ B LNO TZK B LNRW LLNL  4

(200) 2 P3M B 5P: I U UNK J O PUN[ I Q J O PUN[ KW O@PUN[ B O/U TZK B K PW PQYP  4

(201) 2 P"S B 5P: I U OK J O[UXS I O J O[UXS KW ON[/UU B LN[ TZK B K PW LN[NR  4

(202) 2 PU B 5P: I U OK J QXSRO I O J QXSRO KW QS/RO B R/L TZK B K PW L@PU  4

(203) 2 P3O B 5P: I U OK J QLNQNM I R J QLXR[ TVK B L@PW QNLNR[ B MO KW MRL  4

(204) 2 PQ B 5P: I U OK J ROLXS I O J RONMM TZK B PW RNOM/U B RM TZK B KMW PKN[  4

(205) 2 P3R B 5P: I U QNK J [/UNOU I MNK J [/UXRK KW [UNR/U B O/Q TZK B K/UNW PUNLNR  4

(206) 2 LXK B 5P: I U QNK J [NSS P I P3K J [NS/UNK TVK B K[/W [XSYUL B KM TZK B K/LNW UN[NR  4

(207) 2 LYP B 5P: I U QNK J [KNSK I PNP J [KQXS TVK B M/QW [@PP3K B U TZK B SYW PKNM/L  4

(208) 2 LNL B 5P: I U RK J R[ P"S I LNL J R[XSYQ TVK B MO/W [NKKNS B PR TZK B OMW PO@PK  4

(209) 2 LXM B 5P: I U RK J RMNS P I ML J RMXSS TVK B KM/W RNMNSS B UNR KW PP3[ P  4

(210) 2 LS B 5P: I U RK J PK P3[/L I LNK J PK/LNLNK TVK B LQW P3K/LNLNM TZK B K/LNW PLNLL  4

(211) 2 LNU B 5P: I U RK J [R/QNU I LXR J [[NM[ TVK B ONSYW [N[/UNL B P TZK B PMW M/UNUL  4

(212) 2 LXO B 5P: I U [K J [/UNMNR I LS J [/UXRNS TVK B SYQW [UNR/Q B K[ TZK B KMW MMXS/K  4

(213) 2 LNQ B 5P: I U [K J [R P3[ I LXR J [R@P[ KW [NRNS/[ B O/Q TZK B M PW PUNUXS  4

(214) 2 LXR B 5P: I U [K J [NS/[L I P3O J [NS[/L KW [XS/[/L B UQ KW [OQ  4

(215) 2 LX[ B 5P: I U [K J [NSP3K I LXK J [NS PK KW [XSYLXK TZK B PW PPQQ  4

(216) 2 MNK B 5P: I U [K J PPPQXS I M/L J PPP3[ P TVK B PUW PNPP[@P B O KW LXSK W P B 5;: I S LNQ J MKNMNS I M J MKN[K T P B R PW M@PKK B L@P TZK B M/LNW PU W L B 5;: I S MXS J LN[/QS I P3M J M P3RO TVO B O/UW M@P[K B LQ TZK B PMW LNOQ W S B 5;: I L LX[ J QXSSKK I L J [/U@P3OR TVLYP B R/LNW [N[O/LNL B Q THS B SYQNW PKQ W U B 5;: I PK LXK J L@P3M[ I M J L@P3M[ KW LYP3S/[ B RR TZK B UW PONOR W O B 5;: I MK SK [\J [^]`_%acbVd:e QNOU I LXS J QQXO T P B SPW QNQNR B UYPQ TZK B M/LNW [[NK W Q B 5;: I MK MQ J PK/LX[ I PNP J PKNM/U TVK B UQW P3KNSYL B UNM TZK B QLNW PRNRK  W P B 5;: I S LNR J MMNO/L I S J MNS PR T P B OM/W MXSYLNR B L@P TZK B LN[W PR A. -4& m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

(217) Fì. (

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(225) * ˜ I/˜Àè — bê

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(227) ½˜Àè — bê

(228) í“ ;—¾Ÿ™ > ©]hd T ˜Àè À— qê " 5 í   è´G• I¸›  bcê & ST V4â&V‘{Vlf„J`bVlRVd(£˜  1贘À— À— q껞 »)è N€— À— qê¾W¦ "Á£˜ 

(229) ˜ I/˜&è À— qê

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(231) N6I¸˜Àè — T bê T‚

(232) u cPi m oVi^dRV u ˜Àu è —u bê6š·T i d VMgPd V Tu cPm i ©vV c¡ªJV VªJV lRV4ogJm i^ªPVrµou gJi€lRd ScPT ]ki^d CED 薘Om 'ê F’¥‡© ]_ou VWgªJVl]_i^dRV ]kg ge¯vd V ‘qcPahaA©]kd c ]_`qlZ] 6"-è §M I?NPê McPi oVi^dRV A@ š VFi«©*V V %{ibV(â&cP„ cPib„J]kcJi±o`qdcPlv¯¿gPakakg©]kib„{š F   é{g u ceakVa !±¢/£˜ 

(233) ½˜ I/˜Àè À— qê

(234) A T ž ] A ¦ 1£F˜ 

(235) ½˜ I A@

(236) A $ ] A ¦Jë “–G• I¸›  ;Y— !qZ™ F Âè

(237)   è´Z• I¸›  qê

(238) A I ] A í ] A ê. . . . . . . .

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(255) ¡à D $ #(:  â&cP„ u cPib„J]kcJiµo`bd4]ki/d T V‡`qiqsibg©iql À— /ocJi¤‘{VP¨&¯¿g u VrqcPWMjbakVP¨Â¯–`qahakn m VdRV u W]_ibV m ¯ u gJW d T V lfgPa_`bdR]kgJige¯d T VY¯¿gJahakg©]_ib„lfnblRdfVW ge¯&VF¼s`qcedf]hg^iqlë ›1˜Àè À— qê" Ÿ “–•—f˜Àè — bêf™"’“´•K— Ns ™ & akVd " A $ — " I A $ u Vjba_cPoV‡`qiqsibg©iql — {¨5d T Vi#]hdahVFc m ldRg#+è  í-¡;ê  +è  í’êYak]kibVFc u lfnblRdfVW«ë ›»•5í#›1›  -" BŸ I  › 5 5

(256)

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(258)

(259) A . ¥€š ® [i %€u „^` u u V q¨Pu‘€gJd o`qdflœc V c¡©icJi ©vVWMc¡n Vrqj{Vod5d ced¯¿g lRg^WV À— 4akcP„ cPib„J]kcJi o`bdœWMc¡n g^`bdfj{V ¯¿g W j{V o`ba_cedf]hg^im o`bd(è´lfVV(lfu VoT dR]kgJu i}^u ê6š T m u m u u mqm ¤V*ogJ`qa ibgJdR]_oVP¨¯–` d V Wg VJ¨d cedÀlfdfcJi c â&ce„ cJib„P]_cPi `qahV5]_i(c ]hdf]hg^i»dfg 1薘&— À— Oê ; ˜" ¥ u V¼sT `b] u VFl »u 薘&— À— qê u F ¥McPi m u 1贘À— — bê 3F ¥ 4bud T V(akcPdRdfV u ns]hVa m u l C D u F ¥€¨b© T ]ko T u j{gP]_i^dfl g^`bd u g© â‰ceT „ cPziq„P]_cPi Vt akcerbm cPdRu ]kgJidf` iqlvc W]_u ib]kWu ]k­cPdR]kgJi±j gJ‘qahVFW ]_u i^dRgc VªPu V lfVogJi^u ªJVr¬j g^‘bm akVW è>ced % lRd5lf]h„ dpè Bã *X, ê V ]hªcPdR]kgJicPjqj{Vc l&d ]ko6^n4‘€`bd]hd¾l A{c¡ªPg ogJWVl&¯ gJW’â‰ce„ cJib„P]_cPi `€cea g^i¤“–˜À—R˜ I 5 ™fê!š !"# 9

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