An Evolutionary Algorithm for Machine Layout and Job ... - cs.York

4 downloads 0 Views 244KB Size Report
Abstract—Machine layout and material flow between machines are crucial considerations for improving productivity in any manufacturing environment.
 

$Q(YROXWLRQDU\$OJRULWKPIRU0DFKLQH/D\RXWDQG-RE $VVLJQPHQW3UREOHPV 5XKXO6DUNHU0HPEHU,(((7DSDEUDWD5D\DQG -RVp%DUDKRQDGD)RQVHFD 

$EVWUDFW²0DFKLQH OD\RXW DQG PDWHULDO IORZ EHWZHHQ PDFKLQHVDUHFUXFLDOFRQVLGHUDWLRQVIRULPSURYLQJSURGXFWLYLW\ LQ DQ\ PDQXIDFWXULQJ HQYLURQPHQW 7KH PDFKLQH OD\RXW DQG WKHRSHUDWLRQVDVVLJQPHQWSUREOHPVDUHERWKNQRZQWREH13 KDUG SUREOHPV ,Q WKLV SDSHU ZH LQWURGXFH D QHZ FRPELQHG PDFKLQH OD\RXW DQG RSHUDWLRQV DVVLJQPHQW SUREOHP :H SURSRVH DQ HYROXWLRQDU\ DOJRULWKP WR VROYH WKH FRPELQHG PDFKLQH OD\RXW DQG RSHUDWLRQV DVVLJQPHQW SUREOHP 7KH HIIHFWLYHQHVV RI RXU DSSURDFK LV GHPRQVWUDWHG WKURXJK QXPHULFDOH[DPSOHV  ,QGH[ 7HUPV²0DFKLQH /D\RXW -RE $VVLJQPHQW 2SHUDWLRQV $VVLJQPHQW 0XOWLREMHFWLYH (YROXWLRQDU\ $OJRULWKP *HQHWLF $OJRULWKP

0

, ,1752'8&7,21

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da Fonseca is with the Departament of Electrical Engineering and Computer Science, Faculty of Sciences and Technology, New University of Lisbon, Monte de Caparica, 2829-516 Caparica, Portugal (email: [email protected]).

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

3991 c 1-4244-1340-0/07$25.00 2007 IEEE

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

7+(352%/(0

7KHUHDUHEDVLFDOO\WZRW\SHVRISUREOHPVWKDWZHQHHGWR FRQVLGHU o /D\RXWSUREOHPVZLWKFRQYHQWLRQDOPDFKLQHV o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

3992

ZH LQWHQG WR GHYHORS DQ DOJRULWKP WR VROYH ERWK PDFKLQH OD\RXW DQG PDFKLQH RSHUDWLRQ DVVLJQPHQW SURGXFWLRQ SODQQLQJ  SUREOHP 7KH OD\RXW DQG SURGXFWLRQ SODQQLQJ SUREOHPXQGHUFRQVLGHUDWLRQFDQEHGHILQHGDVIROORZV  o 7KH WHUP FHOO LV WR GHVFULEH D PDFKLQH FHQWUH RU ORFDWLRQ 7KH QXPEHU RI FHOOV FHOO DUHD DQG WKHLU DUUDQJHPHQWVDUHJLYHQ o 7KH WHUP PDFKLQH UHSUHVHQWV D PRGHUQ PDFKLQH WRRO VXFK DV 1XPHULFDO &RQWUROOHG 1&  PDFKLQH WRROV 7KH PDFKLQHV FRXOG EH HLWKHU LGHQWLFDO RU QRQLGHQWLFDO LQ WHUPV RI WKH W\SH DQG QXPEHU RI GLIIHUHQWRSHUDWLRQVWREHSHUIRUPHG o $ PDFKLQH LV FDSDEOH RI SHUIRUPLQJ VHYHUDO W\SHV RIRSHUDWLRQVDQGDQRSHUDWLRQFDQEHSHUIRUPHGRQ DOWHUQDWLYHPDFKLQHV o $ PDFKLQH FDQ SHUIRUP RQO\ RQH RSHUDWLRQ DW DQ\ WLPHDQGRSHUDWLRQVWREHSHUIRUPHGLQWKHPDFKLQH DUH QRQSUHHPSWLYH 2QO\ RQH RSHUDWLRQ IRU HDFK PDFKLQH PRGH RI RSHUDWLRQ  ZRXOG EH FKRVHQ LQ VROYLQJWKHSUREOHP o $ SURGXFW UHTXLUHV D QXPEHU RI RSHUDWLRQV $ SURGXFWPD\FKRRVH RQHRUPRUHPDFKLQHVDWHDFK VWDJHRILWVRSHUDWLRQVDQGWKHWUDQVSRUWDWLRQRIWKH SURGXFWV EHWZHHQ WKH PDFKLQHV LV KDQGOHG E\ D PDWHULDOKDQGOLQJV\VWHP ZHDVVXPH$*9  o 7KHUH PD\ EH PRUH WKDQ RQH SURGXFW RU SURGXFW W\SH  ZLWK GLIIHUHQW RSHUDWLRQV DQG RUGHU RI RSHUDWLRQV o 7KH GLVWDQFHV EHWZHHQ PDFKLQHV FDQ EH FDOFXODWHG XVLQJ WKH FHOO FRRUGLQDWHV &XUUHQWO\ LW LV WKH VXP RI WUDYHUVDO LQ [ DQG \ FRRUGLQDWHV 7KH PDWHULDO KDQGOLQJ WLPHV FDQ EH FDOFXODWHG EDVHG RQ WKH YHKLFOH YHORFLW\ DQG GLVWDQFH 1RWH WKDW RQH FDQ UHSODFHWKLVSDUWZLWKDJLYHQWLPHPDWUL[  o 7KHWLPHVDQGFRVWVRI RSHUDWLRQVLQHDFKPDFKLQH IRUDQ\SURGXFWDUHGHWHUPLQLVWLFDQGNQRZQ o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

2007 IEEE Congress on Evolutionary Computation (CEC 2007)

  7$%/(21(/,1(/$ [ @ = > −    − @ LQGLFDWHV WKH ILUVW DQG WKH ODVW FHOO DUH YDFDQW ZKLOH WKH VHFRQG FHOO FRQWDLQV

3994

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o 1XPEHURIPDFKLQHV  o 0DFKLQHFDSDELOLW\$OORSHUDWLRQV o /D\RXW DUUDQJHPHQW [ VTXDUH EORFN DUUDQJHPHQW LHFHOOVIRUPDFKLQHV o 7KHGLVWDQFHEHWZHHQDQ\WZRDGMDFHQWFHOOVRQHXQLW o &RVWIRUPDWHULDOKDQGOLQJSHUXQLWSHUXQLWGLVWDQFH  

2007 IEEE Congress on Evolutionary Computation (CEC 2007)

  o 0DFKLQLQJ FRVW   SHU KRXU IL[HG IRU DOO PDFKLQHV  o 0DFKLQLQJWLPHPDWUL[  

RSHUDWLRQV     DQG  EROG LWDOLF LQ 7DEOH E  UHVSHFWLYHO\  7$%/($0$&+,1(/2&$7,216 ,1;648$5(%/2&.

7$%/(%23(5$7,216 3(5)250('%@ ./0DN@ - ) 3LHUFH DQG : % &URZVWRQ ³7UHH 6HDUFK $OJRULWKPVLQ 4XDGUDWLF $VVLJQPHQW 3UREOHPV´ 1DYDO 5HVHDUFK/RJLVWLFV4XDUWHUO\SS   

>@ 5 ) /RYH DQG - @ -+ &KHQ DQG 6@- %DODNULVKQDQ &+ &KHQJ DQG .) :RQJ ³)$&237 $ 8VHU )ULHQGO\ )$&LOLW\ /D\RXW 237PL]DWLRQ 6\VWHP´ &RPSXWHUV  2SHUDWLRQV 5HVHDUFKSS >@. 'HE $ 3UDWDS 6 $JDUZDODQG7 0H\DULYDQ ³$ )DVW DQG (OLWLVW 0XOWLREMHFWLYH *HQHWLF $OJRULWKP 16*$,,´ ,((( 7UDQVDFWLRQ RQ (YROXWLRQDU\ &RPSXWDWLRQ  SS >@. 'HE $ 3UDWDS 6 $JDUZDODQG7 0H\DULYDQ ³$ )DVW (OLWLVW 1RQGRPLQDWHG 6RUWLQJ *HQHWLF $OJRULWKP IRU 0XOWLREMHFWLYH 2SWLPL]DWLRQ 16*$,,´ 3URFHHGLQJV RI WKH 3DUDOOHO 3UREOHP 6ROYLQJ IURP 1DWXUH9,&RQIHUHQFH3DULV)UDQFHSS

2007 IEEE Congress on Evolutionary Computation (CEC 2007)

3997

Suggest Documents