KHOA HOC VA CONG NGHE MO
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anUAT TOAN MONTE CARLO VA KHA NANG QNG DUNG CUn NO TRONG Lim CHON DONG BO MRV XUC 6 TO
• • •
TREN CAC MO LO THIEN 6 VIET NAM
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ign nay, cdc md Id thien Idn d Viet Nam ndi chung va cdc md than Id thien Idn vung Quang Ninh ndi ridng dang su dyng cac thiet bj md vdi sy da dgng v l chOng loai, tfnh ndng, kich thudc, cdng suit,... da gay rat nhilu khd khan khi lya chpn ddng bd thiet bj hgp ly eho md. Chl xet rieng sy ddng bO giu'a khdu xue ble vd vdn tai la hai thiet bj quan trpng nhat trong ddng bp cung da thay dugc sy phiic tap trong viec lya chpn ddng bg cdc thilt bj.Cung vdi sy phat triln cua cdng nghg thdng tin trong nganh md thi vigc nghidn ciiu cac thuat toan toi uu va md phdng cae qua trinh san xult tren md 10 thidn hign nay cung dang Id nhO'ng vdn de dugc quan tam. Vi vdy vigc nghien eiiu kha nang ling dyng mdt so thuat toan phu hgp trong viec lya chpn ding bd thilt bj cho mot sd md 10 thien Idn Id hit su'c can thiet. Trong bdi bao ndy, tae gia nghien ciiu thuat todn Monte Cario va kha nang ling dung eua nd tren cac md Id thien d l lya chpn DBTB eho md va toi uu hda sy phoi hgp giO'a mdy xuc-d td tren cac mo Id thien d Viet Nam.
1. Tong quan ve phyong phap IVIonte Carlo 1.1. Cac phwong phap Monte Carlo Sau hon nO'a the ky phat triln dot pha, phuong phap Monte Cario dd gin nhu dugc ling dung rpng khap tren mgi ITnh vyc cua khoa hpc, cdng nghg.
COng vdi do, rat nhieu biln the cua phuong phap nay dugc xay dyng nhdm phyc vy cho cae nhu cau tinh todn cy the da dugc ra ddi. Mdt so phuong phap Monte Cario tieu bilu nhu:
• Assorted random model: la thuat ngu- dugc dung trong vat IJ d l md ta mpt he ddng hpc ma ed mOt dilm tdi han nhu la mOt dilm thu hut. Do vgy cac hoat ddng vT md cua chung duoe thye hien trong khdng gian va thdi gian dac trung bat biln cua diem tdi hgn cho mdt sy chuyen pha md
TS. VU OINH HIEU Truxmg Dgi hgc Md-Dja Chat khdng can cdc thdng so dau vao de dat dugc gid tn chinh xdc. Nd dugc ling dung nhieu trong ITnh vyc khac nhau chlng han nhu dja vgt ly, vu tru hpc, sinh hpc, sinh thai hpc, kinh te, xa hdi hpc,...;
• Phuong phap md phdng Monte Carlo tm-c tilp (DSMC): dugc dua ra bdi Gido su Graeme Bird. Day Id phuong phdp su" dyng ky thuat md phdng xac suit de giai eac phuong trinh Boltzman, md ta cac ddng khi loang md trong do quang dudng ty do tmng binh eua phan tii cd cung bac (hogc Idn hon) thang chieu dai vat ly dge tarng cua he;
• Phuong phap Monte Cario ddng lye (DCM):
Id phuong phap md phdng eac trang thai cua phan tli bdng each so sanh ti Id cOa cdc budc rieng le vdi cac so ngau nhien, Phuong phap DCM thudng dung de khao sat eac hd thing khdng can bang nhu: cac phan ling, khueeh tan,...;
• Phuong phap Monte Cario dpng hpc (KMC):
Id phuong phap Monte Cario dya trdn sy md phdng may tinh de md phdng sy tien trien theo thdi gian cua mpt vai qua trinh xay ra trong ty nhien, diln hinh la cdc qua trinh ma chung xuat hidn vdi mpt tf le dugc eho trudc;
• Phuong phap IVIonte Carto lugng tii (QMC): la phuong phap md phdng cae he thong lugng tu vdi myc dich giai quylt cae bai toan nhilu vdt thi. QMC dung phuong phap Monte Cario bang each nay hay each khdc d l tfnh toan cac tfch phdn nhilu chilu;
• Phuong phdp Quasi Monte Cario: la mdt phuong phdp de tinh toan mpt tich phan ma dya trdn eo sd la eac day sd cd sy nhlt qudn thdp. Nd trai ngugc vdi phuong phap Monte Cario thdng thudng, dugc dya tren eac day s l gia ngdu nhien.
1.2. Nen tang cua phuxmg phap Monte Carlo Phuong phap Monte Cario dugc xdy dyng dya tren nen tang:
• Cac sd ngdu nhien: day la nen tang quan trpng, gdp phan hinh thdnh nen "thuong higu" cua
CONG NGHIEP MO, SO 2-2016
KHOA HOC VA CONG NGHE MO p h u o n g phap nay. Cac s6 ngdu nhien khong chf
d u g c SLP dung trong viec md phdng lai eac hien t u g n g ngau nhien xay ra trong t h y e t l ma con d u g c SU dung de l l y mdu ngau nhien cua mpt phan t l i nao dd, chang han n h u trong tinh toan cac tich phan;
•;• Luat so Idn: luat nay dam bao rdng khi ta chpn ngdu nhien cac gia tri (mdu t h i i ) trong mpt day cac gia tn (qudn the), kich t h u d c day mdu t h i i cang Idn thi cac dac trung thong ke (trung binh, p h u o n g sai,...) cua mdu t h i i cang "gan" vol cac dac trung thong ke cua quan the, Luat so Idn r l t quan trpng doi vdi p h u o n g phap Monte Carlo vi no dam bao cho s y on djnh cua cac gia tri trung binh cua cac bien ngdu nhien l<hi sd phep t h u du Idn.
D[nh ly gidi han trung tam: dinh ly nay phat bieu rang d u d i mOt so dieu kien cu the, trung binh sd hpc cua_ mpt l u g n g du Idn cac phep lap cua cac bien ngdu nhien dgc lap se d u g c xap xf theo phan bo chuan. Do p h u o n g phap Monte Cario ia mdt chudi cac phep t h u dwac lap lai nen dinh ly gidi han trung tam se giup chung ta d l dang x l p xi d u o e trung binh va p h u o n g sai cua cac ket qua thu d u g c t l i p h u o n g phap nay. Cac thanh phdn chinh cua p h u o n g phap mo phong Monte Carlo gom co:
ham mat dp xac suat (PDF); ngudn phat sd ngau nhien (RNG); quy luat l l y mdu; ghi nhan; u d c l u g n g sai so; cac kT thuat giam p h u o n g sai; song song hda va vector hda.
^S6 ngau nhien
Monte Carlo Lay mau Ghi nhan U'oc litang sai so Giam phircmgan sai Song sonc hoa va vccior hoa
j K c i q u a
Phan bo Xdc suai H. 1. Nguyen tac hoat ddng cue phwong phap Monte Carlo 2. Co so* k h o a h o e c u a t h u a t t o a n M o n t e C a r l o va l i n g d u n g c u a n d tren cac m d lo t h i e n
2.1. Md hinh hoa toan hgc
Trong cdng nghiep va kinh te, viec lap ke hoach chiu anh h u d n g bdi n h i l u cac yeu t l ben ngoai s y canh tranh va thi t r u d n g . Ngoai ra con phai ke den cac yeu to ben trong n h u p h u o n g phap hoat dpng, trang t h i l t b\ va each quan ly, V i du nhu l y a chpn he thong van tai cho md lp thien, cac yeu to n h u vj tri than quang, ham lugng va ty le quang hoa mac du rat quan trong nhung khong the thay doi, Tuy
CONG NGHIEP MO, SO 2 - 2 0 1 8
nhien thi cung ed nhO'ng y l u to de thay doi n h u li,fa chpn p h u o n g phap van tai (d to,...) va vj trf tuong l i n g trong m d . van d l ehfnh trong phan tfch h^
t h i n g mdu do la l y a chpn t i i toan bp cac nhan i dieu khien d u g c vd khdng dieu khien d u g c , s y |(e|
h g p cae nhdn to dieu k h i l n d u g c dem lai hidu qua kinh t l vdn de nay cd t h i bieu thj n h u sau:
Ham tdi u u :
Z = F ( X „ Y , ) v d i : 1=1,2...M;j=1,2.,.N (1)^
Trong do: Z - Ddnh gia hieu qua (chi phf, Igi n h i ^ nang suit,,,); X,- Cac bien d i l u khien d u g c ; Y,-Cac bien khong d i l u khien d u g c ; F - Ham d i l u khien. „
2.2. Md phdng he thong
Md h i n h d u g c d u a ra ed t h i d u g c d y a trgn CO s d ly t h u y l t h o a c p h a n t i c h du' lieu tryc t j k t l i he t h o n g . 6 p h u o n g phap t h i i hai nay c a c # lieu d u g c ghi nhan lai tu' cac he thdng d u d i cac d i l u kien hoat d p n g khac nhau va mdi quan \^
t h y c nghiem cac y l u to ddu v a o va ddu ra dirpc mo ta qua p h u o n g phap thdng k d , M d u dua ra cung cd the d u n g t i i s y k i t h g p giu'a ly thuyet va t h y e nghiem tim t h I y .
Cac m d hinh t o a n hpc cua cae he thong kk h g p rat k h d khdng chf viec tim ra ma con ca ve giai quyet c h u n g . V d i viec n g h i e n c i i u 1 he thong v a n tai rieng, gia s i i xue bde va do thai d u g c gan v d i nhau v d i ty le s a n l u g n g , Z d u g c xac djnh la toan bp chi phi van t a i . X, la b i l n d i l u khien d u g c (dang v a n t a i , s6 l u g n g kich t h u d c thiel bi. ) Y| la cac b i l n k h d n g d i l u khien d u g c (san l u g n g d l ra, cac dac d i e m , cac vj tri xue boc, So thai .). Viec lap k l h o a c h quan tdm t d i viec gi^m m i i c tdl thieu chi p h i van tai v d i s a n l u g n g xac d|nh qua each l y a c h p n tdt n h l t he thong, van tai, kich c d , sd l u g n g t h i l t bj he t h o n g .
Viec d u a ra mpt he t h i n g m l u v d i cdc cong cu va p h u o n g p h a p tho s o la kha p h i i c tap. Ti§ii bieu trong he t h o n g v a n tai may xuc-d to, tii&i gian nhan tai cua mpt xe va k h I i l u g n g tai ducrc thdng ke khac n h a u . T r a n g thai cua xe va khoi l u g n g tai d u o e t h o n g ke khac n h a u . Trang thai eua xe tren d u d n g la ham eua cae yeu to nhu d a n g d u d n g , d i l u kien d u d n g , khdi l u g n g van tai. T h d i gian di c h u y e n cua xe c u n g la ham cua l u g n g xe va loai x e .
2.3. Chu ky lam viec
Chu ky lam viec cua 1 t h i l t bj van tai co the d u g c the hien n h u sau:
Tv=T^n+fn-t-Tc,+Tnd+Td+TM+T,^, phut. (2) Trong do: T « - T h d i gian chu ky cua thiet bj, phiiS Tmn- T h d i gian tai noi nhan tai, phut; T n - Thdi gis"
nhan tai, phut; Tct - T h d i gian dj chuyen (cd tai), phut; Tmd- T h d i gian tai noi d d tai, phut; T ^ - Thdi gian d d tai, phut; Tkt - T h d i gian di c h u y i n (khong
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ai), phut; Tm - Cac yeu to n h u c h d d g i , di cham ren d u d n g , phut.
Ta c d : Tn=V/Qt, phut (3) Trong do: V - Dung tich cua xe, tan; Qt - T y le
; h a t t a i cua may, t i n / p h u t . V d i he thong may xuc-d t d :
Tn=[V/E]*xTc, phut. (4) Trong d d : E - Dung tfch gau xue, t i n ; Tc- T h d i gian
Dhu ky mpt lan xuc, phut; [ ] * - Gia tri trong ngoac i[rac lam trdn len.
tot=L</Vo, phut (5) Tk,= LkA/k, phut (6) Trong dd: Lc- Khoang each t i i vj tri xuc den noi d o
-iii, k m ; Vc- T i e dp xe khi ed tai, km/phut; V|,- Tdc 3p xe khi khdng eo tai, km/phut.
' Gia trj Tm cd t h i xac djnh qua cdc du' lieu t h d i
^ian d u g c ghi nhdn hoac cd t h i tinh d u g c t i i viec ohan tfch he thong hoat dpng. Gia s i i khdng cd cac yeu to gay tri hoan tdi vide do thai hay tren d u d n g 5i, thi so xe c l n t h i l t cd the tinh d u g c d l dam bao nhdn tai tot n h u sau:
N , chiee. (7)
jl [ ] * - Gia tn trong ngoac d u g c lam trdn len.
i; T r u d n g h g p ehi ed hai xe, thdi gian c h d (W) 3uoc tfnh:
2(Tmn.T,)+W=Tmn.T,.T,i+T^d.Td.Tk, (8) I W=(Td+Tnd^Td+Tk,)-(Tmn+Tn), phUt
I V d i n chu ky van tai thi tong t h d i gian c h d trong r u d n g h o p ed 2 xe la:
. T W = 6,5.(n-1 )rct+Tnd+Td.Tkt-(Tmn+Tn)], phut (9) ,1; V o l N d td:
K W = (ToHTnd^Td*TkO-(N-1 )(T„n*Tn);phut (10)
• TW=[(n-1)/n].[(Tct.Tnd.Td.Tk,)-(^N-1)(Tmn.T,)K11) :. Khi tang gia tri N thi W ed the giam xudng. N l u .^ qua Idn thi khi dd W cd the dat gia tri a m , d i l u Jo CO nghTa xe t h i i nhat da hoan thanh chu ky lam /lec cua minh t r u d c khi eac xe khac d u g c nhgn tai.
^ 2.4. Kich thwdv dgi xe
Mpt chi tieu quan trgng trong vigc l y a chpn t h i l t '.3j do la kha nang san sang eua cac t h i l t bj van tai.
Z6 the t h i l t lap n h u sau:
', Kfeh t h u d c dpi xe=n/a; (12) Trong d d : n - S d xe yeu c l u trong he thong; a -
<ha nang san sang eua 1 x e :
t a = ^^: (13) P
Prong dd: p - So g i d ed the hoat ddng; d - T h d i jian can nghf.
|j Mpt cdch tot h o n la s u dung nhj t h i i c phdn bd i u g c d u a ra bdi Connel.
frong d d : pn - Xac s u i t chinh xac n phan t i i san odng; pa- Xac s u i t ma mpt phan t i i d o n san sang;
Pna - Xac suat ma mdt phan t i i d o n khdng san sang, Pna=1-Pa; N - Tong phan t i i trong he thong;
Nen- Ket h o p cua N, lay n trong 1 lan (n<N).
Pn^.Ncn(P.)"(Pna)^-'' (14) D o n g thdi:
N
Pln=SNCx{Pa)'(Pna)' ,N-x (15)
Tgi ddy: P^i - Xac suat toi thieu n phdn tu- ed the san sang. Khi N tang va n tang, rat thich h g p eho s u dung 1 c h u o n g trinh tfnh toan.
2.5. Mau Monte Carlo
Thuat toan Monte Cario trong viec nghien cO'u mdu d y a tren l i n g dyng eua xac s u i t va t h i n g ke d u g c su' dung kha thuan Igi. (fng dyng p h u o n g phap nay se d i l n ra theo mpt qua trinh n h u sau:
a. Tfnh xac s u i t cua toan bp ham F(x) cua bien x t r e n m i l n (hinh H.2).
(16) y=F(x)= jf(x)dx
Trong dd: f(x) - Ham tan so cua x.
b. Chpn mpt sd b i t ky, r g i i i a 0 va 1 t i i bang so ngdu nhien.
e. T l i xac s u i t toan bp ham F(x), tim gia tri x t u o n g l i n g vdi y=r.
Gia tri md phong cua x d u g c phan phdi theo t i n sd cua ham b i l n x. Cac sd lieu cho thay rd rang xac s u i t cd gia tri mo phong giu'a Xi va Xi+dx cd t h e o t y lef(xi)dj;.
P(xi < gia tri mo phdng < Xudx)=dyi=f(xi)dx Trong t r u d n g h g p b i l n bj gian doan, khi dd:
F(x)= Jf(u), (17)
H.2. Mien biin thien cua mau Monte Carlo
CONG NGHIEP MO, SO 2-2016
KHOA HOC VA CfiNG NGHE MO Sang 1. Cac bien so ngiu nhien tim duoe theo cic phin phdi co ban
binh
Nlu thuat toan Monte Cario dua ra mdt gia tri Idn cua mdu thi trung binh cac mdu se tdi gan gia tri trung binh tieu chuan. Sii dung thuat toan Monte Carlo de dOng trong nghien ciiu md phdng dugc tdm tat lai nhu trong Bang 1.
3. Lfng dung thuat toan Monte Carlo trong lya chgn dong bo may xOc-d to tren md 16 thien
Mdu md phdng hg thong may xOc-d td ed rat nhilu u'ng dyng nhu trong lya chpn thiet bj, phan tfch hogt ddng cua thilt bj, k l hoach san xult va thilt k l dudng van tai.
Vdi cdc md Id thien Idn v dp dyng thuat toan Monte Carlo ta ed the gidi quyet ngay van d l xay ra kha pho biln d l giam tdl miie tdi thilu nhO'ng gian dogn trong van tai do Id sy phu hop giu'a sd lugng xe tai vdi sd may xue xe tai sao cho giam toi thieu miic toi da thdi gian chd dgi cua may xuc ddng thdi giam chi phi trong thdi gian chd dgi.
Gpi M va N la so may xuc va xe tai trong he thong, Cs Id chi phf trong thdi gian may xuc chd (d/ph), Ct la ehi phf thdi gian xe tai chd (d/ph), Wm thdi gian chd tfch luy cua may xuc, Wnia thdi gian chd cOa xe tai. Ta ed:
Wm=Fi(M,N); Wn=F2(M,N);CT=Wm*Cs+Ci (18) Trong dd: Fi, F2 - Ham he thing; CT - Tong ehi phi thdi gian chd.
Ap dyng thuat toan Monte Carlo tinh toan md phdng DBTB may xOe-d to cho cac mo Id thien dugc thye hign qua eac bude nhu sau:
• Bude 1: gan cdc thdng s l diu vao; M, N -S6 may xue, sd d td trong to hgp DBTB; T^- Thdi gian chat tai cua may xue thii i, phut; ATn- Dp Idch thin gian nhdn tai, phut;Thj- Thdi gian van tai tii khidi ra khdi cho may xuc cua xe d td thii j ; ATh - Dp ledi thdi gian van tai, phut; RN,< - So ngau nhien thii KM
• Bude 2: tfnh thdi gian chat tai cho may xiic Tn=Tn,+RNk*ATn:
• Budc 3: tfnh thdi gian di ehuyin eua cdc 6 to tu' khi ra khdi vj trf nhan tai Th =Th,+RNk*ATh;
• Budc 4: tfnh toan, phdn tfch trang thai phoi hgp eua may XLIC va d td: M - S l may xuc trong to hgp DBTB, chile; N - So 6 td trong to hgp DBTB, chile; T^
- Thdi gian chay eua may xue thu- i, i=1, 2,..., m; Tq- Thdi gian chay oia d td thu' j , j=1, 2, 3,..., n; T - Khoang thdi gian d l udc lugng (ttiang, nam...).
Qua trinh tfnh toan diln bien nhu sau:
• Budc 4.a. Chpn d td vdi thdi gian hogt dpng nhd nhat (Tom). Dat Id d td thu' k vdi: T(,m=Tok. Nlu Toi(>T thi thye hien bude 4.h.
• Bude 4.b. Chpn may xOc ed thoi gian hogt 3png Txm nhd nhat. Dat Id may xuc thu- g vdi:
Txm=Txg;
• Budc 4.e. Dgt w=(Txg-Tok). Nlu w<0, thi thyc hien bude 4.d. Nlu w>0, thi thyc hien budc 4.e.
Neu w=0, 0 td cd the dugc an djnh ngay cho mdy xOc. Thyc hien bude 4.f;
• Bude 4.d. Mdy xue g dang dgi d td, thdi gian chd dgi eua may xue Id w^: vvs=(TorTxg). Cap nh§t
CONG NGHIEP MO, Sd 2-2016
KHDA HOC VA ClNG NGHE M O
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trang thai T^m eua mdy xue g: T^=Xy,g+Ws- Thyc hien budc 4.f;
• Budc 4.e. (!) td k dang chd nhan tai, thdi gian chd cOa d td k la Wt: w,=(Txg-Tok). Cdp nhap trgng thai Tok cho d td k: Tok=Tok+Wt;
• Budc 4.f. Dua ra thdi gian chit tai cho d td k bang mdy xuc thu' g, dgt Id Lgk-
C^p nh|ip trang thai T^m eua may xuc vd d td:
Txg=(Txg+Lgk); Tok=(Tok+Lgk);
• Budc 4.g. Dua ra thdi gian di chuyen cua d td thii k tu" noi nhdn tdi. Dgt la t^.
Cgp nhgp trgng fridi Tok eua d td thii k: Tok=Tok+Tk.
Thyc hien budc 4.a.
H.3. So dd khoi md phdng qui trinh li/a chgn d (d
• Bude 4.h. Kit thue md phdng ket thue, xuat ra kit qud: ting khoi lugng san pham, tan; sd lugng ehuyen van ehuyin, chuyin; thdi gian chd cua mli d td d tu'ng mdy xOe, phut; thdi gian chd cua may xue vdi tiing d td, phut.
Qud trinh tfnh todn lya chpn DBTB cho d td ap dyng thuat toan Monte Cario dugc md ta d hinh H.3.
4. Ket luan
Thuat toan Monte Carlo dd ra ddi tu- rat lau va dugc ling dyng rlt nhilu trong nhieu ITnh vyc khdc nhau. Vdi sy phat trien cua ngdnh than thi viec ling dyng mgt thudt toan nhu Monte Carlo vao vigc tfnh toan DBTB cho cdc md cOng Id dilu t i t ylu.
Thuat todn Monte Cario ed rat nhieu uu diem de ling dyng trong vigc tinh todn DBTB trong md:
*> Dua ra 1 gia trj Idn cua mau ngdu nhien do vay
trung binh eac mau se tdi gan den gia tri tieu chuan.
• Tinh toan thdi gian chu ky vgn tai, eho phep phdn tich cac giai phdp thay doi tuyin vgn tai;
• Lfdc tfnh sd lugng d td vdi cac thiet b| chat tai bat ky nen thuan tidn dOng de Igp ke hogeh ngdn hgn;
• Lya chpn cac thilt bj cd kfeh thude phu hgp nhat;
• Tdi uu kfeh thudc dOi xe.
Vdi eac uu dilm vd kha nang ling dyng cua thuat todn Monte Cario ma tae gia da phdn tfch d tren, cd the thdy ring thuat toan Monte Cario hoan toan cd the u'ng dyng de tfnh toan lya chpn DBTB tren md 16 thien va tdi uu hda sy phoi hgp giO'a may xuc-6 td tren md Id thien, nang cao nang suit 1dm vide cua thilt bi cOng nhu hoat ddng san xult eua toan md.G
TAI LIEU THAM KHAO
1. Bui Xudn Nam, Nguydn Le Thu, Doan Trpng Lugt (2010). Mdt phuong phap lya chpn logi 6 t6 van tai ddt da eho eac md than 10 thien vung Quang Ninh. Tgp chi Cdng nghiep Md so 5. Hdi Khoa hpc va Cdng nghe Md Viet Nam. Ha NOi- Tr. 7-9.
2. Doan Trpng Luat, Bui Xuan Nam, Ta Khdi Dgi (2010). Phuong phap dieu khiln hogt dOng cua 6 to khi phdi hgp vdi may xue trong khai thac 10 thien. Tgp chf Cdng nghiep Md so 5. HOi Khoa hpc va Cdng nghe Md Viet Nam. Ha Npi. Tr. 3-4.
3. Tg Khai Dai (2010). Luan van thac sT ky thuat
"Nghien eiiu kha nang ling dung mdt so thugt todn phu hgp trong viec lya chgn dong bd thiet bj cho mpt so md Id thidn Idn vung Quang Ninh",
4. Nguyin Diic Khoat, Bui Xuan Nam, Doan Trpng Lugt (2011). Giai thuat Genetic trong dilu hanh van tai tren md Id thien. Tap chf Cdng nghiep Md sd 2. Hdi Khoa hoc vd Cdng nghd Md Viet Nam. Ha NOi. Tr. 22-23.
5. Lambert C.RJ, Mutmansky J.M. (1987).
Application of integer programming to effect optimum tmek and shovel selection in open pit mines. Proc. I l " " Conf. Of APCOM. Arizona, April:
A75-A105.
NgwoS bien tap: Ho ST Giao
The article presents research results of Monte Carlo algorithm and usability of this algorithm in the selection for machines synchronization and optimization of coordination between excavator-automobile for sui
CONG NGHIEP mo, so 2-2016
