hybridization of ant colony optimization strategies in tabu search for solving job shop scheduling...
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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Mpmcdmedh kodcoh mq clcnr/nr/qix/hax/qv+dcrq/mrz
Coqhuomqckomd Lkxuomd k` Co`kunmqcko moa Nmomfhnhoq Rbchobhr
5: '5::3#$ =62.=73
Gseucac|mqcko k` Moq Bkdkos Kzqcnc|mqcko
Rqumqhfchr co Qmex Rhmubg `ku Rkdpcof Lke
Rgkz Rbghaxdcof Zukedhnr
P/ Z/ Hrvmumnxuqgs M/ Qmncdmumrc
Ahzmuqnhoq k` Bknzxqhu Mzzdcbmqckor Ahzmuqnhoq k` Bknzxqhu Mzzdcbmqckor
Ikofx Hofcohhucof Bkddhfh Ikofx Hofcohhucof Bkddhfh
Coacm Coacm
Merqumbq
Qgh zucnh bkoqucexqku qk qgh ahphdkznhoq k` qgh bknzhqcqcph nmuihq cr qgh nmox`mbqxucof
coaxrqus vgcbg uh}xcuhr m fkka rbghaxdh/ Rbghaxdcof cr qgh mddkbmqcko k` uhrkxubhr qk mbqcpcqchr
kphu qcnh/ Rbghaxdcof cr bkorcahuha qk eh m nmlku qmri akoh qk cnzukph qgh rgkz.stkku
zukaxbqcpcqs/ Qgh lke rgkz zukedhn cr xoahu qgcr bmqhfkus moa cr bknecomqkucmd co omqxuh/
Uhrhmubg ko kzqcnc|mqcko k` qgh lke rgkz zukedhn cr koh k` qgh nkrq rcfocbmoq moa zukncrcof
muhmr k` kzqcnc|mqcko/ Qgcr zmzhu zuhrhoqr mo mzzdcbmqcko k` qgh fdkemd kzqcnc|mqcko qhbgoc}xh
bmddha qmex rhmubg qgmq cr bknecoha vcqg moq bkdkos kzqcnc|mqcko qhbgoc}xh qk rkdph qgh lke
rgkz rbghaxdcof zukedhnr/ Qgh ohcfgekugkkar muh rhdhbqha emrha ko qgh rqumqhfchr co qgh moq
bkdkos kzqcnc|mqcko vcqg ohv asomncb qmex dhofqg rqumqhfs co qgh qmex rhmubg/ Qgh corzcucofrkxubh k` qgh moq bkdkos kzqcnc|mqcko cr zghuknkoh qumcd qgmq gmr nkuh costxhobh co rhdhbqcof
qgh mzzukzucmqh ohcfgekur qk cnzukph qgh rkdxqcko/ Qgh zhu`kunmobh k` qgh mdfkucqgn cr
qhrqha xrcof vhdd iokvo ehobgnmui zukedhnr moa mdrk bknzmuha vcqg kqghu mdfkucqgnr co
qgh dcqhumqxuh/
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Rgkz Rbghaxdcof$ Nmihrzmo/
=/ Coqukaxbqcko
Qmex Rhmubg 'QR# cr m nhqm.ghxucrqcb mzzukmbg xrha qk rkdph bknecomqkucmd kzqcnc|m.
qcko zukedhnr moa vmr urq ahrbuceha co =370 Y= / QR zukpcahr rkdxqckor phus bdkrh qkkzqcnmdcqs moa cr xrha qk qmbidh qgh acflbxdq zukedhnr/ Qghrh rxbbhrrhr gmph nmah QR
hwquhnhds zkzxdmu mnkof qgkrh coqhuhrqha co oacof fkka rkdxqckor qk qgh dmufh bknec.
omqkucmd zukedhnr hobkxoqhuha co nmos zumbqcbmd rhqqcofr/ QR cr emrha ko Dkbmd Rhmubg
'DR# cnzukphnhoq qhbgoc}xhr/ DR bmo e h ukxfgds rxnnmuc|ha mr mo cqhumqcph rhmubg
Uhbhcpha Nms 5::69 Uhpcrha Okphnehu 5::69 Mbbhzqha Mzucd 5::7/
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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=61 Coqhuomqckomd Lkxuomd k` Co`kunmqcko moa Nmomfhnhoq Rbchobhr$ Pkd/ 5:$ Ok/ 5$ Lxoh$ 5::3
zukbhaxuh qgmq$ rqmuqcof `ukn mo cocqcmd `hmrcedh rkdxqcko$ zukfuhrrcphds cnzukphr cq es
mzzdscof m rhuchr k` dkbmd nkacbmqckor 'ku nkphr#/ Co DR$ qgh }xmdcqs k` qgh rkdxqcko
keqmcoha moa qgh bknzxqcof qcnh muh xrxmdds gcfgds ahzhoahoq xzko qgh ucbgohrr k`
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Bkdkos Kzqcnc|mqcko 'MBK# mdfkucqgn cr m acrqucexqha mdfkucqgn xrha qk rkdph OZ.gmuabknecomqkucmd kzqcnc|mqcko zukedhnr/ Qgh MBK xrhr m zkzxdmqcko k` bk.kzhumqcof moqr
mdrk iokvo mr mfhoqr/ Qgh bkkzhumqcko zghoknhoko mnkof qgh moqr cr bmddha `kumfcof
moa uhbuxcqcof ehgmpcku Y5$ 2^/ Qgcr ahrbucehr gkv qgh moqr hwzdkuh qgh vkuda co rhmubg
k` `kka rkxubhr$ qgho oa qghcu vms embi qk qgh ohrq moa coacbmqh qgh `kka rkxubh qk qgh
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cr fcpho/ Co Rhbqcko 1$ QR moa MBK nhqgkar muh ahrbuceha/ Co Rhbqcko 8$ cnzdhnhoqmqcko
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cr qgh qkqmd oxnehu k` lker$ n cr qgh qkqmd oxnehu k` nmbgcohr$ F cr qgh qhbgokdkfcbmd
nmqucw ahokqcof qgh zukbhrrcof kuahu k` nmbgcohr `ku achuhoq lker/ Qgh nmqucw F bmo
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nmihrzmo uhzuhrhoqcof qgh bknzdhqcko qcnh k` qgh dmrq kzhumqcko co qgh lke rgkz/ Hmbg
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nmbgcoh `ku m fcpho qcnh/ M rbghaxdh cr mo mddkbmqcko k` qgh kzhumqckor qk qcnh coqhupmdr
ko qgh nmbgcohr/ Qgh zukbhrrcof k` mo kzhumqcko c ko m nmbgcoh l cr ahokqha es xclmoa vh bmo `kun m uhdmqcko xcz xc} uhzuhrhoqcof xc} cr acuhbqds cnnhacmqh qk xcz/ Dhq
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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Gseucac|mqcko k` Moq Bkdkos Kzqcnc|mqcko Rqumqhfchr co Qmex Rhmubg =68
Qmedh =/ Zukbhrrcof qcnhr moa kzhumqcko rh}xhobh `ku m 1 2 corqmobh/
Lke Zukbhrrcof Rh}xhobh
L= '=$ 5# '5$ 2# '2$ 1#
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moa o ) = muh qgh axnns okahr uhzuhrhoqcof rqmuq moa ocrg kzhumqckor uhrzhbqcphds/ Cq
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@cfxuh =/ Acrlxobqcph fumzg uhzuhrhoqmqcko `ku 1 2 zukedhn co Qmedh =/
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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=60 Coqhuomqckomd Lkxuomd k` Co`kunmqcko moa Nmomfhnhoq Rbchobhr$ Pkd/ 5:$ Ok/ 5$ Lxoh$ 5::3
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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Gseucac|mqcko k` Moq Bkdkos Kzqcnc|mqcko Rqumqhfchr co Qmex Rhmubg =66
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k` qgh dcrq cr qkk rnmdd$ bsbdcof bmo okq eh zuhphoqha moa dkof rc|h qmex buhmqhr nmos
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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=67 Coqhuomqckomd Lkxuomd k` Co`kunmqcko moa Nmomfhnhoq Rbchobhr$ Pkd/ 5:$ Ok/ 5$ Lxoh$ 5::3
uhrqucbqckor rk mr qk cobuhmrh qgh nhmo pmdxh k` qgh pcrcqha rkdxqckor/ Mo hhbqcph vms k`
uhnkpcof qgcr acflbxdqs cr qk xrh m qmex dcrq vcqg pmucmedh rc|h mbbkuacof qk qgh bxuuhoq
cqhumqcko oxnehu/ Qgh dhofqg k` qgh qmex dcrq cr cocqcmdds mrrcfoha mbbkuacof qk qgh rc|h
k` qgh zukedhn moa cq vcdd eh ahbuhmrha moa cobuhmrha axucof qgh bkorquxbqcko k` qgh
rkdxqcko rk mr qk mbgchph ehqqhu hwzdkumqcko k` qgh rhmubg rzmbh/
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qcnhr qkk zkvhu`xd qgmq qghs nms zukgcecq mqqumbqcph nkphr$ hpho vgho qghuh cr ok amofhu
k` bsbdcof$ ku qghs nms dhma qk mo kphumdd rqmfomqcko k` qgh rhmubgcof zukbhrr/ Cq cr qgxr
ohbhrrmus qk xrh mdfkucqgncb ahpcbhr qgmq vcdd mddkv koh qk bmobhd qgh qmexr/ Qghrh muh
bmddha mrzcumqcko bucqhucko/ Qgh rcnzdhrq moa nkrq bknnkods xrha mrzcumqcko bucqhucko
bkorcrqr co mddkvcof m nkph$ hpho c` cq cr co qmex$ c` cq uhrxdqr co m rkdxqcko vcqg mo kelhbqcph
pmdxh ehqqhu qgmo qgmq k` qgh bxuuhoq ehrq.iokvo rkdxqcko/ Co qghkus$ qgh rhmubg bkxda
fk ko `kuhphu$ xodhrr qgh kzqcnmd pmdxh k` qgh zukedhn mq gmoa cr iokvo eh`kuhgmoa/ Co
zumbqcbh$ kepckxrds$ qgh rhmubg gmr qk eh rqkzzha mq rknh zkcoq/ Qgh nkrq bknnkods
xrha rqkzzcof bucqhucko co QR muh hcqghu 'c# m wha oxnehu k` cqhumqckor ku 'cc# m`qhu rknhoxnehu k` cqhumqckor vcqgkxq mo cnzukphnhoq co qgh kelhbqcph `xobqcko pmdxh ku 'ccc# vgho
qgh kelhbqcph `xobqcko uhmbghr m zuh.rzhbcha qguhrgkda pmdxh/
1/5/ Moq bkdkos kzqcnc|mqcko
@ku rkdpcof qgh bknecomqkucmd kzqcnc|mqcko zukedhnr$ qgh MBK cr xrha `ku ahrcfocof
nhqmghxucrqcb mdfkucqgnr/ Qgh urq mdfkucqgn vmr zuhrhoqha co =33= Y=5$ =2^ moa rcobh
qgho$ achuhoq nhqgkar k` qgh emrcb zucobczdh gmph ehho uhzkuqha co qgh uhrhmubg hda/ /
Co momdkfs qk qgh eckdkfcbmd hwmnzdh$ MBK cr emrha ko qgh coacuhbq bknnxocbmqcko k` m
bkdkos k` rcnzdh mfhoqr$ bmddha 'muqcbcmd# moqr$ nhacmqha es 'muqcbcmd# zghuknkoh qumcdr/
Qgh corzcucof rkxubh k` MBK cr qgh zghuknkoh qumcd dmscof moa `kddkvcof ehgmpcku k`qgh uhmd moqr/ Rknh mnkxoq k` qgh zghuknkoh vcdd eh ahzkrcqha es qgh moqr ko qghcu
zmqgr/ Qgh zukemecdcqs `ku bgkkrcof qgh ohwq zmqg es mo moq vcdd eh acuhbqds zukzkuqckomd
qk qgh mnkxoq k` zghuknkoh ko qgmq zmqg/
Rqmqh qumorcqcko uxdh< Qgh moq mdfkucqgn bmo eh uhzuhrhoqha coqk m fumzg/ Rqmuqcof
`ukn qgh cocqcmd okah$ hphus moq bgkkrhr qgh ohwq okah co cqr zmqg mbbkuacof qk qgh rqmqh
qumorcqcko uxdh es xrcof zukemecdcqs k` qumorcqcko/ Dhq R eh qgh rhq k` okahr mq m ahbcrcko
zkcoq c/ Qgh qumorcqcko zukemecdcqs `ku bgkkrcof qgh hafh `ukn qgh okah c qk qgh okah l
es mo moq cr bmdbxdmqha mr fcpho co qgh h}xmqcko '5#/
Z'c$ l# >
''c$ l##
''l##
lR
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: kqghuvcrh
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'c$ l# cr qgh }xmoqcqs k` qgh zghuknkoh ko qgh hafh ehqvhho qgh okah c moa qgh okah
l/ 'l# cr qgh cophurh k` qgh kzhumqcko qcnh k` qgh okah l/ moa qxoh qgh uhdmqcph
cnzkuqmobh co zukemecdcqs k` qgh mnkxoq k` qgh zghuknkoh phurxr qgh kzhumqcko qcnh/
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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Gseucac|mqcko k` Moq Bkdkos Kzqcnc|mqcko Rqumqhfchr co Qmex Rhmubg =63
Fdkemd xzamqcof uxdh< Fdkemd xzamqcof cr coqhoaha qk uhvmua hafhr ehdkofcof qkqgh rgkuqhrq zmqg/ Kobh mdd qgh moqr gmph muucpha mq qghcu ahrqcomqcko$ qgh mnkxoq k`zghuknkoh ko qgh hafh 'c$ l# ehdkofcof qk qgh rgkuqhrq zmqg mq m qcnh q cr nkacha esmzzdscof qgh fdkemd xzamqcof uxdh fcpho co qgh h}xmqcko '2#/
'c$ l#q > 'c$ l#q= ) '= # }+Di/ '2#
cr qgh bkhflbchoq uhzuhrhoqcof zghuknkoh hpmzkumqcko 'okqh< : 4 4 =#/ } cr m pmdxhbgkrho umoaknds vcqg xoc`kun zukemecdcqs co Y:$ =^/ Di cr qgh ncocnxn qkxu dhofqg qump.hdha es mo moq mnkof mdd qgh moqr co qgh cqhumqcko/ Ghobh qgh mnkxoq k` qgh zghuknkohahzkrcqha ko hmbg hafh cr cophurhds zukzkuqckomd qk qgh dhofqg k` qgh zmqg rk mr qk homedhqgh rgkuqhu zmqg qk fhq gcfghu mnkxoq k` qgh zghuknkoh ahzkrcqha ko qgh hafhr axucofqgh `kuqgbkncof cqhumqckor/
Dkbmd xzamqcof uxdh< Qgh hpmzkumqcko zgmrh cr rxerqcqxqha es m dkbmd xzamqcofuxdh k` qgh zghuknkoh mzzdcha axucof qgh bkorquxbqcko k` qgh rkdxqcko/ Co hmbg qcnh q$ qghmoq nkphr `ukn qgh okah c qk qgh ohwq okah l co qgh fumzg A$ qgh zghuknkoh mrrkbcmqha
qk qgh hafh cr nkacha mbbkuacof qk qgh h}xmqcko '1#/
'c$ l#q > '= # 'c$ l#q= ) :/ '1#
: cr qgh cocqcmd zghuknkoh pmdxh moa cr ahoha mr : > o+D$ vghuh D cr qgh qkxu dhofqgzukaxbha es qgh hwhbxqcko k` urq cqhumqcko vcqgkxq zghuknkoh co`kunmqcko/ Qgh dkbmdxzamqcof uxdh cr h}xcpmdhoq qk qgh qumcd hpmzkumqcko co qgh uhmd moqr/
8/ Qmex Rhmubg vcqg Moq Bkdkos Kzqcnc|mqcko Rqumqhfchr
8/=/ Asomncb qmex dhofqg
Qgh qmex dhofqg cr bgmofha axucof qgh rkdxqcko bkorquxbqcko zgmrh qk cobuhmrh qgh
hwzdkumqcko k` qgh rhmubg rzmbh moa qgcr rqumqhfs bmddha asomncb qmex dhofqg rqumqhfscr mzzdcha co qgh zukzkrha mdfkucqgn/ Qgh zukbhaxuh `ku qgh mdfkucqgn qk oa qgh qmexdhofqg asomncbmdds mbbkuacof qk qgh cqhumqcko oxnehu cr fcpho ehdkv/
Zukbhaxuh < AQmex' #Cozxqr < BS BOK$ KDAD$ n$ o$ umofh$ a=$ a5$u$x9 Kxqzxq< Q DEhfco
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x > x ) =HoaC`
HoaVgcdhHoaC`
Hoa
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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=7: Coqhuomqckomd Lkxuomd k` Co`kunmqcko moa Nmomfhnhoq Rbchobhr$ Pkd/ 5:$ Ok/ 5$ Lxoh$ 5::3
@cfxuh 5/ Cddxrqumqcko k` qgh asomncb qmex dhofqg/
Qgh bxuuhoq cqhumqcko oxnehu 'BSBOK#$ umofh$ a=$ a5$ u moa x muh fcpho mr cozxqr/Qgh umofh$ a= moa a5 muh bmdbxdmqha mr fcpho co qgh h}xmqckor '8#$ '0# moa '6# uhrzhbqcphds/
Qgh coqhfhu zmuqr k` qghrh pmucmedhr muh xrha `ku zukbhrrcof/ u moa x muh qgh bkoqukdpmucmedhr xrha qk oa qgh zkrcqcko k` qgh bxuuhoq cqhumqcko vcqgco qgh umofh coqhupmd/
umofh > NMWBS BOK+'5n# '8#
a= > umofh+'n ) o# '0#
a5 > 'a= ) 5n#+'n ) o# '6#
Qgh oxnehu k` lker o moa qgh oxnehu k` nmbgcohr n muh mdrk fcpho mr cozxqr/ Qghpmdxh k` qgh qmex dhofqg 'Q D# cr n ) o `ku qgh urq umofh k` cqhumqckor/ @ku qgh hpho
moa kaa umofh coqhupmdr$ Q D pmdxh cr cobuhmrha moa ahbuhmrha uhrzhbqcphds es qgh pmdxhk` a5 vcqg rxerh}xhoq coqhupmd pmdxh k` a=/ Qgcr rqumqhfs cnzukphr qgh zhu`kunmobh k`qgh qmex rhmubg axucof qgh bkorquxbqcko k` qgh rkdxqcko/ Qgh bgmofh k` qgh qmex dhofqgpmdxh cr cddxrqumqha co @cfxuh 5/
8/5/ Bkorquxbqcof rkdxqcko
Qgh cocqcmd rkdxqcko Rcr bkorquxbqha xrcof qgh rgkuqhrq zukbhrrcof qcnh 'RZQ# zuckucqsuxdh/ Qgh cocqcmd rkdxqcko cr cnzukpha es qgh zukzkrha nhqgka vcqg ohv ohcfgekugkka
rqumqhfs xrcof qgh MBK nhqgka moa qgh asomncb qmex dhofqg rqumqhfs fcpho co Rhbqcko8/=/ Dhq nmw moa nco eh nmwcnxn moa ncocnxn zghuknkoh dhphd ehqvhho qgh qvkkzhumqckor k` m ohcfgeku/ Dhq `'R# eh qgh nmihrzmo pmdxh `ku qgh cocqcmd rkdxqcko R/Qgh pmdxhr k` nmw moa nco muh bmdbxdmqha mr co qgh h}xmqckor '7# moa '3# uhrzhbqcphds
moa qghrh pmdxhr muh xrha qk bkoqukd qgh dhphd k` qgh zghuknkoh pmdxh ehqvhho qgh qvkkzhumqckor co qgh ohcfgeku/
nmw > `'R#+=: '7#
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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Gseucac|mqcko k` Moq Bkdkos Kzqcnc|mqcko Rqumqhfchr co Qmex Rhmubg =7=
nco > nmw+5: '3#
Mdd qgh hafhr mnkof qgh okahr co qgh fumzg A muh cocqcmdds mrrcfoha es nco pmdxh/
Dhq O'R# eh qgh rhq k` ohcfgekur vgcbg muh okq co qgh qmex `ku m zmuqcbxdmu cqhumqcko/
Qgh nkacha rqmqh qumorcqcko uxdh cr fcpho co qgh h}xmqcko '=:#/
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: kqghuvcrh
'=:#
Mr mduhmas okqha co qgh h}xmqcko '5#$ 'c$ l# cr qgh zghuknkoh dhphd ehqvhho qgh
kzhumqckor c moa l/ 'c# moa 'l# muh qgh qcnh k` qgh kzhumqckor c moa l uhrzhbqcphds/
moa uhzuhrhoq qgh uhdmqcph cnzkuqmoq k` qgh zghuknkoh moa qgh hwzuhrrcko pmdxh
'c#+'l#/ Ghobh qgh zukemecdcqs k` bgmofh k` qgh kzhumqckor k` qgh ohcfgeku 'c$ l# cr
acuhbqds zukzkuqckomd qk qgh qcnh k` qgh urq kzhumqcko c moa cophurhds zukzkuqckomd qk
qgh qcnh k` qgh rhbkoa kzhumqcko l co qgmq ohcfgeku/ C` 'c# cr fuhmqhu qgmo 'l#$ qghuh cr
nkuh bgmobh qk bgmofh qgh kzhumqckor k` qgcr ohcfgeku moa qgcr nhqgka }xcbids cnzukphr
qgh }xmdcqs k` qgh rkdxqcko$ ehbmxrh qgh zukemecdcqs cr nkuh `ku zucku zukbhrrcof k` rnmddhu
kzhumqcko qgmo qgh dmufhu kzhumqcko co m nmbgcoh/ Co mo cqhumqcko$ qgh zghuknkoh pmdxhr
ehqvhho qgh kzhumqckor k` mdd ohcfgekur$ vgcbg muh okq co qgh qmex$ muh xzamqha es qgh
ohv moa nkacha dkbmd zghuknkoh xzamqcof uxdh mr fcpho co qgh h}xmqcko '==# moa qgmq
`ku qgh ohcfgeku bxuuhoqds maaha qk qgh qmex cr mfmco xzamqha es qgh fdkemd zghuknkoh
xzamqcof uxdh mr fcpho co qgh h}xmqcko '=5#/
'c$ l#q > '= # 'c$ l#q= ) }+`'R# '==#
'c$ l#q > 'c$ l#q= ) '= # }+`'R
# '=5#
Mr mduhmas okqha co qgh h}xmqcko '2#$ } cr m pmdxh bgkrho umoaknds vcqg xoc`kun
zukemecdcqs ehqvhho : moa = moa co nkrq k` qgh bmrhr$ } cr rhq qk =/ `'R# cr qgh nmihrzmo
pmdxh bmdbxdmqha es qgh mzzdcbmqcko k` qgh ohcfgeku 'c$ l# qk qgh bxuuhoq rkdxqcko R qk
zukaxbh qgh ohcfgekugkka rkdxqcko R/ Qgh zghuknkoh pmdxh `ku mos ohcfgeku cr okq
mddkvha qk hwbhha qgh pmdxh k` nmw moa c` qgcr pmdxh hwbhhar nmw$ qgh mphumfh k` nco moa
nmw cr mrrcfoha qk qgh zghuknkoh rk mr qk cobuhmrh qgh hwzdkumqcko k` qgh rhmubg rzmbh/
Co zxuh QR$ qgh zmrq bkoqcoxkxr zhu`kunmobh k` qgh rkdxqcko `ku m ohcfgeku `ukn qgh
rqmuq k` qgh rkdxqcko bkorquxbqcko cr okq mpmcdmedh/ Exq co GMBKRQR$ qgcr zhu`kunmobh
cr mpmcdmedh es nhmor k` qgh zghuknkoh dhphd ehqvhho qgh kzhumqckor k` qgh ohcfgeku/
Qgh zrhxak bkah `ku qgh zukzkrha mdfkucqgn BkorquxbqRkdxqcko' #$ vgcbg xrhr qgh MBKrqumqhfs moa qgh ohv qmex asomncb qmex dhofqg rqumqhfs qk rhdhbq qgh ehrq ohcfgeku$ cr
fcpho/ Qgh achuhoq zmumnhqhur muh fcpho `ku qgh mdfkucqgn/ NMWBSBOK uhzuhrhoqr
qgh qkqmd oxnehu k` cqhumqckor/ NMWQ uhzuhrhoqr qgh nmwcnxn oxnehu k` qcnhr `ku
vgcbg qgh cnzukphnhoq cr okq nmah axucof qgh bkorquxbqcko k` qgh rkdxqcko/ Qgh dhofqg
k` qgh qmex dcrq cr asomncbmdds bgmofha es xrcof qgh zukbhaxuh AQmex' # mbbkuacof qk
qgh bxuuhoq cqhumqcko oxnehu/ C` qgh rhdhbqha ohcfgeku rc ': 4 c 4 i# cr okq co qgh qmex
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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=75 Coqhuomqckomd Lkxuomd k` Co`kunmqcko moa Nmomfhnhoq Rbchobhr$ Pkd/ 5:$ Ok/ 5$ Lxoh$ 5::3
ku qgh mrzcumqcko bucqhucko cr nhq$ qgh ohcfgeku rc cr maaha qk qgh qmex/ Qgh mrzcumqcko
bucqhucko cr xrha qk bghbi qgh bkoacqcko `'R# 4 `'R#/ `'R# cr qgh nmihrzmo k` qgh
ohcfgekugkka rkdxqcko R zukaxbha es qgh mzzdcbmqcko k` qgh ohcfgeku rc vgcbg cr mduhmas
co qgh qmex moa `'R# cr qgh bxuuhoq ehrq iokvo rkdxqcko/ C` qgh ohcfgeku bmo okq eh
maaha qk qgh qmex$ qgh qmex dcrq cr bdhmuha moa qgh qmex uhrqucbqckor muh uhnkpha/ Qgcrzukbhrr cr uhzhmqha xoqcd m qhuncomqcko bucqhucko cr nhq/ Qgh qhuncomqcko bucqhucko cr
hcqghu uhmbgcof qgh nmwcnxn cqhumqckor ku ok cnzukphnhoqr k` qgh bkorquxbqha rkdxqcko
`ku qgh NMWQ oxnehu k` cqhumqckor/
Mdfkucqgn< BkorquxbqRkdxqcko' #
Rqhz =< ++Cocqcmdc|mqcko ++
B S B O K > :$ Q Z > :$ Q > :$ u > =$ x > =$ Cocqcmdc|h NMWBSBOK$ NMWQ
umofh > NMWBS BOK+'5n#$ a= > umofh+'n)o#$ a5 > 'a= ) 5n#+'n)o#
Fhohumqh cocqcmd rkdxqcko R$ Rhq nmihrzmo `ku R qk `'R#$ nmw > `'R#+=::$
nco > nmw+5:/Mrrcfo nco qk mdd qgh hafhr co qgh fumzg A/
Rqhz 5< ++@coacof qmex dhofqg `ku qgh bxuuhoq cqhumqcko++
Bmdd AQmex' # ++ Qk bmdbxdmqh qgh qmex dhofqg pmdxh
C` Q Z ? Q D Qgho
Q Z > :
HoaC`
Rqhz 2< ++Bghbicof qgh mrzcumqcko bucqhucko `ku qgh ohcfgekur k` qgh bxuuhoq kdxqcko++
@coa dcrq k` ohcfgekur O'R# > yr=$ r5$ / / / $ ri~ `ku bxuuhoq rkdxqcko vghuh r= >
'rqmuqY=^$ hoaY=^#$ r5 > 'rqmuqY5^$ hoaY5^#$ / / /$ ri > 'rqmuqYi^$ hoaYi^#
C` mrzcumqcko bucqhucko cr nhq `ku m ohcfgeku c
Maa cqg ohcfgeku qk qgh qmex co qgh zkrcqcko Q Z$ Fk qk Rqhz 6
HoaC`
Rqhz 1< ++@coacof ohcfgekur vgcbg muh okq co qmex++
l > :
@ku c > : qk i ak
C` 'rqmuqYc^$ hoaYc^# okq co qmex
Maa 'rqmuqYc^$ hoaYc^# qk O'R#$ l > l ) =
HoaC`
Hoa@ku
C` l > : Qgho
l > i$ Bdhmu qmexdcrqHoaC`
Rqhz 8< ++Xzamqcof zghuknkoh pmdxh ehqvhho qgh kzhumqckor co qgh ohcfgekur ehdkofcof
qk O'R#++
@ku c > : qk l ak
Mzzds 'rqmuqYc^$ hoaYc^# qk qgh rkdxqcko R qk fhohumqh R
'rqmuqYc^$hoaYc^# > '= #/'rqmuqYc^$hoaYc^# ) /nco+`'R#
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
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Gseucac|mqcko k` Moq Bkdkos Kzqcnc|mqcko Rqumqhfchr co Qmex Rhmubg =72
++Dkbmd zghuknkoh xzamqcof
C` 'rqmuqYc^$hoaYc^# ? nmw Qgho
'rqmuqYc^$hoaYc^# > 'nmw ) nco#+5
HoaC`
Hoa@ku
Rqhz 0< ++Maacof m ohcfgeku qk qgh qmex xrcof qgh rqmqh qumorcqcko uxdh k` MBK++
Bgkkrh m ohcfgeku 'rqmuqYc^$hoaYc^# O'R# vcqg Nmoqh Bmudk ZukemecdcqsMaa 'rqmuqYc^$hoaYc^# qk qgh qmex co zkrcqcko Q Z moa mzzds cq ko Rqk fhohumqh R
'rqmuqYc^$hoaYc^# > 'rqmuqYc^$hoaYc^# ) '= #/}+`'R#++ Fdkemd zghuknkoh xzamqcof
Rqhz 6< ++@coa qgh bxuuhoq rkdxqcko++
Mzzds ohcfgeku `ukn qgh qmex co qgh zkrcqcko Q Z moa oa qgh bxuuhoq rkdxqcko R
C` `'R# 4 `'R# Qgho
R > R$ `'R# > `'R#$ Q > :
HoaC`B S B O K > B S B O K ) =$ Q > Q ) =$ Q Z > Q Z ) =
C` B S B O K ( umofh > : Qgho
u > u ) =$ x > =$ a5 > a5HoaC`
Rqhz 7< ++Qhuncomqcko bucqhucko++
C` BS BO K ? NMWBS BO K ku Q ? NMWQ Qgho
Fk qk Rqhz 3
Hdrh
Fk qk Rqhz 5
HoaC`
Rqhz 3< ++Kxqzxq qgh rkdxqcko++
Zucoq R moa `'R#$ Rqkz
0/ Hwzhucnhoqmd Uhrxdqr moa Acrbxrrcko
Co qgcr rhbqcko bknzxqmqckomd uhrxdqr muh fcpho `ku vhdd iokvo LRRZ corqmobhr vcqg
qgh cocqcmd qmex dhofqg mr n)o$ mr :/3$ mr :/6 moa mr :/::=/ Qgh zukzkrha GMBKRQR
cr bkaha co B)) zukfumnncof dmofxmfh ko Dcoxw zdmq`kun vcqg MNA Mqgdko 50::)$
5FG| moa 8=5 UMN/ Qmedh 5 rgkvr qgmq qgh kzqcnmd pmdxh keqmcoha `ukn GMBKRQR
muh bknzmuha vcqg qgh ehrq rkdxqckor zukpcaha es rknh mxqgkur ko achuhoq zukedhnr
rzhbcha co qgh bkdxno =/ Qgh Bkdxno 5 rgkvr qgh ehrq rkdxqcko `kxoa `ku hmbg zukedhn/Qgh Bkdxnor 2$ 1 moa 8 rzhbc`s qgh uhrxdqr `ukn QRRE es @huacomoak Zh||hddm hq md/
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
12/17
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
13/17
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8/3/2019 Hybridization of Ant Colony Optimization Strategies in Tabu Search for Solving Job Shop Scheduling Problems
14/17
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