Tối ưu đa mục tiêu trong việc lập lịch cho hệ thống tính toán lưới

Tap ch! Tin hpc va Bi'eu khien hpc, T,2.5, S.l (-2009), 79 87 TOI LTU OA MUC TIEU TRONG VIEC LAP LjCH CHO HE THONG TINH 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 Abstract 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 Tdm t a t Trong bai bao chung toi nghien ciru bai toan lap lich cac he thdng tinh toan ludi va dua mgt thuat toan di truyen de giai quyet no, Chung toi dira mot ham do thich nghi (fitness function) mdi, nham dong thdi tdi uu boa hai yeu td co ban cua bai toan lap lich ludi tinh toan, la: khoang thdi gian de hoan 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 tinh toan cda cac tai nguyen va cong viec, bai bao 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 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, 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 computing system) - la mgt tap hgp rgng ldn va khdng ddng nhat cda cic he thdng t y tri (autonomous systems) p h i n t i n ve dia ly dugc ket ndi vdi 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 nhu: tdi uu, md phdng, k h i m p h i dugc lieu, sinh hgc,.,, Trong mgt ludi tinh toin cac he thdng ty tri phii chia s^ cdng viee (job sharing) vdi Viec chia se cac cdng viec cho cac he thdng t y tri cho tai nguyen he thdng dugc sd- dung hieu q u i va cac cong viec thyc hien dugc mgt each tdi uu dugc ggi la lap lich he thdng tfnh toan ludi [1] Bai toin lap lich li mgt cic t i c vu khd khan chinh cda he thdng tfnh toin ludi vi vay nd da dugc rat nhieu nha khoa hgc quan tam Khdng gidng nhu cic bai toan lap lich he thdng phan tan truyen thdng, lirdi tfnh toan viec lap lich phuc tap ban nhieu cac dac Irinig nhu: ti'nh dgng cda he thdng, sy khdng ddng nhat ve tai nguyen va cdng vice ,, can dinrc i\\u\\\ 80 TRINH THI THUY GIANG, LE TRQNG •VTNH, HOANG CHI THANH, NGUYEN THANH THUY tam xdr Iy Bai t o i n lap lich d u g c xem xet c i hai t r u d n g hgp: tinh (static) va ddng (dynamic) Trong b i i bao chung tdi chi xem xet b i i toan d dang tinh Bai toan lap lich da d u g c chung minh la NP day dd ll] Do vay, viec sd' dung cac thuat toan heuristics Ii cich tiep can t h y e te (de facto) de giii quyet nd TVong nhurng nam qua, nhieu t i c g i i da sdr dung cac t h u a t toan heuristics k h i c de giii quyet 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, Abraham 14] sdr dung thuat toan Tabu Search, Marino 15] sdr dung thuat 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 chi quan t a m don 1^ den mgt hai yeu t d quan trgng nhat cda cdng viec lap lich mdt ludi tfnh toan dd li: cyc tieu makespan (khoing thdi gian hoin toan bd c i c cdng viec) hoac flowtime (tong thdi gian t h y e hien cda c i c cdng viec) Mat khic, de don giin c i c md hinh md phdng cie 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 thdng t y tri - cung nhu yeu eau tfnh t o i n cda cac cdng viec Dieu dan den cac t h u a t toan dugc trinh bay khd ap dung c i c he thong tinh t o i n ludi t h y c te T h u a t toan di truyen (Genetic Algorithm - GA) 17] ngoai fch Igi giim khdng gian tim kiem, hdi tu ve ldi giii toan cue, nd cdn cho phep tdi uu hda da mue tieu (multi-objectives), C i c tac gii 19] da su dung thuat toan di truyen de ddng thdi tdi uu hai yeu td flowtime va makespan viec l i p lich cho ludi tfnh t o i n Tuy nhien, nd van cdn diem yeu nhu da neu tren dd la eac van de ve gia cda t i i nguyen va chi phf truyen t i i dir lieu chua d u g c quan tam den Tiong bai b i o nay, chung tdi cung sii dung mo hinh md phdng va thuat toan di truyen, nhien g i i cda cac t i i nguyen va phf truyen t i i dir lieu se d u g c quan tam Do vay, thuat t o i n d u g c d u a ed nhieu k h i nang iing dung cac ludi tinh t o i n t h y c han c i c thuat 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) Phat bieu bai toan lap lich tong q u i t he thdng ludi tinh t o i n dudi dang hinh thirc (md hinh toan hgc), 2) Giii quyet b i i t o i n d y a vao thuat giii di truyen bang viec d u a ham 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 ludi tfnh t o i n la makespan va flowtime m a cdn quan tam den c i c yeu td phu k h i e nhu la gii sd dung tai nguyen va truyen t i i dir lieu Cac tham sd ham do thfeh nghi la c i c t h a m sd thiet ke nen ddi vdi c i c iing dung t h y c te, ehung t a cd the tiiy bien phu hgp vdi nhieu t r u d n g hgp cae mue tieu can cd su uu tien khac nhau, 3) Mgt nghien ctiu sau rgng bang mo phdng de so s i n h cie p h u o n g i n l i p lich d u a bdi thuat t o i n di truyen va thuat t o i n Simulated Annealing truyen thdng Dieu 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 danh de md hinh h o i bai toan lap lich ludi tfnh t o i n Mue d u a thuat t o i n lap lich d y a tren thuat t o i n di truyen cho ludi tfnh t o i n Myc trinh b i y c i c ket q u i t h y c nghiem Chung tdi d u a cac ket luan va ; ^ ; , TOI u u DA MUC TIEU TRONG 'VIEC LAP LICH 81 de xuat cac hudng p h i t trien Mue 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 he thdng tfnh t o i n ludi dugc biet den vdi nhieu cich thuc khac do phuc t a p cda he thdng va tfnh phan t i n cda c i c iing dung Tuy nhien, bii bao nay, chung toi chi quan t a m den bai t o i n lap lich tinh, dd cac iing dung khong phu thugc Ian Mac dd vay, nhung 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 lip lich x u a t hien nhieu ung dung thyc te TVong kieu lip lich mdi ung dung cd the dugc chia nhieu cdng viec doc lap, cac cdng viec n i y dugc gdi (rieng re) den cic he thdng t y tri ludi.de t h u c hien va tao cic ket q u i (bo phan), ket q u i cudi ciing la sy ket hgp cda cic ket q u i bg phan Chung tdi ciing chi quan t a m den kich b i n , 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 mat 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 toin (ciing dugc biet la t i i tinh toin) cda mdi tai nguyen (he thdng t y tri) 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 ETC se dugc xay dyng, mdi phan t d ETCli]lm] la thdi gian mong mudn (expected time) de tinh toin cdng viec t tai nguyen m G i i tri n i y cd the dugc tinh toin 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 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 toin { J i , J2, , J„} thao t i e tren tap dur lieu ki'ch thudc {Di,D2, , D^} Chiing t a cung gii sd la mdi cdng viec se dugc xii Iy toan bg mgt tai nguyen nhat 2) m tai nguyen (cung dugc ggi la he thdng t y tri - autonomous system) vdi k h i nang tfnh toin {Mi,M2, ,Mm} ed gii tri kinh te tuong ung la {vi,V2, ,Vm} cho moi mot dan vi tii tfnh toan va chi phf truyen thdng tren mdt dan vi du' lieu giii den cac tai nguyen la {Ci,02, ,C,n}- 3) {Tl, r2, •••, Tm} la thdi gian ma tai nguyen i se ket thuc cdng viec trudc dd (chi tii trgng da sd dung t r u d c dd) Bai toin dat la: Lap lich de he thdng tfnh toin t h y c hien t a t c i cac cdng viec cho: 1) Flowtime la cyc tieu, nghia la: r/= V ^ (1) max {T,,;, + - ^ } } 2) Makespan cyc tieu, nghia la: T^ = { Mm^ (2) 82 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)} " ' ' i(i)S{l m};ie{l n} "4) Chi phf truyen t i i du' lieu cue tieu, nghla la: C = min{ ' (3) , ' 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 j{i)e{i m} ^ (5) Mj Dieu chfnh la b i n chat cda viec can c i c he thdng tfnh toan ludi Nghia la tdng sd lugng cdng viec t h y c hien tren mgt he thdng bat ky se m a t nhieu thdi gian (din den k e t q u i d u a khdng cd gii 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 gii cda sy truyen t i i dii lieu d tren cung rat can nhan manh dd la: vi tfnh toin ludi, cie he thdng t y tri thudng dugc ndi vdi b i n g c i c mang d u d n g true tdc cao (nhu leased line), vay thdi gian truyen t i i du lieu (do tre - latency) cd the bd qua ma chi can quan t a m den chi phi d u d n g truyen 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 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 the sdng, Cac c i the t r i i qua mgt q u i trmh p h i t trien va sinh s i n de tao nhung c i t h e mdi cho the he tiep theo TVong q u i trinh tien hda nhung ca the xau (theo mot tieu chuan nao dd hay cdn ggi l i dia thich nghi vdi mdi trudng) se bi dao t h i i , Ngugc lai, nhirng c i the tdt se dugc giu lai Lien quan den giii t h u i t di truyen cd c i c khii niem sau: - Bieu dien ciia cd the: De i p dung dugc t h u i t t o i n di truyen, viec dau tien la phii tim duoc each bieu dien cda cic c i the cho mdi ca the bieu dien mdt giii phap cda bai toan dang dugc quan t i m , - Ddnh gid thich nghi Do thi'ch nghi la k h i n i n g phi^i hgp cda mdi ca t h e (giii phap) ddi vdi mdi trirdng (bai t o i n ) , Viec xay dung thich nghi cung la mot b u d c quan trong t h u i t toin di truyen De d i n h gii dugc thi'ch nghi cda c i c c i the giii t h u a t di truyen sii dung mgt ham do thieh nghi (Fitness Function) - Lai ghep: La q u i trinh tao c i the mdi d y a tren nhieu c i the da cd, ggi la cac ca the cha-me, Hai c i the dugc tao bang cich hoin doi c i c gen tii ca the cha me TOI UU DA MUC TIEU TRONG VIEC LAP LICH - Dot bien: L i qua gen cda nd, - Chon lpc vd thay nd - reproduction) cda nd TVong q u i tdt Nhurng c i the giir lai v i thfeh 83 trinh tao c i the mdi ti^r mgt c i the ban dau bang each thay doi mot sd the: Chgn lgc va thay the (ciing dugc biet nhu la q u i trinh sinh soi niy la qua trinh chgn nhirng c i the tii quan the hien tai de tao the he sau trinh dien sy d i o t h i i nhurng c i the xau, chi giur lai nhimg ca the cd thich nghi ldn han hoac bang vdi thi'ch nghi tieu chuan se dugc nghi cda cac c i the quan the se hoan thien ban sau nhieu the he, - Dieu kiin ditng: Thuat 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 thuat 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 thudng phii dinh nghia dieu kien diing cho thuat toin, 3.2 Thuat t o a n di t r u y e n t r o n g viec lap lich Nhu da trinh bay phan gidi thieu, thuat toin di truyen khdng chl giim khong gian tim kiem cda bai toan ma cdn cho phep tdi uu da mue tieu, Phan n i y t i p trung trinh bay thuat toin di truyen cho bai toan lap lich 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 thuat toan di truyen cho bai toin 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 cic sd nguyen khoing ti^r |1, m] im l i sd lugng cac tai nguyen) sa,o cho phan schedule[i] chi 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] ~ chi rang: cdng viec thu se dugc giao cho tai nguyen (he thdng) sd t h y c hien Khdi tgo qudn the ban idu: Sinh P ( P la tham 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 cic sd nguyen khoing tir den m va lan sinh thii i ii = l n) t u o n g iing vdi cic phan schedule]i] cda ca the Chu y rang sau 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 dugc vugt qua k h i nang tinh t o i n cda tai nguyen dd Hdm ip thich nghi (Fitness Functions): sau: Fk= Dinh nghia thi'ch nghi cda mdt ca the k nhu T^ + ax ^ Tl +£ix — , •-• ' ' (6) Vk -b £i X Gk dd, a, ei, £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]], TJP = max iTi-\rETGli]]schedule]{]], — 71 , (7) (8) 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 i=l Cscheduleli]- (^0) Phep todn lai ghep: Sii dung phep toan lai ghep mot diem Sinh ngau nhien mdt sd nguyen k 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) hai phan Hai ci the eon dugc sinh bang each hoan doi phan thii hai (tfnh tii diem lai ghep) cda cic ca the cha me Chu y rang cie ca the sinh cdng phii kiem tra tfnh hgp le cda ehung gidng nhu qua trinh khdi tao ngau nhien Qua trinh lai ghep dugc thyc hien vdi moi cap cd the cda cic ci 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 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 dugc sinh cung phii kiem tra tfnh hgp le cda chung gidng nhu qua trinh khdi tao ngau nhien Qua trinh dot bien dugc thyc hien vdi mgi ci 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 thfeh nghi cao nhat cac ci the cda the he trudc, cic c i the dugc sinh 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 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 thi'ch nghi cho cie ci the thugc Pit); d Trong (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 toan Cic tham sd cda thuit toan GA dugc an dinh trudc chay, vl viy phirc tap cda thuat toin cd the tfnh nhu sau 85 TOI UU DA MUC TIEU TRONG VIEC LAP LICH - Q u i trinh khdi tao 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) - Q u i trinh lai ghep: PiP - l).O(n) = -t ( P l o g P) P'^.Oin) - Qua trinh dot bien: P.Oin) - Q u i trinh chgn Igc: ( P log P ) (vl chi can sap xep) Do vay 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 ( n ) ) + P.Oin) + O ( P l o g P ) ) = G.P'^.Oin.m)) 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 Chuang tinh md phdng dugc thyc 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 n g G i i sd sd cdng viec la n = 200 va sd cic t i i nguyen cda ludi tfnh toin m = 15 Chung toi cho sinh ngau nhien t i i tinh toin cho moi cong viec khoing t u 150, 200] va kich thudc dii lieu khoing tur 110, 30], K h i nang tfnh toin cda cic tai nguyen cung dugc sinh ngiu nhien khoing llOOO, 2000] vdi chi phi tfnh cho viec su dung mdi don vi tii nguyen khoing iL 10] v i chi phi truyen dir lieu khoing tir ]!, 5], Sinh ngau nhien t i i ti'nh toin dang sd dung cda mdi tai nguyen khoing t u 1500, 1200], Dur lieu n i y dugc giu nguyen cho tat c i cic md phdng 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 cic thf nghiem cda chung tdi, cic tham sd Pc va pm dugc thiet lip theo khuyen cao chung cda thuat toan di truyen dd l i Pc = 0, 02 va p ^ = 0, 17] Chung tdi chgn P = 50 (kich thudc cda quan the) va G = 50 (sd the he tdi da qua trinh tien hoi) theo cic t i c gii 19] Xac dinh t h a m sd ciia h a m d o d o thich nghi Nhu da biet, makespan v i flowtime l i hai yeu td quan trgng cda bai toin lip lich, nhien cic nghien ciiu trude day 12 — 6] deu chi rang makespan la quan trgng ban flowtime, Vi vay, chung tdi chi chgn a khoing (0, 1) (do trgng sd cda makespan cdng thiic (6) la 1), Han nua thi nghiem chdng toi mudn uu tien cic tham sd makespan va flowtime vay gii 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 mgi mo phdng, Vdi gii tri cda a thay doi, ket q u i md phdng dugc dua Bing 1, Bdng Hieu q u i cda t h u i t toan gii t n a thay doi a makespan flowtime 0,3 0,2 72,4 ^ 72,41 67723 67726 0,4 74,6 67730 0,5 75,10 67869 0,6 75,92 67932 Dya vao ket q u i thyc nghiem, cd the thay rang vdi a < 0,4 thuat toin dat dugc hieu q u i tdt va on dinh Do vay cic thi nghiem so sinh vdi cac thuat toin khac chung loi 86 TRINH THI THtJY GIANG, LE TRONG VINH, HOANG CHI THANH, NGUYEN THANH THUY c h g n a = 0, , • • : - 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 gii ]3] chi rang, thuat t o i n Simulated Annealing d a t d u g c hieu q u i cao hon c i c thuat t o i n Heuristics k h i c (khi chi quan tam den g i i tri cua makespan) Do vay 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 dugc md t i JS], Ket q u i so sich dugc chi B i n g 2, ; Bdng So s i n h hieu q u i cda cie 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 B i n g chl rang thuat t o i n d u g c nghien curu bii d u a phuong 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 nhieu, nhien sy k h i e cda Flowtime la rat d i n g ke, 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 thuat t o i n di truyen cho bai toan l i p lich he thdng tfnh t o i n ludi Bang viec d u a mot ham 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 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 dugc de x u a t da d u a 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 13], Dieu n i y da dugc kiem chiirng bang cic t h d nghiem, Tuy viy, bai b i o cung chua quan t i m den viec phat bieu hinh thurc cho cic tham sd sii dung ham do thi'ch nghi mdi Day la phan viec se dugc nghien ciiu tiep tuc t u o n g lai ,,,„ TAI LIEU T H A M K H A O 11] C, Kesselman, The Grid: Blueprint for a New Computing Infrastructure, Publisher Inc, 2002, Morgan Kaufmann 12] G Richie and J Levine, "A fast, effective local search for scheduling independent jobs in heterogeneous 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 (232242) 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 Communications, 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 87 16] G Ritchie and J Levine, A hybrid ant algorithm for scheduling independent jobs in heterogeneous 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, Addison-Wesley Publishing Company Inc., 1997 and Machine Learning, , 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 he thdng tinh toan ludi The Third National Sym.posium Fundamental and Applied Information Technology Research - FAIR2007, Nha Trang, \ug, 2007 Nhgn bdi ngdy - - 2008 Nhdn lai sau sua ngdy 8-12 -2008 ... nguyen) sa,o cho phan schedule[i] chi 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] ~ chi rang: cdng viec thu se dugc giao cho tai nguyen... 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 thi''ch nghi cho cie ci the thugc Pit); d Trong (dieu kien diing chua... a t c i cac cdng viec cho: 1) Flowtime la cyc tieu, nghia la: r/= V ^ (1) max {T,,;, + - ^ } } 2) Makespan cyc tieu, nghia la: T^ = { Mm^ (2) 82 TRINH THI THUY GIANG, LE TRONG VINH, H O A N G