An Exact Algorithm for Solving Difficult Detailed Routing Problems

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Difficult Detailed Routing Problems. Kolja Sulimma. J. W. Goethe-Universitдt Frankfurt [email protected]. Wolfgang Kunz. J. W. Goethe-Universitдt Frankfurt.
An Exact Algorithm for Solving Difficult Detailed Routing Problems Kolja Sulimma

Wolfgang Kunz

J. W. Goethe-Universität Frankfurt

J. W. Goethe-Universität Frankfurt

[email protected]

[email protected]

ABSTRACT

 

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2. ALGORITHM

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2

0

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3. IMPLEMENTATION

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}†F6ILKG HJG E%gC ME%MF"I.T;ILGBFILKMIjN.TA.x%THjHjG \FE%MF"ILHWT;NLMZHVILBNLMR G FTK!THjK–HjM8I&B7ORSF!T7E%G AHjG ®M+e z KM8NLM6T;NLMDg?ILBh0i/T7HjHjG \+Ft E%MF"ILH GF6ILKMXHjM8IT7F!RILKMZTC \+B7NLG]ILKE©G]ILM8N.T;ILMHB;Y1M8NILKMXkKB+C M HjM8IOPBNnM,TA.K?BO ILKM|a=AB+C DE%FHe z KMRB+\CM8\+H&T7NLM~\+MFM8N.T7ILMR Q"STnNLMA8DNLHjG Y1MTC \+B7NLG ILKE²ILKT7IFMM,RHlABFHVI.T7F IlILG E%MOBNWMTA.K BO/ILKMU³6‹Ž„ o†…/‡ FM8k“THjHjG \+FE%MF"ILHe z KMnkBNLHVIA,T7HjMnNLDF"ILG E%M BO/ILKMUT7C\BNLG]ILKEœG HWILKM8NLM0OPBNLM ´,µ!¶· _`Ph0i „ o c }uI%G HgMHjHjG E%G HVILGA(ILB>E~DC]ILG gC]S=ILKM(kJBNLHVI6A,T7HjMF DE~QM8NB7O gB+HjHjG QCM(RB+\+C M\H|kG]ILKILKMkB7NLHVIA,T7HjM%F DEQM0NUBOWIjN.T7A0x>THVt HjG \+FE%MF"ILHT7HILKM0S5A,T7F¸FMY1M0NB"AA8DNvHjG E~DC]I.TFMB+DHjC S"e£•BN M8pTE%gC MT(AB+C DE%F?kG]ILK>h0i{IjN.T7A0x?T7HjHjG \+FE%M8F ILHUATFKT,Y1MFB RB\+C M\HnT7IZTC Cb‚)T7F!RwTABCDE%FkG]ILK–„o†…d‡RB+\C M\+HEDHVIXKT;Y+M C MHjHWILK!T7Fh8i ¹ `PhL¹+„c0iIjN.T7A0x(THjHjG \FE%MF"ILHe ˆ#G]ILKnILKGH{G E%gC ME%MF"I.T;ILGBFnQMFA0KE6T7NLx H!kG]ILK|DgZILBºIjN.TA.x H ABDCRQMnNLBDILM,R(GFvT~NLM,THjBF!T7QC M|TE%B+DF"IWBO[ILG E%M+e

3.2 Implementation B

}†F–ILKGHUG E%gCM8E%MF"I.T7ILG B+FwIjN.TA.x?THjHjG \FE%MF"ILHUT;NLMHVILBNLM,R–G F TnKMTgDHjGF\nILKMF DE~QM8N[BO{Y GTH FMMRM,R~ILBUA0NLM,T7ILMILKMIjN.T7A0x THjHjG \FE%MF"ITH~ILKM6x1M8S"e z N.T7A0x=THjHjG \+FE%MF"ILH|kG]ILK'C MHjHY GTH T7NLMZgNLB"AMHjHjMR y NLHVI,‚ NLMHjDC ILG F\G FvT&NLB+DILG F\~kG]ILKvT|E%GFG EDE F DE~QM8NB7OUY G@T7He z KG H6gNLB RDAMH6TA8G NLA8DG]I6ILK!T7I6KTH6C B,kM8N gB,kM8NvAB+FHjDE%gILG BF¸TF!R#HjE6T7CC M8NwRMCTS¸RDM–ILB'ILKM–C B,kM8N NLMHjG HVI.TFAM&TFRA,T7g!TA8G I.T7FAMUB7O[ILKMZkG]NLMHXT7HXkJMC C/T7HT~QM8IjILM8N SG MCR#RDNLG F\’E6TF DOPTA8ILDNLGF\e£»G FGE%G ®G F\'ILKM?FDEQM8N6B7O Y GTHXE%G\K"IZT7C HjB(NLMHjDC]IZG F?THjE6TC C M8NZC@TS"BDIG]OlA8B+E%g!T7A8ILG B+FvG H DHjMRTHXTgBHVIjtugNLB"AMHjHjG F\%HVILMgde f H/TWKM8DNLG HVILG ANLDF"ILGE%M[BgILG E%G ®,T7ILG BFnILKM THjHjG \+FE%MF"ILH{kJM8NLM FB7IJgNLB"AMHjHjM,R6ABCDE%F%Q"SABCDE%FQDIJG F(T&RMgILKt y NLHVI E6T7Ft FM0N,e z KG H€G H[TWC BI/ObTHVILM0NGF&E6T7F SZA,THjM8H[QMA,TDHjMlILKM8NLMlDHjD!T7CC]S T7NLM~T%C BInB7OJgBHjHjG QC MBgILG E6TC{NLB+DILG F\+HZOBNUT%\GY+MF?gNLB+QC ME G FHVI.T7FAMTFRILKMTC \+B7NLG ILKE¼A,T7F'HVILB+g'THHjB"B+F‰THILKM y NLHVI B+FMnG HXOB+DF!RG FHVILM,T+RB7O[MF DE%M0N.T7ILG F\|ILKME½T7C C§e

3.3 Implementation C

}†F~ILKG HG E%gC ME%MF"I.T;ILGBF|kJMWDHjME~DC]ILG]tuY+T7CDM,R|RMAG HjG B+FRGT7t \N.T7E%H¾u»¿Z¿nH‚!À ÁÂÝILBUNLMgNLMHjMF"I ILKMA0KT7N.T7A8ILM8NLG HVILG AOPDFA8ILG BF BO[ILKMUHjM8IXBOIjN.TA.xTHjHjG \+FE%MF"ILHe z KG HXG HZT7FwTggNLB1T7A0KHjGE%G]t CT7NILB~ILKMnB+FMngNLM8HjMF"ILM,RG F>À Ä;ÂueJ­JDIUÀ Ä;Â]Å#RMHjgG]ILMUG]ILHWILG ILC M0Å HjB+C Y1M8H|ILKM(KT7N.RM8N|E6T®M%NLB+DILG F\wgNLBQC MEve f H~TF=M8Æ)M8A8IB7O ILKM6E%B7NLM\MFM8N.T7CTggNLB1T7A0K’ILKM(kJBNLHVI%A,T7HjMNLDF ILG E%MILKM8NLM \NLB,kHXM8pgB+FMF"ILG@T7C C SG Fh[ª,a[eÇZDNXTC \BNLG]ILKE^K!T7HT|NLDF"ILG E%M C G FM,T;NG FILKMnA.K!TFFMC)C MF\ILKva[e z BHVILBNLM%ILKMHjM0I~B7OIjN.TA.x>THjHjG \+FE%MF"ILH&kJM%AB+FHVIjNLDA8IUILKM A.K!T7N.T7A8ILM8NLG HVILG AOPDFA8ILG B+FŸvÈÉ"Š˜˜8˜jh.Ê o€ËÌ É7° Í,Š7ÊILK!T7I/NLM8ILDNLFH¬ OPB7NlTILDgMC"ILKT7IG HAB+F"I.TG FM,RG F~ILKMWHjM8IBOIjN.T7A0x|THjHjG \FE%MF"ILH TFR ± OBNT~ILDgMC{ILKT7IG HFB7I,e »¿n¿ÎBgM8N.T7ILG BFHA,TFQMnDHjM,R(ILBE%B RG]O@ST7C C€THjHjG \FE%MF"ILH G FUILKMHjM8I€HjG E~DC]I.TFMB+DHjC S"e€•BN/M8pTE%gCM[ILBgQI.TG FUILKMHjDQHjM8I BO€TC C{THjHjG \+FE%MF"ILHILK!T;IWK!T,Y1MZTFM8E%gIqS~IjN.TA.x%Œ[ILKMZA8BObT7A8ILBN BOŸ=OBNÏ,Ð · °GH&ABE%gDILM,R{e(Ñ B+E%MDHjM8OPDClBgM8N.T7ILG BFH~T7NLM NLM,RDAM,R6ILBHjG E%gC MUgBGF"ILM8NWNLMRG]NLMA8ILG B+FHe •B7N&TF?M8pT7E%gC M~BF?KB,k«ILKM|A.K!TFFMCdNLB+DILM0NUB+gM8N.T;ILMHnBF ILKMZ»¿n¿3HjM8INLMgNLMHjMF"I.T7ILG BFH‚AB+FHjG@RM8NWABC DE%F6Á~B7O€•€G \DNLM ¬+e •€G \DNLM|Ò|HjKB,kHTC C{ILKMZYTC GR(IjN.T7A0x(THjHjG \FE%MF"ILHJILKT7IA,T7F

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