Lai Khde Ldl vd Dtg Tap chi KHOA HOC & CONG NGHE 8 6 ( I 0 ) : 2 I 3 - 2 I 8
UTVG DUNG GIAI THUAT DI TRUYEN
CHO BAI TOAN DIEU KHIEN TOI UU DA MUC TIEU
Lai Khac Lai'*, Bang Ngoc Trung"
'Dai hoc Thdi .\guyen. 'Trirang DH Ky ihiidl Cong nghiep - DLl Thdi Nguyen
TOM T A T
Trong thuc te hien nay hau het cac bai toan dieu khien trong cac day chuyen cdng nghe la biii toan tdi uu da muc tieu.Viec iing dung cac giai thuat tinh toan tien hda hua hen nhieu trien vpng. Bai bao nay trinh bay mot irng dung mdi de giai bai loan tdi uu da muc tieu dd la diing thuat loan giai thuat di truyin (GA-Genetic Algorithm), noi dung bai bao cho thay tinh uu viet cua giai thuat di truyen vdi qua trinh tim kiem cue trj loan cue.
Til' khoa: Dieu khien tdi ini. Da muc lieu, Gidi thudt di truyen.
DAT V A N D E
Bai toan tdi uu da muc tieu cd mat hau het trong cac bai toan dieu khien day chuyen cdng nghe hien dai trong cdng nghiep ndi rieng va md rdng ra nhieu ITnh vuc khac. Tuy nhien chua cd nhieu nghien cuu ve cac bai toan nay. Hien nay cac de tai khoa bgc chii yeu mdi chi giai quyet va u'ng dung cac bai toan tdi uu mdt muc tieu. Vi du ta xet cdng nghe gia nhiet phdi kim loai trong Id nung la mgt trong nhung qua trinh cd tham sd bien ddi chain, trong dd cac ham muc tieu dat ra vdi Id gia nhiet nhu sau; nung nhanh nhat hocic nung chinh xac nhat, nung it bj Qxi hda nhat; trong cac bai toan dieu khien mirc ciia day truyen san xuat nudc nggt thi cac ham muc tieu cd the la: dn djnh mirc dung dich H chinh xac nhat hoac thdi gian dn djnh nhanh nhat...
Da cd nhieu phuong phap tiep can khac nhau nham giai quyet cac loai bai toan nay, song gan day viec irng dung cac giai thuat tinh toan tien hda da bat dau cho thay dugc uu diem ndi bat.Tuy vay nhirng nghien ciru ve ITnh vuc Uciy trong nudc ta chua nhieu. nhat la chua dua ra dugc nhiing md hinh irng dung thuc te cu the trong khi nhu cau irng dung lai rat cao, da cd mdt so tac gia de cap va nghien ciru vi du nhu: trong [2] tac gia Nguyen Manh Xuan da su' dung giai thuat tien hda de tim Idi giai toi uu cho cac ham muc tieu trong md hinh
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bai toan phan bd ddng chay va xir ly nudc thai; trong [5] tac gia Lai Khac Lai de cap den viec SU' dung giai thuat di truyen de tdi uu hda suy luan md... cac ket qua nghien ciru nay mdi chi dirng lai d cac ham muc tieu cd san, tinh thuc tien chua cao. Day chinh la ly do ma de tai nay tap trung chii yeu vao viec xay dung bai toan tdi uu nhieu muc tieu cho day chuyen cdng nghe thuc te va irng dung giai thuat di truyen (Genetic Algorithm - GA) de giai quyet bai toan tdi uu dd.
Ndi dung bai bao vdi ket qua chay chuong trinh tinh toan bang giai thuat di truyen va md phdng diet! khien vdi ddi tugng la mirc dung dich H trong binh trdn khuay cho thay tinh uu viet ciia viec sir dung giai thuat di truyen vdi qua trinh tim kiem cue trj toan cue tren CO' che chgn Igc thich nghi tu nhien va ca che song song an cho nhting bai toan tdi uu hoac tdi uu da muc tieu va cd the trien khai de ap dung rdng rai cho nhieu ddi tugng dilu khien va trong nhieu ITnh vuc nhu; khi tugng, thuy van...
GlAl THUAT Dl TRUYEN Khai quat giai thuat di truyen
Giai thuat di truyen (GA-Genetic Algorithm) la giai thuat tim kiem, chgn lira cac giai phap toi uu de giai quyet cac bai toan thuc te khac nhau, dua tren co che chgn Igc ciia tu nhien;
Tir tap Idi giai ban dau, thdng qua nhieu bude tien hda, hinh thanh tap ldi giai mdi phii hgp hon, va cudi cimg dan den ldi giai toi uu toan cue.
Lgi Khac Ldi vd Dtg Tap chi KHOA HOC & CONG NGHE 86(I0):2I3 -218 Cac nha khoa hge da nghien cim va xay dung
nen giai thuat di truyen dua tren co' sd chgn Igc tu nhien va quy luat tien hda. Giai thuat di truyen su' dung cac thuat ngu' dugc lay tir di truyen bgc nhu; lai ghep, dot bien, NST, ca the... (I> day moi ca the dugc dac trung bdi mgt tap nhiem sac the, nhung de don gian khi trinh bay, ta xet trudng hgp te bao mdi ca the chi mgt NST. Cac NST dugc chia nhd thanh cac gen dugc sap xep theo mgt day tuyen tinh. Mdi ca the (hay NST) bieu dien mgt Idi giai cd the ciia bai toan. Mgt xu' ly tien hda duyet tren tap cac NST tuong duong vdi viec tim kiem ldi giai trong khdng gian ldi giai ciia bai toan.
Giai thuat di truyen cd the mo ta van tat nhu sau:
P roced uce Giaijhugt dijriiyen;
Begin /;=0,'
Khdi tgo ngdu nhien qudn the P(t);
Ddnh gid dd phii hgp timg cd the trong P{t)-, Repeat
t-,= t+\;
Chgn cdc cd the tir P{t - 1);
Lai lew cdc cd the dd chgn tgo ra P{t) mdi;
Dot bien cdc cd the trong P{t) theo .xdc sudt P,„;
Ddnh gid do phit hgp cdc cd the trong tgp P{');
Until (thda man dieu kien dung);
End;
Cac ky thuat trong giai thuat di truyen Giai thuat di truyen kinh dien sii' dung ma hda nhj phan, mdi ca the dugc ma hda la mgt chudi nhj phan cd chieu dai co djnh.
Md hda- bleu dien cdc bien bdng vec ta nhiphdn
Ta sir dung vecto nhj phan cd do dai L nhu mgt NST de bieu dien gia trj thuc ciia bien
X G [ / ^ ; W 1. Do dai L ciia NST phu thugc vao yeu cau cu the ciia bai toan. Mgt bit ma hda X irng vdi mgt gia trj trong khoang
0 ; 2 ' se dugc anh xa len gia trj thuc thudc mien [/^;w 1. Nhd dd, ta cd the kiem soat mien s.\a tri cua cac bien va tinh chinh xac ciia
chimg. Ty le co gian ciia anh xa dugc tinh nhu sau;
Gia trj x tuong irng vdi chuoi NST nhj phan la; X = /, + decimali^NST) * g. Trong dd, decimal [NST) la gia trj thap phan cua chudi
ll -I NST nhj phan va g - ' ^ ' Khdi tgo qudn the
De khdi tao quan the, chi can dan gian tao pop - size (kich ca quan the) nhiem sac the ngau nhien theo tiing bit. Phan con lai cua thuat giai di truyen rat don gian; Trong mdi the he, ta lugng gia tiing NST (tinh gia trj cua h a m / t r e n cac chudi bien nhj phan da dugc giai ma), chgn quan the mdi thda man phan bd xac suat dua tren do thich nghi va thuc hien cac phep dot bien va lai de tao ra cac ca the the he mdi. Sau mgt so the he, khi khdng cdn cai thien them dugc gi nua, NST tdt nhat se dugc xem nhu ldi giai cua bai toan tdi uu (thud'ng la toan cue).
Hdm thich nghi
Sau khi khdi tao quan the hoac d thdi diem cac the he mdi dugc tao thanh, chung ta phai SU' dung ham thich nghi de danh gia mirc do thich nghi cua mdi nhiem sac the nham cd ca sd cho viec lira chgn bd me cho cac phep lai tao va dot bien.
Cac phuong phap xac djnh do thich nghi:
+ Xac djnh theo ty le thich nghi (Fitness scaling)
+ Xac djnh theo phuong phap ciia sd thich nghi (Fitness windowing )
+ Xac djnh theo thu' hang thich nghi (Fitness ranking )
Todn tif chgn lgc
O mdi the he, dua tren gi trj ciia ham thich nghi, cac ca the cd do thich nghi tdt se dugc chgn Igc de tao thanh quan thi d the d thi he mdi va chuan bj cho viec thuc hien cac phep toan lai ghep va dot biin sau nay.
Mgt sd phep chgn Igc thudng dugc sir dung bao gdm;
Lai Khde Ldi vd Dtg Tap chi KHOA HQC & CONG NGHE 86(I0):213-2I8 -(- Sir dung banh xe Roulette
•f Chgn Igc xep hang + Chgn Igc canh tranh Todn tit- lai ghep .
Trong giai thuat di truyen, sd lugng cac ca the trong quan the d mdi the he la khdng ddi.
Phep chgn Igc da chgn ra mdt sd ca the cd do thich nghi cao va loai bd di mdt sd ca the thich nghi thap. Su thieu hut sd lugng ca the trong quan the mdi se dugc bii dap bang lay cac ca the thich nghi cao la the he cha me, tao ra cac the he con bang phep lai ghep va dot bien tren cac ca the thich nghi cao nay.
Mdt sd phuong phap lai ghep;
-I- Lai ghep mgt diem -I- Lai ghep nhieu diem + Lai ghep mat na Todn tir dot bien
Dot bien la thay ddi cac bit tren chudi nhiem sac the mdt each ngau nhien de tao ra tinh da dang. Phep dot bien dugc dieu khien bdi xac suat dot bien P,„. Neu khdng dot bien thi giai thuat chi di tim kiem ldi giai d khdng gian khdi tao. Tuy nhien, neu P,,, qua ldn, qua trinh tim kiem trd thanh tim kiem ngau nhien.
Cac phuong phap giai bai toan toi uu da muc tieu
Md hinh todn hge cita bdi todn Y ( X ) - ^ m i n ( m a x )
X e D c R"
Y(X) = (V,(X),...,Y,(X))eR'- goi la vec to muc tieu.
X ggi la phuang an, D la tap cac phuang an.
V|,...,Yii ggi la cac ham muc tieu.
Khi XU' ly tap nghiem Pareto, vai trd ciia ngudi SU' dung (NSD) hay ngudi nhan Idi giai ciia bai toan ddng vai trd quan trgng. NSD se can CU' vao lgi ich ciia minh de chgn phuong an cho hgp ly, each do ggi la ket hgp QHDMT vdi NSD. Cd thi ndi Igi ich d day la mot ham U : Y(D) -^ R thudng dugc gia thiet thda man mgt vai dieu kien nao dd dimg de do sd thich cua NSD.
Phucmg phdp nhugng bd ddn
B I : Giai k bai toan mgt muc tieu rieng re, sau do lap bang thudng phat.
B2: Can cir vao bang thudng phat, vdi gia trj Y / ' NSD buoc Y| nhugng bd mdt lugng AY|
va giai bai toan:
m a x Y , ( X ) vdi X e D ; Y|(X)>Y|" - AY, Gia sir Y2 la trj tdi uu ciia bai toan nay, chuyen sang B3.
B3: NSD can cir vao YT va YT bude Y^
nhugng bd lugng AY2 va giai bai toan;
m a x Y , ( X ) vdi X e D ; Y|(X)>Y|" - AY,;
Y2(X) >Y2* - AY,;
Gia SU' Y3 la trj tdi wucuar bai toan nay, chuyen tiep sang bude tiep....
Bk: NSD can cu' vao Yk-," va Yk-i' bude Y^i nhugng bd lugng AY^., va giai bai toan;
ITiax Y^(X) v d i X e D ; Y|(X)>Y,"-AY,;
Y:(X) >Y,' - AY2;...,Y,.,(X) )>Y,.,'- AY,.,, Nghiem ciia bai toan cudi ciing nay lay lam nghiem ciia bai toan.
Phuojig phdp thda hiep
B l : Giai k bai toan mgt muc tieu rieng re, gia sir nghiem tdi uu la X, (i=l,...,k).
Dat M, = Y,(X,) va dua vao bien phu W:
M,-T(.V)
\M\
< \^ vdi mgi i= l,...,k Ve trai trong cdng thiic tren ggi la do lech tuong ddi chung.
B2: Giai bai toan min Vsl vdi X e D tir dd tim dugc nghiem tdi uu X" va W"
Trong trud'ng hgp nay, lgi ich ty le vdi do lech tuong ddi, phuong an X, la tdt hon X, neu do lech tuong ddi chung cua X, nhd hon Xi.
Phuang phdp tim nghiem cd khoang cdch nhd nhdt den nghiem ly tuang
Phuong phap nay gia djnh cd mdt nghiem ly tudng , X, tdt ban X2 neu khoang each tir X, den nghiem ly tudng nhd ban khoang each tuang urng ciia X,.
Lgi Khac Ldi vd Dtg Tap chi KHOA HOC & CONG NGHE 86(10):213-2I8 Djnh nghTa: Gia sir X', X" eR", khoang each
giua X' va X" la so d„ xac djnh bdi:
\X — X'\ a la tham sd a > l Khi do bai toan maxY(X) vdi X e D dua ve bai toan
(
« ^ I i \aZl>:w-^:|
mir
Van de xac djnh tham sd a phu thugc vao tirng bai toan.
U'NG DUNG GlAl THUAT DI TRUYEN
CHO BAI T O A N T O I U U D A M I J C T I E U
Dat bai toan
Gia SLI' dieu khien muc dung dich H trong binh khuay trdn theo sa dd dieu khien va so do khdi nhu hinh I dudi day
Trong dd;
-I- Ham truyen dat ciia bg chuyen ddi ddng dien - khi nen (I/P);
MC Al...
0.01-0.002
2 0 - 4 ^0.5 KG I miir niA
-I- Ham truyen dat cua van: tin hieu vao la ap suat khi nen va tin hieu ra la luu lugng nude cap thdng qua co cau van;
w/(.)=o;_„(5)= 50
-O.Ob %{s) = W,.^„{s)--125 -0,0U'
I'Llii n e n
Bo dieu khien
Pat ,
%
1 1
4-,. : { Scnsoi ')<- -po luong;;
Hinh 1. Sa dd dieu khien miic ciia binh trdn -I- Ham truyen dat ciia thiet bj do miic: tin hieu vao la khoang each va tin bieu dau ra la dien ap;
W„(,s'): 0.016 + 0,005.s'
Bai toan tdi uu dat ra d day la thiet ke bd dieu khien PD sao cho dn djnh mirc dung djch H chinh .xac nhat va thdi gian dn djnh nhanh nhat, tuong ung vdi hai ham muc tieu nhu sau;
I EI.<|
•S.' H 1
K ' > > w
H,
J '
H(s)-<fy« [*-
Hinh 2. Sa dd khdi dieu khien miic
Muc tieu 7; J^ = L'-(t)dt - > min Muc tieu 2: ,/^ - \e(t)dt nun
Til' hinh 2 tinh toan va nit ra dugc phuong trinh vi phan;
0 . 0 1 5 . ^ +(1.4A', + D — + 1.4./c',.e = 0 dr " dl
Ta cd phuong trinh dac trung la;
0,015.A-- + OAK,^ + \)k + \,4.K, = 0 Vdi dieu kien A > 0 thi phuong trinh tren cd mgt nghiem rieng la
e(t) = e'" +e'"
Chgn 2 5 < A:,, < I 0 0 suy ra L35</i„<50 Trong dd:
/S--
- I , 4 A ; , - 1 ^ -i4K^-\-J(i4K^^+\f-(\mK,
O.QB 0.03
/^_H4^,-'+VA_-l4/^~I+^(l4A;,+lf-Q0m./C 0.(B " 0.(B
Thay t=3(s) cudi cimg ta cd dugc bai toan toi uu hai muc tieu dieu khiln muc dung djch H nhu sau;
Lai Khac Ldi vd Dtg Tap chi KHOA HOC & CONG NGHE 86(10):2I3 -218
2k. - I - -
- 6 ^ " ' - ' ^ " + -
J,=
k,+k,
— -^ min
2k, -^ mm
25<K^<]00 ],35<K^<50
Giai quyet bai toan
Diing thuat toan giai thuat di truyen viet tren phan mem Matlab vdi quan the khdi tao ban dau gdm 30 ca the, sau cac bude lai ghep, chon Igc, dot bien giai bai toan da muc tieu tren ta thu d u g c ket qua tdi uu ciia bd gia trj (Kp va KD) sau: Kp = 25.895; K D = 18.349 lam cho J, va J2 min. Vay dd chinh la bd gia trj tdi uu cua bd dieu khien PD trong so' dd dieu khien miic tren vdi luu dd thuat toan ciia giai thuat di truyen nhu hinh 3.
Dieu khien muc
10 15 20 25 Thoi gian mo phong
Hinh 4. Ket qua md phdng vdi bo thdng sd tdi uu Kp =25.895; K D = 18.349
So sanh kel quj mo |)hong
A 6 Tdoi qijri mo phong
Binh 5. Kit qua md phdng vdi bo thdng sd tdi uu Vci bd thdng sd khac
Cac ket qua md phdng d u g c chi ra tren hinh 4 Vci hinh 5. Trong dd; Hinh 4 irng vdi ciic thdng so tdi uu tim d u g c bang giai thuiit di
truyen cdn Hinh 5 la dap ung qua do irng vdi bd thdng sd tdi uu va no thdng sd khac.
Bat dau
Kticn tao cac tham so: So Lan larj. y£z siiat dot bwn
Khca tao qiiiti the ban dau fri?au riMen)
Dem= 1
•4
1. Chpn ngau nl'uen 2 ca the xl, x2 2. La: ghep tao 2 con_yl,ji2
3. Dot bienjd tu^ theo xii: suit dot bien pm 4. Neuyl "toi hrji" x\ thi thay J1 bcdjil
Neu_)i2 "tot hcii' x2 tlii thay x2 hiijQ 5. Dem = Dem-H
< Dem <= So lan lap
Ghi nlian cjuan ttie cuoi ding
I
Ket diuc
Hinh 3. Luu dd thuat loan KET LUAN
Qua ket qua md phdng tren Matlab Simulink vdi cac bd gia trj cua (Kp va K,,) lay tir tap nghiem ciia thuat toan giai thuat di truyen, ta cd the tim thay mdt be) nghiem tdi uu ma d do ta thay chat lugng dieu khien mirc dung dich H tang rd ret, do sai lech va thdi gian qu<i do deu nhd ban so vdi cac bd gia trj khac. Vdi ket qua nay cho phep md rdng h u d n g thiet ke bd dieu khien PID tdi uu cho Ccic day chuyen cdng nghe Vci day cting chinh Li hiicVng mdi trong tinh toan mem sc d u g e ap dung trong cac bai tOcin tdi uu thuc te trong tuong lai.
Lgi Khde Ldi vd Dtg Tap chi KHOA HOC & CONG NGHE 86(10): 2 1 3 - 2 1 8 TAI LIEU T H A M KHAO
[1]. Nguyen Doan Phudc. Phan Xuan Minh. Han Thanh Trung (2003), Ly thuyet dieu khidn phi tuyen, Nxb Khoa hoc va Ky thuat. Ha Noi.
[2]. Vu Manh Xuan (2006) "Tinh todn tien hoa trong tdi uu da muc lieu" De tai nghien ciru khoa hoc cap Bo - Ma sd: B2006 TNO1 - 04.
[3], Nguyin Thuong Ngd (1999), Ly thityit dieu khien tu ddng hien dgi. Nha xuat ban Khoa hpc Ky thuiit.
[41. Vu Manh Xuan. Nguven Thanh Thiiy (2007)
"Giai thudt di truyen vdt cdc gen phu thugc nhau'\
bao cao Hdi thao Qudc gia "Ngien cuu ca ban va iing dung cdng nghe thdng tin'.
[5]. Lai Khac Lai (2001) ' T h i l t kl he dilu khiln md nhd su dung thuat gen" Tgp chi Khoa hoc cdng nghe trudng Dgi hge Ky thudt Cdng nghiep.
trang 10-16.
[6]. Nguyen Dinh Thuc (2001). Lap trinh lien hda.
Nha xuat ban Giao due.
[7]. Goldberg. D.E. (1989), Genetic Algorhhm in search, optimization and machine learning, Addsion - Wesley, Reading, MA.
S U M . M A R /
A P P L I C A T I O N G E N E T I C A L G O T I T H M T O S O L V E M U L T I - O B . I E C T I V F O P T I M I Z A T I O N P R O B L E M S
Lai Khac Lai ', Dang Ngoc Trung"
Thai Nguyen Universin: College of Technology! - TNU
In fact today most of the control problem in the technology chain optimization problems are multi- purpose. Application ot evolutionarv computation algorithms promising prospects. This article presents a new application to solve multi-objective optimization algorithm that uses genetic algorithms (GA- Genetic Algorithm), contents of the article shows the superiority of genetic algorithm with the process of finding a global extreiiium.
Key words: Optimization control: Multi objective: Genetic Algorithm.
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