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Original Article
109101 "X '2 |xQ=tW '30 1 |xQwO
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|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
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QO |O}rm pt=wa R= |m} O}rwD |R}Qxt=vQ@ p=Ut QO C=}rta |r=wD w |Ov@u=tR |xt=vQ@
'C=a}=[ p}rkD 'x}=tQU CW=@v= R= |Q}owrH Ea=@ xm CU= |O}rwD |=yu=tR=U C}kiwt
x@ `kwtx@ |} woMU=B w =yu; |xv}y@ OQ@Q=m w Cq;u}W=t |Q=m}@ hPL =} Vy=m
u; Q@ ZQi |Ov@u=tR w |R}Qxt=vQ@ OQ=Ov=DU= |=yVwQ QO "OwW|t u=} QDWt |=yVQ=iU
`wvD p}rOx@ ZQi u}= &ODi=|t j=iD= u}at w |a]k \}=QW l} QO xt=vQ@ |=QH= xm CU=
u}vJ QO "CU}v |rta w CUQO ZQi 'u; Q@ sm =L C}a]k sOa \}=QW w R=}v OQwt `@=vt
Q=OQwNQ@ |}q=@ C}ty= R= |R=Uxv}y@ |=Hx@ pL |=yVwQ |Q=wDU= |UQQ@ |]}=QW
CU= |Dr=L QO |O=OUv= |y=oQ=m |R}Qxt=vQ@ |xrUt pL j}kLD u}= |rY= hOy "CU=
pL |=Q@ |Q=mD@==Qi VwQ CWy j}kLD u}= QO "CU= Q}PB Q}}eD =yQ=m VR=OQB u=tR xm
OQmrta |@=}RQ= |=Q@ 1 =D@ |Q=wDU= Q=}at R= "CU= xDiQo Q=Qk xO=iDU= OQwt Qwm Pt |xrUt
|xOvyOu=Wv =y|UQQ@ |xH}Dv "CU= xOW xO=iDU= u}at=v \}=QW QO |O=yvW}B |=yVwQ
"CU=yVwQ Q}=U x@ C@Uv u=tRtyQ}e |wHwCUH =@ l}DvS VwQ QDq=@ |Q=wDU=
maleagha@ kntu.ac.ir
mohammad 1504@kntu.ac.ir
rbashirzadeh@kntu.ac.ir
shafaei@kntu.ac.ir
|=ysD}Qwor= 'Q=wDU= |R}Qxt=vQ@ '|O=OUv= |y=oQ=m |R}Qxt=vQ@ %|O}rm u=oS=w
"|iO=YD Cr=L QO |R}Qxt=vQ@ '|Q=mD@==Qi
t t "1
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&O}; p}=v |QDQ=wDU= MU=B x@ C}a]k sOa \}=QW QO Ov=wD@ xm CU= ?wr]t |WwQ p=Ut XwYNQO |O=}R C=k}kLD '|y=oQ=m O}rwD p=Ut OQ@Q=m |v=w=Qi x@ xHwD =@
|QDsm C}U=UL R= C}a]k sOa \}=QW x@ C@Uv VwQ |HwQN xm =vat u}O@ p}rOx@ |O}rwD C=Hv=NQ=m R= |Q=}U@ QO 'pta QO "CU= xOW s=Hv= |y=oQ=m O}rwD
p=Ft |=Q@ "CU= C}a]k sOa Vy=m Q@ RmQtD 'swO OQm}wQ QO [3] "OW=@ Q=OQwNQ@ |v=}t |xQ}NP C}OwOLt O}=@ C=a]k |}=}t}W w |m} R}i C}i}m Ci= R= |Q}owrH
u}W=t |@=QN R= |W=v C}a]k sOa Q}F-=D u=wD|t xv=Q}oW}B C=Q}taD QFw-t |=QH= =@
u}W=t wO u}@ C=a]k Q=_Dv= u=tR =} u}W=t wO u}@ xOW xQ}NP Q=m O=OaD pmWx@ =Q
xDiQo Q_v QO C}a]k sOa w CU= Q_v Ot pw= OQm}wQ xr=kt u}= QO "O=O Vy=m =Q
u=} QH p=Ut XwYNQO xDiQo CQwY |=yQ=m |UQQ@ seQ|ra [1] "CiQo Q_v QO
"CU=yQ=m s=Hv= u=tR x@ \w@ Qt xOW |a]k ,qt=m =Q \}=QW xOW s=Hv= C=ar=]t |t=tD QO u}kkLt [2] '|O=OUv= |y=oQ=m
"CU= 2 xv=Q}oW}B |=yxt=vQ@ uDN=U |=Q@ |WwQ |xaUwD 'j}kLD u}= hOy
hrDNt `@=vt OwHw p}rOx@ ZQi u}= s}v=O|t xm u=vJ "Ov=xOQm ZQi u}at w
* ]}Lt C=i=QLv= Q@ x@re |=Q@ |i=m h=]av= R= O}=@ xt=vQ@ u}= Q=DWwv u}= QO 'Qw_vt u}tyx@ [3] "CU}v jO=Y \}=QW |t=tD QO C}a]k sOa O=H}=
Vy=m w \NQ@ |
u}= QO xOW |UQQ@ pOt R= hOy 'XN= Qw]x@ "OW=@ Q=OQwNQ@ C=i=QLv= u}= Q}F-=D
C}a]k sOa \}=QW QO |O=OUv= QiY |v=}t |xQ}NP =@ |y=oQ=m O}rwD |xrUt
3
"CU= C@=F Q=Okt l} R= C=}rta |xvt=O Qw@a sOa p=tDL= |R=Uxv}W}@ j}kLD
"CU= xDiQo Q=Qk xar=]t OQwt
u=} QH |xrUt u}OvJ |=Q@ Q=wDU= |xt=vQ@ l} PN= Qw_vtx@ |D=W}=tR; TBU |x=Q= 'pw= OQm}wQ QO %OQ=O OwHw |rm OQm}wQ wO =yC}a]k sOa =@ xr@=kt |=Q@
QO "CU= xOW s=Hv= nQR@ w \UwDt 'lJwm |=yxR=Ov= QO 4 |O=OUv= |y=oQ=m
ut[ w '?=NDv= p=Ut pL |=Q@ hrDNt |Q=mD@==Qi VwQ CWy OQmrta 'xt=O=
pwUt xOvU} wv "1392 4 1 VQ}PB '1392 2 9 x}LqY= '1391 7 15 Ci=}QO %M}Q=D
"CU= xOW xU}=kt R}v =yu; uOw@ Q=wDU= 'Qo}Om} =@ u=WOQmrta |xU}=kt
|Ov@u=tR QO xO=iDU= OQwt |=yVwQ |xRwL QO xDiQoCQwY C=ar=]t u}kkLt
[5w4] "Ov=xO=O Q=Qk |UQQ@ OQwt =Q C}a]k sOa Cr=L QO =yQ=m
Q}eDt \}=QW p}rOx@
QO |iO=YD w =} wB \}Lt QO |Q}os}tYD |=Q@ |y=oQ=m K]U |=yxt=vQ@ '|]}Lt
KqY= x@ O}=@ |y=o OvJ R= Qy p}rO u}tyx@ "Ow@ Ovy=wNv wo?=wH |vqw] COt
|R}Qxt=vQ@ |t=ovy xJ "1 %OwW|t KQ]t p=w-U wO =Hv}= QO "CN=OQB =yxt=vQ@
#OQ}o CQwY |R}Qxt=vQ@ xvwoJ "2 #OQ}o CQwY
x@ =Q sDU}U MU=B '|R}Qxt=vQ@ |=QH= u=tR XwYNQO p=w-U x@ |} woMU=B
'O@=} V}=Ri= |R}Qxt=vQ@ pL=Qt O=OaD xJQy "Ovm|t XNWt |]}Lt hrDNt p=Ut
|Q}os}tYD |=Q@ "O@=}|t V}=Ri= R}v sDU}U |xv} Ry xH}DvQO w sDU}U |} woMU=B
|R}Qxt=vQ@ 'xDUw}B |R}Qxt=vQ@ %OQ=O OwHw |irDNt |=yVwQ |R}Qxt=vQ@ OQwtQO
"|@}mQD |R}Qxt=vQ@ |=yVwQ w '5 |k=@]v= |R}Qxt=vQ@ '|}xQwO
OwQw =} 'u}W=t l} |@=QN Ovv=t syt C=k=iD= R= TB xDUw}B |R}Qxt=vQ@ VwQ QO
[6]
C@=F |=yxQwO QO xt=vQ@ |}xQwO |R}Qxt=vQ@ QO "OwW|t RwQ x@ xt=vQ@ syt Q=m l}
|=yxQwO uDiQo Q_v QO =@ |}xQwO |R}Qxt=vQ@ R= |}xvwtv QO "OwW|t RwQx@ Q}eDt w
|R}Qxt=vQ@ "OwW|t RwQ x@ u; R= |YNWt w C@=F OYQO `wkw R= TB xt=vQ@ [7] Q}eDt
xm OQ}o|t CQwY |t=ovy OOHt |R}Qxt=vQ@ 'u; QO xm CU= |Qo}O VwQ |k=@]v=
XNWt RQt l} R= '|ak=w Cr=L w xt=vQ@ R= |YNWt pt=a |=yCw=iD `wtHt
|R}Qxt=vQ@ |=yVwQ |UQQ@ QO "OW=@ QDW}@ xOWu}}aD V}B R= |xv=DU; OL R= =}
xDUw}B |R}Qxt=vQ@ w |}xQwO |R}Qxt=vQ@ R= ?mQt |R}Qxt=vQ@ VwQ l} 'R}v |@}mQD
[8] "OW x=Q= 6 QwLtxFO=L VwQ s=v x@ =Q C}a]k sOa Cr=L QO |R}Qxt=vQ@ |=yVwQ 'swO p=w-U x@ |} woMU=B |=Q@
[9] %Ov=xOQm |Ov@s}UkD xDUO Q=yJ QO
&7 |r=aiv= =} |Wvm=w ,qt=m |R}Qxt=vQ@ "1
&8 |r=aiv= |xv=} woV}B |R}Qxt=vQ@ "2
&xv=Q}oW}B ,qt=m |R}Qxt=vQ@ "3
"9 |r=aiv= |xv=Q}oW}B |R}Qxt=vQ@ "4
OW=@ Q}osWJ |oDiW; u=R}t xm OwW|t xO=iDU= |t=ovy CUNv |R}Qxt=vQ@ R=
QO "OvR=U umtt Q}e =Q xv=Q}oW}B |R}Qxt=vQ@ w OvwW XNWt Q}O Q=}U@ C=aq]= =}
'OwW|t xO=iDU= sDU}U Cr=L uDiQoQ_v QO =@ xOW RwQx@ C=aq]= R= 'VwQ u}=
u}v=wk =@ OL=w u; QO =ys}tYD 'OwW|tv xO=O sDU}U x@ |}xv=Q}oW}B |xt=vQ@ I}y
u}tyx@ "OQ}o|t Q=Qk =t TQDUO QO s=o x@ s=o C=aq]= w 'OwW|t xDiQo XNWt
"Ovt=v|t \NQ@ =} u}qv; |R}Qxt=vQ@ =Q |R}Qxt=vQ@ `wv u}= p}rO
Q_vQO uwO@ xv=} woV}B |xt=vQ@ l} =OD@= '|r=aiv= |xv=} woV}B VwQ QO
^iL |=Q@ |r=aiv= |xt=vQ@ l} R= TBU "OwW|t |R}Q|B |r=tDL= C=i=QLv= uDiQo
|R}Qxt=vQ@ `wv u}= [10] "OwW|t xO=iDU= xt=vQ@ u}= OQmrta Ow@y@ w xt=vQ@ |Q}PBu=mt=
OyO MQ h=QLv= xm |t=ovy =yvD w Ovm|tv ^=Lr ,=t}kDUt =Q xt=vQ@ QO C}a]k sOa
R=Q@= |=Q@ x=Q u} QDy@ |r=aiv= |R}Qxt=vQ@ Qo}O CQ=@ax@ "Ovm|t K}LYD =Q xt=vQ@
"O@=}|t =Q xO=O MQ h=QLv= x@ Vvm=w
|OQmrta |=yQ=}at s=Om R= xm OQ}o@ s}tYD O}=@ R}Qxt=vQ@ 'Oa@ |xrLQt QO
10 u=} QH QO u=tR 'C=}rta |xvt=O uwJty |DvU |=yQ=}at R= pta QO "Ovm xO=iDU=
|=yQ=}at CU=} wB w Q}eDt \}Lt xm |]}=QW QO =t= 'OwW|t xO=iDU= OQmQ}O =}
Qw_vt u}= |=Q@ "OQ=O OQ@Q=m C}a]k sOa Q@ x@re |=Q@ 12 |Q=O}=B w 11 |Q=wDU=
xt=vQ@ u}= '\}Lt QO OwHwt C=i=QLv= QF=Q@ &OwW|t s=Hv= x}rw= |R}Qxt=vQ@ l} =OD@=
'|]}Lt C=i=QLv= u=R}t x@ xDU@ "OwW ^iL u; |Q}PBu=mt= =D OQ=O KqY= x@ R=}v
102
"""|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
|Q=wDU= |=yQ=}at "OW=@ Cw=iDt x}rw= |xt=vQ@ =@ ,qt=m xt=vQ@ CU= umtt |DL
xv}tm xt=vQ@ QO =Q C=i=QLv= u}= Q}F-=D w OvQ=O Q=mwQU C=i=QLv= u}= =@ |Q=O}=B w
"Ovvm|t
w OW=@ xO=t; |r=tDL= \}=QW =@ xr@=kt QO Ov=wD@ xm CU= Q=wDU= |}xt=vQ@
|Q=wDU= xv=Q}oW}B |R}Qxt=vQ@ QO u}=Q@=v@ "OyOv CUO R= =Q OwN |OQmrta C}i}m
|R}Qxt=vQ@ |SD=QDU= R= xm |t=ovy 'C}a]k sOa =@ xr@=kt C}r@=k R= CU= CQ=@a
x=Q= xt=vQ@ |Q=wDU= |UQQ@ |=Q@ |irDNt |=yQ=}at u}kkLt "OwWv xO=iDU= OOHt
Cw=iD u=R}t =Q |Q=wDU= u=v; "OR=U|t xv}tm =Q |}=Q=m Q=}at Tv=}Q=w xm [11] Ov=xO=O
'u=v; Q_v R= |DQ=@ax@ w Ov=xOQm |iQat |ak=w w xOW |R}Qxt=vQ@ hOy `@=wD Q=Okt
|v=OvJ Q}}eD '|]}Lt C=i=QLv= =@ xyH=wt QO u; OQmrta xm CU= Q=wDU= |}xt=vQ@
|=yu=tR Q}}eD uDiQov Q_vQO =@ [12] 'C=ar=]t u}= R= |}xvwtv QO "Ov=t@ xv}y@ w Ovmv
=yQ=m VR=OQB u=tR QO xv}W}@ Q}}eD TBU 'OwW|t O=H}= xv}y@ |xt=vQ@ VR=OQB
Q}}eD u}= Q=Okt Qwm Pt |xar=]t QO "Ov=t@ xv}y@ u=vJty xt=vQ@ u}= xm xOw@ |}xvwox@
C=Q}}eD s=tD |woMU=B |Q=O}=B `=aW Qo= &CU= xOW xO}t=v |Q=O}=B `=aW xv}W}@
|=Q@ O}=@ CQwY u}= Q}e QO &CU= Q=wDU= xt=vQ@ 'OW=@ VR=OQB |=yu=tR umtt
"OQm |Q}os}tYD |[Dkt s=Ok=
|=yQ=}at "1 [12] %OvOQm s}UkD xDUO wO x@ =Q |Q=wDU= |=yQ=}at u=QoVywSB
"2 &Ovvm|t xHwD xDUw}B `wkwx@ |xt=vQ@ OQmrta x@ \ki xm |ak=w OQmrta Q@ |vD@t
|xt=vQ@ w xDUw}B `wkw x@ |xt=vQ@ OQmrta Cw=iD x@ xm 13 QwLt|v=t}WB |=yQ=}at
Ciy |ak=w OQmrta Q@ |vD@t |=yQ=}at |va} pw= |xDUO |=Q@ "OvR=OQB|t xv}y@
xm CU= QmP x@ sRq "CU= xOW |iQat Q=}at Q=yJ swO |xDUO |=Q@ w 'Q=}at
CWPo =@ xm OvQ=O OQ@Q=m |t=ovy QwLt|v=t}WB |=yQ=}at |va} swO |xDUO
=Q |rai |xt=vQ@ s}y=wN@ w OwW XNWt =yC}a]k sOa xt=vQ@ CiQW}B w u=tR
xU}=kt 'Ow@ Oy=wN TQDUO p@=k C=aq]= OwHw CQwYQO xm xv}y@ |xt=vQ@ =@
xOW O=yvW}B Q=O}=B p=Ut |=Q@ Q=}at VW u}vJty xOWO=} |xar=]t QO "s}vm
"CU=
Q=}at Qw@a sOa ut[Dt =yQ=}at u}= xm Ov=xOQm xQ=W= |Qo}O u}kkLt
=Pr [13] "OvDU}v |r=tDL= hrDNt |=yCr=L QO hQ=aDt OL l} R= |}=Q=m
%R= Ow@ CQ=@a xm OvDiQo Q_v QO =D@ |Q=wDU= s=vx@ |Qo}O |}=Q=m Q=}at u=v;
p@=k Q}e XNWt OL R= xt=vQ@ l} |}=Q=m Q=}at Qw@a sOa p=tDL= |R=Uxv}W}@
"pw@k
=@ |y=oQ=m |Ov@u=tR |xrUt 'jwi |x} Q_v R= xO=iDU= =@ |Qo}O u=QoVywSB
u=tR uOw@ QDsm p=tDL= uOQm xv}W}@ hOy `@=D uDiQo Q_vQO =@ =Q u}W=t M w Q=m n
uOQw; CUO x@ |=Q@ =yu; [14] "OvOQm pL 'Q=_Dv= OQwt p}tmD u=tR R= =yQ=m p}tmD
=@ w xDiQo Q_v QO |Q=QmD O}rwD R= |a}Uw sHL (Cmax ) C=}rta |xvt=O `}RwD
'=Q C=}rta |xvt=O `}RwD |RmQt OL |x}[k R= xO=iDU= =@ =yQ=m O=}R O=OaD ZQi
u}= QO xm CU= |r=L QO u}= "OvOQm ZQi p=tQv '=yQ=m VR=OQB u=tR `}RwD R= =OH
"Q}N =} Ovm|t Q}}eD |v=QL@ Q}Ut '=yQ=m VR=OQB u=tR Q}}eD =@ CU}v XNWt xrUt
xO=iDU= |RmQt OL |x}[k R= u=wD|tv 'Ovm Q}}eD |v=QL@ Q}Ut xm |DQwY QO xm =QJ
OW Oy=wN Q}eDt `}RwD OvJ `wtHt C=}rta |xvt=O |v=QL@ Q}Ut Q}}eD =@ =Q}R OQm
ZQi =@ xrUt u}= QO hOy `@=D "CU}v jO=Y |RmQt OL |x}[k ZQi Qo}O w
ZQiV}B Q=Okt Cw=iD R= CU= CQ=@a 'xt=vQ@ C=}rta |xvt=O `}RwD uOw@ p=tQv
"xt=vQ@ C=}rta |xvt=O Tv=}Q=w Q@ s}UkD (Cmax ) xt=vQ@ C=}rta |xvt=O w (X )
C=ar=]t |xYqN "CU= xOW xO=iDU= l}DvS sD}Qwor= l} R= xrUt u}= pL |=Q@
|a]k xm CU= QmP x@ sRq "CU= xOW x=Q= 1 pwOH QO xv}tR u}= QO xOW s=Hv=
"""w |r}=[i OtLt '=k;p; =[QOtLt
"|a]k Q}e \}=QW QO |y=oQ=m |R}Qxt=vQ@ xRwL QO xOW s=Hv= |=yQ=m |r=tH= C=}@O= QwQt "1 pwOH
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=yQ=m VR=OQB
u=tR Q}}eD |iO=YD
hOy `@=D Q}}eD |Q=wDU=
|Q=mD@= |=yVwQ
=yQ=m VR=OQB
|r@k xr=kt x@ C@Uv
VR=OQB u=tR Q}}eD |iO=YD |Q=mD@= sD}Qwor=
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=yOQmQ}O |vRw `wtHt uOQm xv}tm l}DvS sD}Qwor=
x}rw= O=wt p} wLD OQmQ}O
C=}rta xvt=O uOQm xv}tm u=tR Q}}eD |iO=YD
l}DvS sD}Qwor=
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Kasperski 3
|O=OUv= Ovv=t@ Q=_Dv= QO u}W=t wO u}@ Ovv=wD|tv =yQ=m w CU}v u=tRty Q=m OvJ
VR=OQB u=tR Qou=Wv tij Qo= "OwW|t ZQi u=Um} =yQ=m |t=tD p} wLD u=tR w
Q=m `wQW u=tR Sij 'i u}W=t |wQ j Q=m p}tmD u=tR Cij 'i u}W=t |wQ j Q=m
u=}@ u}vJ xrUt pOt 'OW=@ =yQ=m C=}rta |xvt=O Cmax w i u}W=t |wQ j
%OwW|t
Objective = max[Probability(Cmax < X )]
( 1)
Cmax = CnM
( 2)
Carillo 2
v=
B
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B
v=
B
x Q}oW}
x Q}oW}
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v= B
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x Q}oW}
Daniels 1
m u=vJty &CU= u; |=yQDt=Q=B w =yQ=m |t=tD uOw@ XNWt |=vatx@ xt=vQ@ uOw@
|=OD@= QO =yQ=m |t=tD uOw@ TQDUO QO w uOw@ XNWt |=vatx@ xt=vQ@ |}=DU}=
"CU= |R}Qxt=vQ@
QDsm Cq=kt QO =D@ |Q=wDU= Q=}at 'CU= XNWt R}v 1 pwOH QO xm u=vJ
|Q=wDU= Q=}at =@ |O=OUv= |y=oQ=m O}rwD |xrUt x@ uwvm =D w xDiQo Q=Qk |UQQ@ OQwt
|y=oQ=m O}rwD |xrUt pL j}kLD u}= R= hOy u}=Q@=v@ "CU= xOWv xDN=OQB =D@
OwHwt |Q=mD@==Qi |=yVwQ u} QDy@ R= xO=iDU= =@ =D@ |Q=wDU= Q=}at =@ |O=OUv=
X=N Qw]x@ w |ak=w |=}vO QO "CU= |y=oQ=m p=Ut |=Q@ C=}@O= QO xOW x=Q=
xm OyO|t u=v}t]= =t x@ =D@ |Q=wDU= Q=}at R= xO=iDU= '|y=oQ=m u=} QH p=Ut QO
C11 = t11
( 3)
Oy=wNv QDW}@ |YNWt OL R= xOW u}}aD p=tDL= K]U QO xrUt C=}rta xvt=O
Sij = maxfCi(j 1) ; C(i 1)j g 1 j n; 1 i M (4) =@ =t '100 ?wr]t C=}rta |xvt=O w 0 9 p=tDL= K]U ZQi =@ p=Ft |=Q@ "Ow@
Cij = maxfSij + tij ; C(i+1)(j 1) g 1 j n;
C=}rta |xvt=O OQ=wt 90 QO xm s}DUy |}xt=vQ@ p=@vO x@ R} QolU}Q |OQm}wQ
"OW=@ xDW=O 100 R= QDsm
1i<M
( 5)
|UQQ@ OQwt |xrUt 2 VN@ QO %CU= CQwY u}O@ xr=kt xt=O= Q=DN=U
CMj = SMj + tMj 1 j n
( 6)
|Q=mD@= pL ?NDvt |=yVwQ 3 VN@ QO "OwW|t x=Q= xrUt pOt w xOW h} QaD
Ci1 = S(i 1)1 + ti1 1 < i M
( 7)
4 VN@ QO "OwW|t |iQat Qwm Pt |xrUt pL |=Q@ xO=iDU= OQwt |Q=mD@==Qi w
|xvt=O QO |}=yh=QLv= O=H}= Ea=@ xrUt VR=OQB |=yu=tR QO uOw@ |iO=YD x@ 5 VN@ QO C}=yv QO "CU= xOW x=Q= hrDNt p=Ut pL R= pY=L G}=Dv
u=tR R= xrUt C=}rta |xvt=O CU= umtt xQ=wty p}rO u}tyx@ "OwW|t C=}rta
"s}R=OQB|t |D; C=k}kLD |=Q@ C=O=yvW}B w j}kLD |Q}oxH}Dv
xQy@ u; R= xrUt u}= QO xm |iOy `@=D u}=Q@=v@ "OwW QDW}@ =yQ=m p}tmD ?wr]t
R= w XNWt Q=Okt R= =yQ=m p}tmD u=tR xm CU= p=tDL= u}= |R=Uxv}tm 's}=xOQ@
"1|x]@=Q OwW QDsm X |xOW u}}aD V}B
xrUt h} QaD "2
Qou=Wv 3 |x]@=Q 'C=}rta |xvt=O =} =yQ=m p}tmD u=tR Qou=Wv 2 |x]@=Q
u=tR Qou=Wv 5 |x]@=Q w '=yQ=m `wQW u=tR Qou=Wv 4 |x]@=Q 'pw= Q=m p}tmD u=tR Q=m n u=Um} |r=wD u}}aD p=@vO x@ =t 'Q_v Ot |y=oQ=m u=} QH O}rwD |xrUt QO
Ov=wD|t |v=tR i u}W=t |wQ j Q=m xm OvQ=O|t u=}@ \@=wQ u}= "CU=yQ=m p}tmD
=yQ=m |t=tD xm OwW|t ZQi "s}DUy OwHwt u}W=t M |wQ Q@ fj = 1; :::; ng
i 1 u}W=t |wQ j Q=m VR=OQB w p}tmD i u}W=t |wQ j 1 Q=m xm OwW `wQW Q@ =yQ=m |R=UxO=t; u=tR u}vJty w Ov=TQDUO QO (t = 0) |}=OD@= |x_Lr R=
u}rw= w u}W=t u} QN; x@ \w@ Qt ?}DQDx@ R}v 7 w 6 |x]@=Q "OW=@ xO}UQ u=}=B x@
|}=Hx@=H u=tR R= "CU= xOW xDiQo Q_v QO =yQ=m VR=OQB u=tR =@ =yu}W=t |wQ
"CU= Q=m s=Hv= x@ QO=k u}W=t Qy u=tR Qy QO "CU= xOW Q_v hQY R}v =yu}W=t u}@ =yQ=m
103
x
P (E; T ) =
T
(T 2 + E 2 )
t }= WQO 14 |DWo}=H |y=oQ=mu=} QH|xrUt pL|=Q@|OOaDt|=yVwQ
?=NDv= VwQ OvJ 'C=}@O= QwQt QO OwHwt pL |=yVwQ u}@ R= "CU= xOW x=Q=
l} Qy QYDNt K}[wD R= p@k "CU= xOW |R=U|tw@ q=@ |xrUt =@ ?U=vDt w xOW
"s}vm xQ=W= =ysD}Qwor= |t=tD QO x@=Wt C=}[Qi x@ CU= sRq =ysD}Qwor= u}= R=
w u}ov=}t ?=UDL= =@ xrUt QO =yC}r=ai u=tR |Q}PB Q}}eD uDiQoQ_v QO |=Q@ u=tR R= Cr=L 80 'p=tQv `}RwD R= xO=iDU= =@ w =yQ=m VR=OQB u=tR Tv=}Q=w
"OwW|t xQ}NP w O}rwD |iO=YD CQwYx@ =yQ=m VR=OQB
VR=OQB u=tR 1/9 w 1 u}@ |iO=YD Qw]x@ =yQ=m VR=OQB u=tR Tv=}Q=w Q=Okt "Ovm|t Q}}eD =yQ=m
u}}aD u}W=t Qy Q@ Q=m Qy u=tR u}ov=}t w =yQ=m |r=wD x@ xHwD =@ X Q=Okt "OwW|t
'Cw=iDt u=tR 40 |=R=x@ C=}rta |xvt=O Q=Okt Q=@ 40 '|vOW ?=wH Qy |=Q@ x@U=Lt =yC}r=ai |=Q@ 'xOW ?=NDv= jwi u=tR 80 u}@ R= |iO=YD Qw]x@ xm
"OwW|t x@U=Lt |Q=wDU= u=R}t xOW x@U=Lt Q}O=kt x@ xHwD =@ w OwW|t
VwQ Ciy xOW s=Hv= |=y|UQQ@ =@ jwi |xOW KQ]t |xrUt pL |=Q@
u}= j}@]D =@ C}=yvQO "OW ?=NDv= C=}@O= QO OwHwt jiwt |Q=mD@==Qi hrDNt
"s}OQm xrUt pL x@ s=Ok= Q_v OQwt |xrUt =@ |Q=mD@==Qi |=yVwQ
hrDN \ Q
@ D Q=Okt u} QDy@ w |rai hOy `@=D Q=Okt Cw=iD E &Q[=L p=L |=tO T
27 uOWOQU |Ov@u=tR O@ ?=wH l} VQ}PB p=tDL= P (E; T ) &hOy
=@ |}=tv
"CU= Ti = Ti 1 pwtQi |Q}oQ=mx@
`=
28 C}atH |xQ=@wO O}rwD "1"1"4
r D iO=YD ?=wH l} OvW=@ xDW=O OwHw |rai C}atH QO xOW O}rwD u=OvRQi Qo=
sD}Qwor= |xr}Uwx@ |iO=YD ?=wH u}= "OwW|t |Q=QmD ?=wH u} Ro}=H w xOW
"OwW|t C}atH QO OwHwt ?=wH u} QDO@ u} Ro}=H w xDi=} Ow@y@ O} Q@D |R=Ux}@W
=@ VyH s=Hv= R= TB w xOW ?=NDv= CrwQ |xNQJ =@ Or=w l} VyH s=Hv= |=Q@
OwN Or=w u} Ro}=H xOW O=H}= OvRQi "OwW|t xO=O Ow@y@ O} Q@D |R=Ux}@W sD}Qwor=
"OwW xOy=Wt xtD=N \}=QW =D OwW|t Q=QmD QOkv; Ov}=Qi u}= w OwW|t
O} w |
29 O} Q@D |R=Ux}@W w xawvtt |wHwCUH |@}mQD sD}Qwor= "2"4
|O=yvW}B
|=Q@ 'u}r \UwD Q=@ u}rw= O} Q@D |R=Ux}@W w xawvtt |wHwCUH |@}mQD sD}Qwor=
[17] "OW x=Q= |DWo}=HQ}e |y=oQ=m u=} QH |xrUt
u}= OQmrta xm O=O u=Wv w=
sD}Qwor= u}= "CU= |}=yvDx@ =ysD}Qwor= u}= R= l} Qy OQmrta R= QDy@ |@}mQD sD}Qwor=
T=U=Q@ C=Q}taD w |Q=Oxov C}OwOLt =@ |DWo}=H |y=oQ=m u=} QH |xrUt |=Q@
[18] "OW x=Q= C=}rta |xvt=O \UwDt Vy=m w \}=QW
|iO=YD CQwYx@ x}rw= ?=wH
'Z} waD |=yQ=DN=U R= |m} ?=NDv= =@ |o}=Uty ?=wH O=H}= "OwW|t ?=NDv=
30 |O=OUv= |Q=Po}=H '|Q=Po}=H
=@ sD}Qwor= u}= QO "CU= |iO=YD CQwYx@
31 xawvtt CU}r R= CmQL l} uOQm GQ=N u=mt= [19] xOW |iQat \}=QW |Q}oQ=mx@
Q}O=kt x@ C@Uv u; hOy `@=D uOw@ QDy@ \QWx@ u; R= |o}=Uty ?=wH O=H}= w
|O}OH |xawvtt CU}r =tO Vy=m Q=@ Qy =@ "OQ=O OwHw uwvm =D xOW xOy=Wt
Qy =@ "CU= 100 =D 7 u}@ |DN=wvm} |iO=YD Q}eDt u; |xR=Ov= xm OwW|t O=H}=
u; uOW s=tD =@ w xOW =QH= xawvtt |wHwCUH sD}Qwor= xawvtt CU}r O=H}= Q=@
?=wH u=wvax@ xOt; CUO x@ ?=wH O=tHv= |=tO x@ uO}UQ =@ "O@=}|t Vy=m =tO
Q=QmD u}= "OwW|t =QH= =OD@= R= xQ=@wO sD}Qwor= w xOW xDiQo Q_v QO sD}Qwor= |x}rw=
|}=tv `@=D =@ uOW OQU |Ov@u=tR "OwW s}_vD QDt=Q=B u}= =D OwW|t s=Hv= Q=@ N
"CU= 32 utRDrB O@ |=y?=wH |@=}RQ= Q=}at
P (E; T ) = e
|O=yvW}B pL VwQ "3
|O=yvW}B l}DvS sD}Qwor= "1"3
QO xm xJv; j@=]t xm U= 2011 p=U x@ \w@ Qt xOW x=Q= Q=m VwQ u}rw=
|xrUt |=Q@ l}DvS sD}Qwor= VwQ l} u; |] 'OW u=}@ C=}@O= QwQt CtUk
sD}Qwor= u}= QO "CU= xOW xO=O xaUwD |}xrLQt M |y=oQ=m u=} QH |R}Qxt=vQ@
15 |D@=kQ ?=NDv= l} R= u}Or=w ?=NDv= |=Q@
xm =vat u}O@ &CU= xOW xO=iDU=
?=NDv= R= TB "CU= QDW}@ OvQ=O |QDq=@ VR=Q@ `@=D xm |v}Or=w ?=NDv= p=tDL=
17 VyH w 16 `]=kD Qorta wO u}Or=w
`]=kD Qorta "OQ}PB|t CQwY u}Or=w |wQ
19
18 xOvQ=Oy=ov `]=kD '|@=NDv=
u}vJty "CU=
|v} Ro}=H VyH 'VyH Qorta w
`@=D O}OH pUv xm OvwW|t u=Wu}Or=w u} Ro}=H xOW O}rwD O}OH pUv |DQwYQO
"OW=@ xDW=O |QD?U=vt VR=Q@
[14] C
E
T
|O=yvW}B 33u=tRty Q}e |rLt |wHwCUH =@ l}DvS sD}Qwor= "3"4 |O=yvW}B |O} Q@D |R=Ux}@W w l}DvS |@}mQD VwQ "4
` t |R U m Q t @ } H y oQ m u } H | t |= @ }Q r= }=
|O=yvW}B 20O} Q@D |R=Ux}@W w l}DvS |@}mQD sD}Qwor= "1"4
wtH
= xv}t
=}a = |DWo =
| = =
= Q
xrU
Q sD wo
u
N=wvm} ?=NDv= CQwYx@ `]=kD |=Q@ u}Or=w ?=NDv= [20] "OW x=Q= u=} QH QO u=tR
Ow@y@ u=tRty Q}e |rLt |wHwCUH =@ Or=w wO ?=NDv= R= TB "OQ}o|t s=Hv=
34
O}rwD u=OvRQi ' p@wO |}x]kvwO `]=kD Qorta =@ `]=kD Ow@y@ R= TB w xOW xO=O
|xU}=kt =@ C}=yv QO "OwW|t xO=O Ow@y@ u=tRty Q}e |rLt |wHwCUH =@ xOW
"OQ}o|t CQwY O}OH C}atH O}rwD |=Q@ |v} Ro}=H 'xDi=} Ow@y@ u=OvRQi w u}Or=w
Ow@y@ |Q=Po}=H Qorta =@ ?=wH =OD@= u=tRtyQ}e |rLt |wHwCUH sD}Qwor= QO
Qorta u}= =@ |Ow@y@ Qo= w OwW|t C@F C=Q}}eD OW O=H}= Ow@y@ Qo= "OwW|t xO=O
C
w |Q=Oxov C}OwOLt =@ |DWo}=H |y=oQ=m u=} QH |xrUt |=Q@ sD}Qwor= u}=
|xvt=O \UwDt |R=Uxv}tm Q=}at w Cq;u}W=t |@=QN w 21 \}=QW T=U=Q@ C=Q}taD
22 CrwQ |xNQJ Q=mwR=U wO =@ `]=kD |=Q@ u}Or=w ?=NDv= [15] "OW x=Q= C=}rta
w `]=kD |=Q@ xO=iDU= OQwt |=yQorta "OQ}o|t CQwY 23 CN=wvm} ?=NDv= w
?=wH O=H}= hrDNt |=yQ=DN=U "CU= 25 |Q=Po}=H w 24 |}x]kvwO `]=kD 'VyH
?=wH O=H}= |=Q@ Z} waD Q=DN=U C}=yv QO w xDiQo Q=Qk |UQQ@ OQwt |o}=Uty
'O@ |=y?=wH VQ}PB sOa =} VQ}PB |@=}RQ= Q=}at "CU= xOW ?=NDv= |o}=Uty
104
"""|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
" U= 26 |Jw=m \UwD xOW x=Q= Q=}at u=ty
[16] C
"""w |r}=[i OtLt '=k;p; =[QOtLt
"OwW|t KqY= =yuwtwQi u; R= TB w xDiQo pmW xJQwt l} =yvD Q=QmD Qy QO
=Q =yuwtwQi w OvQ}o|t NEH VwQ R= =Q OwN |x}rw= ?=wH VwQ wO u}=
xv}tm w xv}W}@ uwtwQi =OD@= M-MMAS pw= VwQ QO "Ovvm|t |v=UQRwQx@
'=yuwtwQi T} QD=t u=ty =} T T} QD=t R= xO=iDU= =@ u; R= TB w OwW|t x@U=Lt
sD}Qwor= ZQat QO Q=@ 3 x}rw= ?=wH u}= "OwW|t =yQ=m Vv}J x@ `wQW =OD@= R=
QO "OwW pY=L |QDy@ ?=wH =D OwW|t xDW=Po 38 QwLtQ=m |rLt |wHwCUH
Q_v QO Q}N@D MQv T=U=Q@ '=yuwtwQi |v=UQRwQx@ 'swRwtwQm p}tmD R= TB C}=yv
s=Hv= 'xJQwt u}= pt=m CWo l} QF= QO xOv=t |=Hx@ uwtwQi u=R}t w xOW xDiQo
"OwW|t
|x}rw= Q=Okt QO M-MMAS pw= VwQ =@ PACO swO VwQ Cw=iD
|v=UQRwQx@ |xwLv w '=yuwtwQi |=Q@ xv}W}@ w xv}tm Q}O=kt OwHw sOa '=yuwtwQi
xDW=O pw= VwQ x@ C@Uv |Dw=iDt OQmrta swO VwQ =D xOW Ea=@ xm CU=yuwtwQi
"OW=@
QD
t=Q=B s}_vD "5
Y=L Ow@y@ u}rw= =@ "OwW|t xO=iDU= Ow@y@ |=Q@ Z} waD Qorta R= OWv pY=L
U D o= "OwW|t =QH= Ow@y@ |=Q@ |Q=Po}=H Qorta xQ=@wO w 'C@F C=Q}}eD xOW
xtD=N |rLt |wHwCUH Q=QmD 'OWv pY=L |Ow@y@ Qorta wO u}= R= s=OmI}y
|iO=YD |OOa `]=kD R= p@k wHwCUH Qorta u}= |=yQ=QmD O=OaD "CU= xDi=}
umtt |=yQ=QmD O=OaD xv}W}@ `]=kD R= Oa@ w umtt |=yQ=QmD O=OaD xv}W}@ w xv}tm
"CU=
p
\ w Q
|O=yvW}B 35QwLtC}atH O} Q@D |R=Ux}@W sD}Qwor= "4"4
|xvt=O |R=Uxv}tm Q=}at =@ |y=oQ=m u=} QH |Ov@u=tR |xrUt |=Q@ sD}Qwor= u}=
|=ysD}Qwor= Q}=U =@ xU}=kt QO sD}Qwor= u}= |rY= Cw=iD [21] "OW x=Q= C=}rta
|=Hx@ u=tRty w |R=wt CQwYx@ x]kv OvJ |wHwCUH QO O} Q@D |R=Ux}@W
`wQW |iO=YD |x}rw= C}atH l} =@ sD}Qwor= u}= "CU= x]kv l} QO wHwCUH
Q=}at "O};|t CUO x@ Z} waD Qorta =@ |o}=Uty ?=wH "Ovm|t wHwCUH x@
x=Q= `@=D R= =tO Vy=m |=Q@ "CU= utRDrB |=y?=wH VQ}PB sOa =} VQ}PB |@=}RQ=
QO |rw '`} QU q=@ |=tO QO `@=D u}= [22] "CU= xOW xO=iDU= |Ovwr \UwD xOW
"OwW|t OQU xDUy; u}}=B |=tO
u; |=yQDt=Q=B R= QF-=Dt |O=}R OL =D |Q=mD@==Qi w |Q=mD@= |=ysD}Qwor= OQmrta Ti = Ti 1
1 + Ti 1
|=yQDt=Q=B "CU}v u=Um} Cw=iDt |=ysD}Qwor= QO =yQDt=Q=B u}= w CU= sD}Qwor=
|=Q@ xOW |UQQ@ Kw]U w xr=kt u}= QO xOW xO=iDU= |=ysD}Qwor= OQmrta QO QFw-t Ow@y@ |rLt[23|]wHwCUH Q=DN=U l} =@ C}atH R= |QUm =tO Vy=m Q=@ Qy R= TB
QO NEH Q=DN=U =@ j@=]t =Q swO w pw= Q=m =OD@= Q=DN=U u}= "OwW|t xO=O
K]U x@ uO}UQ |=Q@ xm CU= QmP x@ sRq "CU= xOW QmP 2 pwOH QO =yu; R= l} Qy
w xOW ?=NDv= |iO=YD CQwYx@ Q=m wO 'xOv=t|k=@ |=yQ=m u}@ "OyO|t Q=Qk |r=wD
u}tyx@ "OwW u}}aD O}=@ =yQDt=Q=B Kw]U ?}mQD u} QDy@ '=ysD}Qwor= OQmrta |xv}y@
u}= "OwW|t C@F C=Q}}eD OW O=H}= |Ow@y@ xJv=vJ &OwW|t Z} waD =yv; C}akwt
|=yV}=tR; KQ] R= '=yQDt=Q=B hrDNt Kw]U ?}mQD OQmrta |UQQ@ |=Q@ p}rO
s}_vD sD}Qwor= u}= |=yQDt=Q=B Q}=U Q=vm QO O}=@ w P "OwW|t Q=QmD Q=@ P Ov}=Qi
sD}Qwor= |=QH= u=tR =Hv}= QO |OQmrta |=yXN=W "CU= xOW xO=iDU= |Jwo =D
"OwW
CQwYx@ |OQmrta |=yXN=W R= s=OmQy XN=W xm CU= C=}rta |xvt=O w
xv}y@ K]U w x@U=Lt =yXN=W |vRw \UwDt C}=yv QO w xOW x@U=Lt xv=o=OH
|O=yvW}B QQmt |xv=Y} QL |wHwCUH sD}Qwor= "5"4
"CU= xOW ?=NDv=
[24] "OW x=Q= |DWo}=H |y=oQ=m u=} QH |xrUt |=Q@ sD}Qwor= u}=
u}= Q=m T=U=
|rY= |xO}= "CU= QDy@ ?=wH x@ uO}UQ |=Q@ =yQ=m |r=wD |R=UR=@ w ?} QND VwQ
|OOa G}=Dv "6 xOt; CUO x@ |r=wD "CU= xOW xDiQo NEH VwQ R= =yQ=m |r=wD |R=UR=@ |=Q@
QO OwHwt ?NDvt VwQ CWy |Q=wDU= u=R}t |xU}=kt |=Q@ VN@ u}= QO Oa@ |xrLQt QO "OwW|t xDiQo Q_v QO sD}Qwor= |OwQw u=wvax@ NEH VwQ R=
,=D}=yv w 'VwQ CWy u}= =@ p=Ft u}= pL w |OOa p=Ft l} u=}@ x@ 'C=}@O= |x_i=L l} QO w xOW hPL ?=NDv= ?=wH R= |iO=YD CQwYx@ =yQ=m R= |[a@
|Ov@u=tR xQ=@wO w hPL |r=wD R= O}=@ xm |}=yQ=m O=OaD "OwW|t xQ}NP Ckwt
|HwQN |xt=vQ@ C=}rta |xvt=O u}ov=}t u=R}t w |Q=wDU= G}=Dv |xU}=kt
"s}R=OQB|t QO xOv=t|k=@ |=yQ=m "OwW s}_vD O}=@ xm CU= xrUt u}= |=yQDt=Q=B <RH OvwW
"OvQ}o@ Q=Qk Qo}Om} Q=vm QO '=yQ=m hPL R= p@k |r=wD j@=]t O}=@ |rY= |r=wD
?=wH R= CU= |Q=wDU= u=R}t u}}aD |=Q@ xU}=kt |=v@t xm X Q=Okt u}}aD |=Q@
u=wvax@ '=yC}r=ai u=tR u}ov=}t uDiQo Q_v QO =@ xv=Y} QL |wHwCUH sD}Qwor= ?=NDv= |iO=YD CQwYx@ Ckwt |x_i=L QO |=yQ=m R= |m} Oa@ |xrLQt QO
u=tR NEH sD}Qwor= |Q}oQ=m@ =@ xOW ?=NDv= Q=m "OwW|t hPL x_i=L R= w
u}= ?=wH "CU= xOW xO=iDU= hrDNt |=yxR=Ov= =@ p=Ut QO =yQ=m s=Hv= u=tR
u=} QH |xrUt |=Q@ w}r nvw}m xm NEH VwQ x@ C@Uv =Q |QDl}Q=@ OwOL VwQ O=OaD &OwW |r=N Ckwt |x_i=L =D OwW|t Q=QmD QOku; Q=m u}= "OwW|t |Ov@
x=Q= pwtQi R= |rLt |xv}y@ s=O R= Q=Qi |=Q@ "OwW s}_vD O}=@ Ov}=Qi u}= |=yQ=QmD
x@ p=Ut 'xvwtv |xrUt O}rwD |=Q@ "Ovm|t O=H}= CiQo Q=m x@ |DWo}=H |y=oQ=m
xO=iDU= O} Q@D |R=Ux}@W sD}Qwor= QO O@ |=y?=wH VQ}PB |=Q@ utRDrB \UwD xOW
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y W vB
= C w=
1. -robust
2. proactive
3. makespan
4. blocking
5. adaptive scheduling
6. event driven
7. reactive
8. predictive-reactive
9. proactive-reactive
10. owtime
11. robustness
12. stability
13. regret based
14. permutation ow shop
15. tournament selection
16. crossover
17. mutation
18. precedence preservative crossover (PPX)
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
swap crossover
hybrid genetic and simulated annealing algorithm
condition-based maintenance
Roulette wheel
uniform selection
two point cross over
insertion
Cauchy
cooling schedule
population reproduction
hybrid tabu search and simulated annealing algorithm
block insertion
tabu list
Poltzman
asynchronous genetic local search algorithm
twice two point cross over
population based simulated anealing
M-MMAS
PACO
job-index-based local search
108
"""|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
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"""w |r}=[i OtLt '=k;p; =[QOtLt
References `@=vt
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