Tap ch! Tin hpc va Bi'eu khien hpc, T,2.5, S.l (-2009), 79 87
T O I LTU OA MUC TIEU TRONG VIEC LAP LjCH CHO HE THONG T I N H TOAN LU^O^I
TRINH THI THIJY GlANGl, r,E TRONG VINH^ HOANG CHI THA.X'H', NGUYEN THANH THUY^
^Dai hpc Khoa hgc Tu nhiin. Dgi hgc Quoc gia Hd Ngi - . . -Dgi hgc Bdch khoa Hd Ngi
A b s t r a c t . In this paper, we study the problem of scheduling in grid computing system and propose a genetic algorithm for it. We propose a new fitness function which considers simultaneously two critical factors in the probem of scheduling, that are: makespan factor and flowtime factor. In addition, the new fitness function considers not only the load of systems and jobs but also the cost of data transfer for scheduling. Experimental resutls show that our algorithm can archive a scheduling method that is better than the simulated annealing-based algorithm do.
Tdm t a t . Trong bai bao nay chung toi nghien ciru bai toan lap lich trong cac he thdng tinh toan ludi va dua ra mgt thuat toan di truyen de giai quyet no, Chung toi dira ra mot ham do do thich nghi (fitness function) mdi, nham dong thdi tdi uu boa hai yeu td co ban cua bai toan lap lich trong ludi tinh toan, do la: khoang thdi gian de hoan thanh toan bo cac cong viec (makespan) va tong thdi gian thuc hien cua cac cong viec (flovvtime), Hon niia, ngoai viec quan tam den tai trong tinh toan cda cac tai nguyen va cong viec, bai bao nay cung quan tam den gia cua viec sd dung cac tai nguyen va gia cda viec tru,yen dir lieu den cac tai nguyen. Cac ket qua thyc nghiem chi ra rang thuat toan cda chung toi de xuat co phuong an lap lich tot hon thuat toan lap lich truyen thdng dira tren thuat toan Simulated Annealing,
1. GlOfI T H I E U
Ludi tfnh toan (computational grid) - hay cdn ggi l i he thdng tfnh t o i n ludi (gi'id comput- ing system) - la mgt t a p hgp rgng ldn va khdng ddng nhat cda c i c he thdng t y tri (autonomous systems) p h i n t i n ve dia ly d u g c ket ndi vdi nhau bdi lien mang m i y tfnh ll|, Ludi tinh toin duoc sir dung de giii quyet cac van de phiic tap thugc nhieu ITnh vyc khac nhau nhu:
tdi uu, md phdng, k h i m p h i d u g c lieu, sinh hgc,.,, Trong mgt ludi tinh t o i n cac he thdng t y tri phii chia s^ cdng viee (job sharing) vdi nhau. Viec chia se cac cdng viec cho cac he thdng t y tri sao cho tai nguyen he thdng d u g c sd- dung hieu q u i va cac cong viec thyc hien dugc mgt each tdi uu d u g c ggi la lap lich trong he thdng tfnh toan ludi [1]. Bai t o i n lap lich l i mgt trong c i c t i c vu khd khan chinh cda he thdng tfnh t o i n ludi. vi vay nd da dugc rat nhieu nha khoa hgc quan tam. Khdng gidng nhu cic bai toan lap lich trong he thdng phan tan truyen thdng, trong lirdi tfnh toan viec lap lich phuc t a p ban nhieu do cac dac Irinig nhu:
ti'nh dgng cda he thdng, sy khdng ddng nhat ve tai nguyen va cdng vice .,, can dinrc i\\u\\\
8 0 TRINH THI THUY GIANG, LE TRQNG •VTNH, HOANG CHI THANH, NGUYEN THANH THUY t a m khi xdr Iy. Bai t o i n lap lich d u g c xem xet trong c i hai t r u d n g hgp: tinh (static) va ddng (dynamic). Trong b i i bao nay chung tdi chi xem xet b i i toan d d a n g tinh.
Bai toan lap lich d a d u g c chung minh la N P day dd ll]. Do vay, viec sd' dung cac t h u a t toan heuristics I i cich tiep can t h y e te (de facto) de giii q u y e t nd. TVong nhurng nam qua, nhieu t i c g i i d a sdr d u n g cac t h u a t toan heuristics k h i c nhau de giii q u y e t b i i t o i n lap lich nhu: Ritchie [2] sdr dung t h u a t t o i n tim kiem cue bg (local search), Yarkhan 13] sir dung t h u i t t o i n Simulated Annealing, A b r a h a m 14] sdr dung t h u a t toan Tabu Search, Marino 15] sdr dung t h u a t t o i n di truyen (genetic algorithms), Ritchie J6] sdr dung t h u i t toan Iai giua Ant Colony Optimization va Tabu Search ... Tuy nhien, cae cich tiep can nay chi quan t a m d o n 1^ den mgt trong hai yeu t d quan t r g n g n h a t cda cdng viec lap lich trong mdt ludi tfnh toan dd l i : cyc tieu makespan ( k h o i n g thdi gian h o i n thanh toan bd c i c cdng viec) hoac flowtime (tong thdi gian t h y e hien cda c i c cdng viec). Mat k h i c , de d o n giin trong c i c md hinh md phdng c i e t i c g i i la t h u d n g chi quan t a m mgt each t u g n g t r u n g den c i c tai nguyen cda he thong - k h i nang tfnh t o i n cda c i c he t h d n g t y tri - cung nhu yeu eau tfnh t o i n cda cac cdng viec.
Dieu nay d a n den cac t h u a t toan d u g c trinh bay khd ap dung trong c i c he t h o n g tinh t o i n ludi t h y c t e .
T h u a t toan di truyen (Genetic Algorithm - GA) 17] ngoai fch Igi g i i m khdng gian tim kiem, hdi t u ve ldi giii toan cue, nd cdn cho phep tdi uu hda d a mue tieu (multi-objectives), C i c t a c g i i trong 19] d a s u dung t h u a t toan di truyen de ddng t h d i tdi uu hai yeu td flowtime va makespan trong viec l i p lich cho ludi tfnh t o i n . Tuy nhien, nd van cdn diem yeu n h u d a neu tren dd la eac van de ve gia cda t i i nguyen va chi phf truyen t i i dir lieu c h u a d u g c quan t a m den. Tiong bai b i o nay, chung tdi cung sii dung mo hinh md phdng va t h u a t toan di truyen, t u y nhien g i i cda cac t i i nguyen va phf truyen t i i dir lieu se d u g c quan t a m . Do vay, t h u a t t o i n d u g c d u a r a ed nhieu k h i nang iing dung trong cac ludi tinh t o i n t h y c han c i c t h u a t t o i n d a d u g c trinh bay.
Ddng gdp chi'nh cda b i i b i o cd the tdm t a t nhu sau:
1) P h a t bieu bai toan lap lich tong q u i t trong he thdng ludi tinh t o i n d u d i dang hinh thirc (md hinh toan hgc),
2) Giii quyet b i i t o i n d y a vao t h u a t giii di truyen bang viec d u a ra ham do dd thich nghi (fitness function) mdi cho t h u i t toan di truyen khong chi de quan t a m ddng thdi den c i hai yeu td quan trgng cda bai toan lap lich trong ludi tfnh t o i n la makespan va flowtime m a cdn quan t a m den c i c yeu td phu k h i e nhu la g i i sd dung tai nguyen va truyen t i i dir lieu. Cac tham sd trong ham do do thfeh nghi la c i c t h a m sd thiet ke nen ddi vdi c i c iing dung trong t h y c te, ehung t a cd the tiiy bien phu hgp vdi nhieu t r u d n g h g p khi cae mue tieu can cd s u uu tien khac nhau,
3) Mgt nghien ctiu sau rgng bang mo phdng de so s i n h c i e p h u o n g i n l i p lich d u a ra bdi thuat t o i n di truyen va t h u a t t o i n Simulated Annealing truyen thdng. Dieu nay d u a c kiem chiing thdng qua cac md phdng.
Phan edn Iai cda bai bao d u g c to chiic nhu sau. Mue 2 danh de md hinh h o i bai toan lap lich trong ludi tfnh t o i n . Mue 3 d u a ra t h u a t t o i n lap lich d y a tren t h u a t t o i n di truyen cho ludi tfnh t o i n . Myc 4 trinh b i y c i c ket q u i t h y c nghiem. Chung tdi d u a ra cac ket luan va
.. .. ; ^ ; ., .. .. .. TOI u u DA MUC TIEU TRONG 'VIEC LAP LICH 81 de xuat cac h u d n g p h i t trien trong Mue 5.
2. L A P L I C H T R O N G C A C H E T H O N G T I N H T O A N L U d i
Lap lich trong he thdng tfnh t o i n ludi d u g c biet den vdi nhieu cich t h u c khac nhau do do phuc t a p cda he thdng va tfnh phan t i n cda c i c iing dung. Tuy nhien, trong b i i bao nay, chung toi chi quan t a m den bai t o i n lap lich tinh, trong dd cac iing dung khong phu thugc Ian nhau. Mac dd vay, n h u n g van de ve trao doi dii lieu, tfnh kinh te (gii) cda viec sdr dung cic tai nguyen ciing se duge quan t i m . Kieu l i p lich nay x u a t hien trong nhieu ung dung thyc te. TVong kieu l i p lich nay mdi ung dung cd the d u g c chia thanh nhieu cdng viec doc lap, cac cdng viec n i y d u g c gdi (rieng re) den c i c he thdng t y tri trong ludi.de t h u c hien va tao ra c i c ket q u i (bo phan), ket q u i cudi ciing la s y ket hgp cda c i c ket q u i bg phan.
Chung tdi ciing chi quan t a m den kich b i n , trong do cac iing dung dugc gdi tdi ludi la doc lap va khdng cd uu tien.
De de dang cho viec p h i t bieu bai toan va khdng m a t tfnh tong q u i t , t a gii sii rang da biet trude c i c thdng tin sau: k h i nang tfnh t o i n (ciing d u g c biet la t i i tinh t o i n ) cda mdi tai nguyen (he thdng t y tri) trong ludi; udc Iugng ve t i i tinh toan (computational load) cda mdi cong viec, t i i tfnh toan da sd dung cda moi tai nguyen. Mgt md hinh nhu vay dugc ggi la rad hinh E T C (Expected Time to Compute) [8]. Tiong mo hinh nay, mot ma tran E T C se dugc xay dyng, trong do mdi phan t d ETCli]lm] la thdi gian mong mudn (expected time) de tinh t o i n cdng viec t trong tai nguyen m. G i i tri n i y cd the d u g c tinh t o i n bang each chia k h i nang tfnh t o i n cda tai nguyen m cho t i i tinh t o i n cda cdng viec t. Vdi md hinh ETC, chiing ta cd the p h i t bieu bai t o i n lap lich trong ludi tfnh t o i n nhu sau. G i i sir cd:
1) n cong viec ddc lap can p h i i lap lich vdi t i i ti'nh t o i n { J i , J2,..., J„} thao t i e tren t a p dur lieu ki'ch t h u d c {Di,D2,..., D^}. Chiing t a cung gii sd la mdi cdng viec se dugc xii Iy toan bg trong mgt tai nguyen duy nhat.
2) m tai nguyen (cung d u g c ggi la he thdng t y tri - autonomous system) vdi k h i nang tfnh toin {Mi,M2,...,Mm} ed g i i tri kinh te t u o n g ung la {vi,V2, ...,Vm} cho moi mot dan vi tii tfnh toan va chi phf truyen thdng tren mdt d a n vi du' lieu giii den cac tai nguyen nay la {Ci,02, ...,C,n}-
3) {Tl, r 2 , •••, Tm} la thdi gian m a tai nguyen i se ket thuc cdng viec t r u d c dd (chi ra t i i trgng da sd dung t r u d c dd).
Bai t o i n d a t ra la: Lap lich de he thdng tfnh t o i n t h y c hien t a t c i cac cdng viec sao cho:
1) Flowtime la cyc tieu, nghia la:
r / = min V ^ . (1)
2) Makespan cyc tieu, nghia la:
T^ = min { max {T,,;, + - ^ } } (2)
Mm^
8 2 TRINH THI THUY GIANG, LE TRONG VINH, H O A N G CHI THANH, NGUYEIN THANH THUY 3) G i i su dung tai nguyen cyc tieu, nghia la: • :• ' , "
l/ = min{ ^ JiXVj^i)}. ' ' ' . (3) i(i)S{l..m};ie{l..n} ,
"4) Chi phf truyen t i i du' lieu cue tieu, nghla la: '.
C = min{ Y. DiXCj^i-,}. (4) j(i)e{l..m};ie{l..n}
Mdt chu y rat quan trgng la gia tri cda bieu thiic sau p h i i dd ldn:
n
min ^ . (5)
j{i)e{i..m} Mj
Dieu nay chfnh la b i n chat cda viec can c i c he thdng tfnh toan ludi. Nghia la t d n g sd lugng cdng viec khi t h y c hien tren mgt he thdng b a t ky se m a t nhieu thdi gian ( d i n den k e t q u i d u a ra khdng cd g i i tri t h y c te bdi tfnh thdi gian cda nd), vi v i y chung t a p h i i giii quyet nd tren he thdng tinh t o i n ludi.
Viec dinh g i i cda s y truyen t i i dii lieu d tren cung r a t can nhan m a n h dd la: vi trong tfnh t o i n ludi, c i e he thdng t y tri t h u d n g d u g c ndi vdi nhau b i n g c i c m a n g d u d n g true tdc do cao (nhu leased line), do vay thdi gian truyen t i i d u lieu (do tre - latency) cd the bd qua m a chi can quan t a m den chi phi d u d n g truyen.
3 . T H U A T T O A N D I T R U Y E N C H O V I E C L A P L I C H 3 . 1 . Gio"! t h i e u v e t h u a t t o a n di t r u y e n
T h u i t t o i n di truyen 17] d u g c xay dyng d y a tren quy luat tien hda sinh hoc hay p h i t trien t y nhien cda mot quan t h e sdng, Cac c i the t r i i qua mgt q u i t r m h p h i t trien va sinh s i n de tao ra n h u n g c i t h e mdi cho the he tiep theo. TVong q u i trinh tien hda n h u n g ca t h e xau (theo mot tieu chuan nao dd hay cdn ggi l i dia thich nghi vdi mdi t r u d n g ) se bi dao t h i i , Ngugc lai, nhirng c i t h e t d t se d u g c giu lai. Lien quan den giii t h u i t di truyen cd c i c k h i i niem sau:
- Bieu dien ciia cd the: De i p dung d u g c t h u i t t o i n di truyen, viec dau tien la p h i i tim d u o c each bieu dien cda c i c c i t h e sao cho mdi ca the bieu dien mdt giii p h a p cda bai toan dang d u g c quan t i m ,
- Ddnh gid do thich nghi Do thi'ch nghi la k h i n i n g phi^i h g p cda mdi ca t h e (giii phap) ddi vdi mdi trirdng (bai t o i n ) , Viec xay d u n g do thich nghi cung la mot b u d c quan trong trong t h u i t t o i n di truyen. De d i n h g i i dugc do thi'ch nghi cda c i c c i t h e giii t h u a t di truyen sii dung mgt ham do do thieh nghi (Fitness Function).
- Lai ghep: La q u i trinh t a o ra c i the mdi d y a tren nhieu c i t h e da cd, ggi la cac ca t h e cha-me, Hai c i t h e con d u g c tao ra bang cich hoin doi c i c gen tii ca t h e cha me.
TOI UU DA MUC TIEU TRONG VIEC LAP LICH 8 3 - Dot bien: L i qua trinh tao ra c i the mdi ti^r mgt c i the ban dau bang each thay doi mot sd
gen cda nd,
- Chon lpc vd thay the: Chgn lgc va thay the (ciing dugc biet nhu la q u i trinh sinh soi niy nd - reproduction) la qua trinh chgn nhirng c i the tii quan the hien tai de tao ra the he sau cda nd. TVong q u i trinh nay dien ra sy d i o t h i i nhurng c i the xau, chi giur lai nhimg ca the tdt. Nhurng c i t h e cd do thich nghi ldn han hoac bang vdi do thi'ch nghi tieu chuan se dugc giir lai v i do thfeh nghi cda cac c i the trong quan the se hoan thien ban sau nhieu the he, - Dieu kiin ditng: T h u a t t o i n di truyen la mgt q u i trinh n g i u nhien, nen khong the d i m b i o chac chan t h u a t t o i n di truyen se diing sau hiiu han budc, Vi vay, de d i m b i o thuat toan di truyen se ket thuc, ngudi dung t h u d n g p h i i dinh nghia dieu kien diing cho thuat toin, 3.2. T h u a t t o a n di t r u y e n t r o n g v i e c lap lich
Nhu da trinh bay trong phan gidi thieu, thuat t o i n di truyen khdng chl giim khong gian tim kiem cda bai toan m a cdn cho phep tdi uu da mue tieu, Phan n i y t i p trung trinh bay thuat t o i n di truyen cho bai toan lap lich trong ludi tfnh t o i n vdi bdn mue tieu can tdi uu hoa dong thdi nhu da trinh bay d Mue 2,
Bieu dien cua cdc cd the:
De ap dung t h u a t toan di truyen cho bai t o i n lap lich, tien hanh ma hda cac ca the nhu sau: mdi c i the la mgt vecta, ggi la schedule, vdi kich thudc n t h i n h phan (n la sd cac cong viec) vdi gii tri l i c i c sd nguyen trong khoing ti^r |1, m] im l i sd lugng cac tai nguyen) sa,o cho thanh phan schedule[i] chi ra cong viec i dugc gdi cho tai nguyen (c6 sd hieu la gia tri) schedule[i] t h y c hien. Vf du, schedule]3] ~ 5 chi ra rang: cdng viec t h u 3 se dugc giao cho tai nguyen (he thdng) sd 5 t h y c hien.
Khdi tgo qudn the ban idu:
Sinh ra P ( P la t h a m sd thiet ke) ca the ban dau mot cich ngau nhien. Mdi c i the dugc sinh ngau nhien bang cich sinh ngau nhien n Ian c i c sd nguyen trong khoing tir 1 den m va lan sinh thii i ii = l...n) t u o n g iing vdi c i c thanh phan schedule]i] cda ca the. Chu y rang sau khi sinh ngau nhien can kiem tra tfnh hgp le cda c i the, nghia la tdng t i i tinh toan cda cac cong viec gia-o cho mdt tai nguyen (he thdng t y tri) n i o dd khong d u g c vugt qua k h i nang tinh t o i n cda tai nguyen dd.
Hdm do ip thich nghi (Fitness Functions): Dinh nghia do thi'ch nghi cda mdt ca the k nhu sau:
Fk= 1 ^ — , •-• ' ' ( 6 )
T^ + ax Tl +£ix Vk -b £i X Gk
trong dd, a, e i , £2 G (0, 1) la tha,m sd thiet ke de dieu chinh, Tl,TJJ^, Vk va Gk dugc tinh nhu
TI = Y^ETC]i][schedule]i]], .. . (7)
TJP = max iTi-\rETGli]]schedule]{]], , (8)
7 — 1 . . 7 1
84 TRINH THI THUY GIANG, LE TRONG VINH, HOANG CHI T H A N H , NGUYEN THANH THUY
Vk = 'YjiX •Vsched-ule[i\ , l^J
n
Ck = 'YP>iX Cscheduleli]- ( ^ 0 ) i = l
Phep todn lai ghep: Sii dung phep toan lai ghep mot diem. Sinh ngau nhien mdt sd nguyen k trong khoing ttr [2, n — 1], k duge ggi la diem Iai ghep va chia mdi c i the dugc chgn de lai ghep (ggi la cha me) thanh hai phan. Hai c i the eon dugc sinh ra bang each hoan doi phan thii hai (tfnh tii diem lai ghep) cda cic ca the cha me. Chu y rang cie ca the con sinh ra cdng phii kiem tra tfnh hgp le cda ehung gidng nhu trong qua trinh khdi tao ngau nhien.
Qua trinh lai ghep dugc thyc hien vdi moi cap cd the cda cic c i the vdi mot sac xuat Iai ghep la Pc iPc la tham sd thiet ke).
Phep todn igt bien: Sinh ngau nhien mdt sd nguyen fc trong khoing tu ll,n], fc dugc ggi la diem dot bien. Sinh ngau nhien mgt sd nguyen j thay the cho phan tii schedule]k]. Ca the con dugc sinh ra cung phii kiem tra tfnh hgp le cda chung gidng nhu trong qua trinh khdi tao ngau nhien.
Qua trinh dot bien dugc thyc hien vdi mgi c i the vdi mdt sac xuat dot bien la PmiPm ' i tham sd thiet ke).
Chgn lgc cdc cd the cho the he tiep: P ca the ed do thfeh nghi cao nhat trong cac c i the cda the he trudc, cic c i the dugc sinh ra bdi qui trinh Iai ghep va dot bien se dugc lya chgn cho the he ke tiep.
Dieu kiin dimg: Thuat toin se durng sau G the he (G li tham sd thiet ke) hoac gii tri trung binh ve do thfeh nghi cua cic c i the khdng thay doi.
Tdm lai, thuit toin di truyen cho viec lip lich dugc viet nhu sau:
Bat dau a. i = 0;
b. Khdi tao quan the ban dau Pit);
c. Tfnh do thi'ch nghi cho cie ci the thugc Pit);
d. Trong khi (dieu kien diing chua thoi man) lap i. t = t-\-l;
ii. Lya chgn P(i) tur P(i - 1);
iii. Lai ghep tren P(i) de nhan dugc Q(i);
iv. Dot bien tren P(i) de nhan dugc Rit);
V. Chgn lgc tii P(i - 1) U Qit) U P(t) de nhan dugc Pit);
e. Het lap;
Ket thuc;
3.3. Do phii'c t a p ciia t h u a t t o a n
Cic tham sd cda thuit toan GA dugc an dinh trudc khi chay, vl viy do phirc tap cda thuat toin cd the tfnh nhu sau.
TOI UU DA MUC TIEU TRONG VIEC LAP LICH 85 - Q u i trinh khdi t a o quan the ban dau la: P.Oin)
- Tfnh t o i n c i c flowtime v i makespan cho mdi ca the: Oin.m) -t 0 ( P l o g P ) - Q u i trinh lai ghep: PiP - l ) . O ( n ) = P'^.Oin).
- Qua trinh dot bien: P.Oin).
- Q u i trinh chgn Igc: 0 ( P log P ) (vl chi can sap xep)
Do vay do phu'c t a p se la: P.O(n)-|-G(P.(0(n.m)-bC)(PlogP))-bP2.(C)(ra.m)-j-PIog P-b 0 ( n ) ) + P.Oin) + O ( P l o g P ) ) = G.P'^.Oin.m)).
4. C A C K E T Q u A T H I ^ N G H I E M
Cac ket q u i t h d nghiem trinh bay d day la ket q u i trung binh cda 20 lan chay thir nghiem doc lap. C h u a n g tinh md phdng d u g c t h y c hien bang ngdn ngd C+"'' chay tren may tfnh dan cd bg vi xd Iy Intel PenlV 2.7 Ghz, RAM 1Gb.
Kich bdn m o p h 6 n g
G i i sd sd cdng viec la n = 200 va sd c i c t i i nguyen cda ludi tfnh t o i n m = 15. Chung toi cho sinh ngau nhien t i i tinh t o i n cho moi cong viec trong khoing t u 150, 200] va kich thudc dii lieu trong khoing tur 110, 30], K h i nang tfnh t o i n cda c i c tai nguyen cung dugc sinh ngiu nhien trong khoing llOOO, 2000] vdi chi phi tfnh cho viec su dung mdi don vi t i i nguyen trong khoing iL 10] v i chi phi truyen dir lieu trong khoing tir ]!, 5], Sinh ngau nhien t i i ti'nh toin dang sd dung cda mdi tai nguyen trong khoing t u 1500, 1200], Dur lieu n i y dugc giu nguyen cho t a t c i c i c md phdng trong bai,
Cac t h a m sd ciia t h u a t t o a n di t r u y e n
TVong c i c thf nghiem cda chung tdi, c i c tham sd Pc va pm dugc thiet l i p theo khuyen cao chung cda t h u a t toan di truyen dd l i Pc = 0, 02 va p ^ = 0, 6 17]. Chung tdi chgn P = 50 (kich thudc cda quan the) va G = 50 (sd the he tdi da trong qua trinh tien hoi) theo cic t i c gii trong 19].
X a c dinh t h a m s d c i i a h a m d o d o t h i c h nghi
Nhu da biet, makespan v i flowtime l i hai yeu td quan trgng cda bai t o i n lip lich, tuy nhien cic nghien ciiu t r u d e day 12 — 6] deu chi ra rang makespan la quan trgng ban flowtime, Vi vay, chung tdi chi chgn a trong khoing (0, 1) (do trgng sd cda makespan trong cdng thiic (6) la 1), Han n u a trong thi nghiem chdng toi mudn uu tien cic tham sd makespan va flowtime do vay g i i tinh t o i n tren tai nguyen va chi phi truyen t i i du lieu dugc xem nhu cac tham sd phu, cho nen chung tdi chgn ei = £2 = 0, 02 va giu nguyen trong mgi mo phdng, Vdi gii tri cda a thay doi, ket q u i md phdng d u g c d u a ra trong B i n g 1,
Bdng 1. Hieu q u i cda t h u i t toan khi gii t n a thay doi a
makespan flowtime
0,2 72,4 ^ 67723
0,3 72,41 67726
0,4 74,6 67730
0,5 75,10 67869
0,6 75,92 67932
Dya vao ket q u i t h y c nghiem, cd the thay rang vdi a < 0,4 thuat t o i n dat dugc hieu q u i tdt va on dinh. Do vay trong c i c thi nghiem so s i n h vdi cac thuat t o i n khac chung loi
8 6 TRINH THI THtJY GIANG, LE TRONG VINH, HOANG CHI THANH, NGUYEN THANH THUY c h g n a = 0, 3 . , • . • : - So s a n h h i e u q u d c d a t h u a t t o a n di t r u y e n vo'i t h u a t t o a n k h a c
Cac t i e g i i trong ]3] chi ra rang, t h u a t t o i n Simulated Annealing d a t d u g c hieu q u i cao hon c i c t h u a t t o i n Heuristics k h i c (khi chi quan t a m den g i i tri cua makespan). Do vay trong thd- nghiem nay, chung tdi chi so s i n h t h u i t t o i n d u g c de x u a t vdi t h u a t toan Simulated
Annealing d u g c md t i trong JS], Ket q u i so sich d u g c chi ra trong B i n g 2, .;
Bdng 2. So s i n h hieu q u i cda c i e t h u a t toan
Makespan Flowtime
Simulated Amiealing 74,23
68154
Genetic Algorithm 72,41
67726
Ket q u i so s i n h trong B i n g 2 chl ra rang t h u a t t o i n d u g c nghien curu trong b i i d u a ra p h u o n g i n lap lich tdt han t h u i t t o i n lap lich d y a tren simulated annealing, G i i tri cda Makespan khdng k h i c nhau nhieu, tuy nhien sy k h i e nhau cda Flowtime la r a t d i n g ke,
5. K E T L U A N V A D E X U A T
TVong bai b i o nay, chung tdi da trinh bay t h u a t t o i n di truyen cho bai toan l i p lich trong he thdng tfnh t o i n ludi. Bang viec d u a ra mot ham do do thich nghi mdi, ddng thdi quan t i m den c i c i c yeu td quan trgng: khoing thdi gian hoan t h a n h t a t cac cdng viee, tong thdi gian t h y c hien cda c i c cdng viec, gia sd dung t i i nguyen va truyen t i i du- lieu, t h u a t t o i n d u g c de x u a t d a d u a ra c i c p h u o n g i n lap lich tdt han t h u a t t o i n d u g c md ta trong 13], Dieu n i y da d u g c kiem chiirng bang c i c t h d nghiem, Tuy viy, bai b i o nay cung chua quan t i m den viec p h a t bieu hinh thurc cho c i c tham sd sii dung trong ham do do thi'ch nghi mdi.
Day la phan viec se d u g c nghien ciiu tiep tuc trong t u o n g lai. ,,,„.
T A I L I E U T H A M K H A O
11] C, Kesselman, The Grid: Blueprint for a New Computing Infrastructure, Morgan Kaufmann Publisher Inc, 2002,
12] G. Richie and J. Levine, "A fast, effective local search for scheduling independent jobs in het- erogeneous computing environments", Technical report, Centre for Intelligent Systems and their Applications, School of Informatics, University of Edinburgh, 2003.
13] A. Yarkhan and J. Dongarra, Experiments with scheduling using simulated annealing in a grid environment, Proc. of 3^'^ International Workshop on Grid Computing, USA, 2002 (232- 242).
14] A. Abraham, R, Buyya, and B, Nath, Natures heuristics for scheduling joijs on computational grids, Proc. of the S*'^ IEEE International Conference on Advanced Com.putmg and Com- munications, India, 2000,
15] V, D, Martino and M. Mililotti, Scheduling in a grid computing environment using genetic algorithms, Proc of IPDPS, USA, 2002.
TOI UU DA MUC TIEU TRONG VIEC LAP LICH 8 7 16] G. Ritchie and J. Levine, A hybrid ant algorithm for scheduling independent jobs in heteroge-
neous computing environments, Proc. of 23^ Workshop of the UK Planning and Scheduling Special Interest Group, UK, 2004.
17] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning,
Addison-Wesley Publishing Company Inc., 1997. , 18] M. Maheswaran, et al.. Dynamic mapping of a class of independent tasks onto hetergeneous
computing systems. Journal of Parallel and Distributed Computing 52 (2) (2005) 415-429.
19] Trinh Tbi Thuy Giang, Le Trong VTnh, Hoang Chf Thanh, Nguyen Thanh Thdy, Thuat toan di truyen cho viec lap lich trong he thdng tinh toan ludi. The Third National Sym.posium Fundamental and Applied Information Technology Research - FAIR2007, Nha Trang, .\ug, 2007.
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