Multi-objective Particle Swarm Optimization Algorithm for ... - cs.York

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

,,1752'8&7,21

$

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



{

}

& PD[ = PD[ &L  L =  Q

 

 0DQXVFULSWUHFHLYHG0DUFK  6 &KDQGUDVHNDUDQ LV ZLWK WKH 6UL 5DPDNULVKQD 0LVVLRQ 9LG\DOD\D 3RO\WHFKQLF &ROOHJH &RLPEDWRUH ,QGLD HPDLO FKDQGUXVVE#\DKRRFRLQ  6 * 3RQQDPEDODP LV ZLWK WKH 6FKRRO RI (QJLQHHULQJ 0RQDVK 8QLYHUVLW\  3HWDOLQJ -D\D 6HODQJRU 0$/$@ & 5DMHQGUDQ DQG + =LHJOHU ³$QWFRORQ\ DOJRULWKPV IRU PLQLPL]LQJ WRWDO IORZWLPH LQ SHUPXWDWLRQ IORZ VKRSV´ &RPSXWHUV ,QGXVWULDOHQJLQHHULQJYROSS >@ & 5DMHQGUDQ DQG + =LHJOHU ³$QWFRORQ\ DOJRULWKPV IRU SHUPXWDWLRQ IORZVKRS VFKHGXOLQJ WR PLQLPL]H PDNHVSDQ  WRWDO IORZWLPH RI MREV´ (XURSHDQ -RXUQDO RI 2SQ 5HVHDUFK YRO  SS >@ @ 9LVZDQDWK .XPDU *DQHVDQ $SSD ,\HU 6LYDNXPDU DQG * 6ULQLYDVDQ³+LHUDUFKLFDOPLQLPL]DWLRQRIFRPSOHWLRQWLPHYDULDQFH DQGPDNHVSDQLQMREVKRSV´ &RPSXWHUV 2SHUDWLRQV5HVHDUFK YRO SS >@ 5. 6XUHVK DQG .0 0RKDQDVXQGDUDP ³3DUHWR DUFKLYHG VLPXODWHG DQQHDOLQJ IRU SHUPXWDWLRQ IORZ VKRS VFKHGXOLQJ ZLWK PXOWLSOH REMHFWLYHV´ 3URFHHGLQJV RI WKH ,((( FRQIHUHQFH RQ &\EHUPDWLFVDQG,QWHOOLJHQW6\VWHPV'HF6LQJDSRUH >@ : .XVLDN ³&RPSOHWLRQ WLPH YDULDQFH PLQLPL]DWLRQ RQ D VLQJOH PDFKLQH LV GLIILFXOW´ 2SHUDWLRQV 5HVHDUFK /HWWHUV YRO SS   >@ -6ULGKDUDQG&5DMHQGUDQ³6FKHGXOLQJLQ IORZ VKRSDQG FHOOXODU PDQXIDFWXULQJ V\VWHP ZLWK PXOWLSOH REMHFWLYHV $ JHQHWLF DOJRULWKPLF DSSURDFK´ 3URGXFWLRQ 3ODQQLQJ DQG &RQWURO YRO SS >@ )76 &KDQ 7& :RQJ 7& DQG /@ )$ 2JEX DQG '. 6PLWK ³7KH DSSOLFDWLRQ RI WKH VLPXODWHG DQQHDOLQJ DOJRULWKP WR WKH VROXWLRQ RI WKH Q P &PD[ IORZ VKRS SUREOHP´ &RPSXWHUV DQG 2SHUDWLRQV 5HVHDUFK  YRO  SS  ±  >@ -90RFFHOOLQ061DJDPR³(YDOXDWLQJWKHSHUIRUPDQFHRIWDEX VHDUFK SURFHGXUHV IRU IORZ VKRS VHTXHQFLQJ´ -RXUQDO RI WKH 2SHUDWLRQDO5HVHDUFK6RFLHW\ YROSS >@ . 5DPHVKNXPDU 5. 6XUHVK DQG .0 0RKDQD VXQGDUDP ³'LVFUHWH SDUWLFOH VZDUP RSWLPL]DWLRQ '362  DOJRULWKP IRU SHUPXWDWLRQ IORZ VKRS VFKHGXOLQJWR PLQLPL]H PDNHVSDQ´ /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFH 6SULQJHU 9HUODJ *0%+   YROSS >@ )DLWK 7DVJHWLUHQ 0HKPHW 6HYNOL @ * 3UDEKDKDUDQ % 6KDKXO +DPLG .KDQ 3 $VRNDQ DQG 0 7KL\DJX³$3DUWLFOHVZDUPRSWLPL]DWLRQDOJRULWKPIRUSHUPXWDWLRQ IORZ VKRS VFKHGXOLQJ ZLWK UHJXODU DQG QRQUHJXODU PHDVXUHV´ ,QWHUQDWLRQDO-RXUQDORI$SSOLHG0DQDJHPHQWDQG7HFKQRORJ\ YRO 1RSS >@ .DO\DQPR\ 'HE ³0XOWL2EMHFWLYH 2SWLPL]DWLRQ 8VLQJ (YROXWLRQDU\$OJRULWKPV´)LUVW(GLWLRQ-RKQ:LOH\ 6RQV >@ 7 3DVXSDWK\ &KDQGUDVHNKDUDQ 5DMHQGUDQ DQG 5. 6XUHVK ³$ PXOWLREMHFWLYH JHQHWLF DOJRULWKP IRU VFKHGXOLQJ LQ IORZ VKRSV WR

4018

PLQLPL]H PDNHVSDQ DQG WRWDO IORZ WLPH´ ,QWHUQDWLRQDO -RXUQDO RI $GYDQFHG 0DQXIDFWXULQJ 7HFKQRORJ\ 3XEOLVKHU 6SULQJHU9HUODJ /RQGRQ/WGYROSS >@ &KDQGUDVHNKDUDQ5DMHQGUDQ³+HXULVWLFVIRUVFKHGXOLQJLQIORZVKRS ZLWK PXOWLSOH REMHFWLYHV´ (XURSHDQ -RXUQDO RI 2SHUDWLRQDO 5HVHDUFKYROSS >@ $OL $OODKYHUGL ³7KH WZR DQG P PDFKLQH IORZVKRS VFKHGXOLQJ SUREOHPV ZLWK ELFULWHULD RI PDNHVSDQ DQG PHDQ IORZWLPH´ (XURSHDQ -RXUQDO RI 2SHUDWLRQDO 5HVHDUFK YRO  SS   >@ $OL $OODKYHUGL ³$ QHZ KHXULVWLF IRU PPDFKLQH IORZVKRS VFKHGXOLQJ SUREOHP ZLWK ELFULWHULD RI PDNHVSDQ DQG PD[LPXP WDUGLQHVV´&RPSXWHUV 2SHUDWLRQV5HVHDUFK YROSS  >@ 9LQFHQW 7¶NLQGW 1LFRODV 0RQPDUFKH )DEULFH 7HUFLQHW DQG 'DQLHO /DXJW³$QDQWFRORQ\RSWLPL]DWLRQDOJRULWKPWRVROYHDPDFKLQH ELFULWHULD IORZVKRS VFKHGXOLQJ SUREOHP´ (XURSHDQ -RXUQDO RI 2SHUDWLRQDO5HVHDUFKYROSS >@ +LVDR ,VKLEXFKL 7DGDVKL @ 5&(EHUKDUW- .HQQHG\³$ QHZRSWLPL]HUXVLQJSDUWLFOH VZDUP WKHRU\´ ,Q 3URFHHGLQJV RI WKH 6L[WK ,QWHUQDWLRQDO 6\PSRVLXP RQ 0LFUR0DFKLQHDQG+XPDQ6FLHQFH-DSDQSS >@ - .HQQHG\ 5& (EHUKDUW DQG @ @ 6 &KDQGUDVHNDUDQ 6* 3RQQDPEDODP 5. 6XUHVK 1 9LMD\DNXPDU $Q $SSOLFDWLRQ RI 3DUWLFOH 6ZDUP 2SWLPL]DWLRQ $OJRULWKP WR 3HUPXWDWLRQ )ORZVKRS 6FKHGXOLQJ 3UREOHPV WR 0LQLPL]H 0DNHVSDQ 7RWDO )ORZWLPH DQG &RPSOHWLRQ 7LPH 9DULDQFH,Q3URFHHGLQJV RIWKH,(((,QWHUQDWLRQDO&RQIHUHQFH RQ $XWRPDWLRQ6FLHQFHDQG(QJLQHHULQJ&$6(  6KDQJKDL &KLQDSS,6%1

2007 IEEE Congress on Evolutionary Computation (CEC 2007)