A Novel Particle Swarm Optimization Approach for Grid Job Scheduling

Transcription

1 A Novel Parcle warm Opmzaon Approach for Grd ob chedulng Hesam Izaan, Behrouz Tor Ladan, Kamran Zamanfar, Ajh Abraham³ Islamc Azad Unversy, Ramsar branch, Ramsar, Iran Deparmen of Compuer Engneerng, Unversy of Isfahan, Isfahan, Iran {Ladan, ³Norwegan Cener of Excellence, Cener of Excellence for Quanfable Qualy of ervce, Norwegan Unversy of cence and Technology, Trondhem, Norway Absrac Ths paper represens a Parcle warm Opmzaon (PO) algorhm, for grd job schedulng. PO s a populaon-based search algorhm based on he smulaon of he socal behavor of brd flocng and fsh schoolng. Parcles fly n problem search space o fnd opmal or near-opmal soluons. In hs paper we used a PO approach for grd job schedulng. The scheduler ams a mnmzng maespan and flowme smulaneously. Expermenal sudes show ha he proposed novel approach s more effcen han he PO approach repored n he leraure.. Inroducon Compuaonal Grd [] s composed of a se of vrual organzaons (VOs). Any VO has s varous resources and servces and on he bass of s polces provdes access o hem and hence grd resources and servces are much dfferen and heerogeneous and are dsrbued n dfferen geographcally areas. A any momen, dfferen resources and servces are added o or removed from grd and as a resul, grd envronmen s hghly dynamc. ervce s an mporan concep n many dsrbued compuaons and communcaons. ervce s used o depc he deals of a resource whn he grd []. Grd servces and resources are regsered whn one or more Grd Informaon ervers (GIs). The end users subm her requess o he Grd Resource Broer (GRB). Dfferen requess demand dfferen requremens and avalable resources have dfferen capables. GRB dscovers proper resources for execung hese requess by queryng n GI and hen schedules hem on he dscovered resources. Unl now a lo of wors has been done n order o schedule jobs n a compuaonal grd. Ye accordng o he new naure of he subjec furher research s requred. Cao [] used agens o schedule grd. In hs mehod dfferen resources and servces are regarded as dfferen agens and grd resource dscovery and adversemen are performed by hese agens. Buyya [] used economc based conceps ncludng commody mare, posed prce modelng, conrac ne models, barganng modelng ec for grd schedulng. As menoned n [8] schedulng s NP-complee. Mea-heursc mehods have been used o solve well nown NP-complee problems. In [0] Yarhanan and Dongarra used smulaed annealng for grd job schedulng. GAs for grd job schedulng s addressed n several wors [], [], [] and [6]. Abraham e al. [5] used fuzzy PO for grd job schedulng.

2 Dfferen crera can be used for evaluang he effcacy of schedulng algorhms and he mos mporan of whch are maespan and flowme. Maespan s he me when grd fnshes he laes job and flowme s he sum of fnalzaon mes of all he jobs. An opmal schedule wll be he one ha opmzes he flowme and maespan [5]. The mehod proposed n [5] ams a smulaneously mnmzng mae span and flowme. In hs paper, a verson of dscree parcle swarm opmzaon (DPO) s proposed for grd job schedulng and he goal of scheduler s o mnmze he wo parameers menoned above smulaneously. Ths mehod s compared o he mehod presened n [5] n order o evaluae s effcacy. The expermenal resuls show he presened mehod s more effcen and hs mehod can be effecvely used for grd schedulng. The remander of hs paper s organzed n he followng manner. In econ, we formulae he problem, n econ he PO paradgm s brefly dscussed and econ descrbes he proposed mehod for grd job schedulng, and econ 5 repors he expermenal resuls. Fnally econ 6 concludes hs wor.. Problem Formulaon GRB s responsble for schedulng by recevng he jobs from he users and queryng her requred servces n GI and hen allocang hese jobs o he dscovered servces. uppose n a specfc me nerval, n jobs {,,..., n} are submed o GRB. Also assume he jobs are ndependen of each oher (wh no ner-as daa dependences) and preempon s no allowed (hey canno change he resource hey has been assgned o). A he me of recevng he jobs by GRB, m nodes { N, N,..., N m} and servces, {,,..., } are whn he grd. Each node has one or more servces and each job requres one servce. If a job requres more han one ndependen servce, hen we can consder as a se of sub-jobs each requrng a servce. In hs paper, schedulng s done a node level and s assumed ha each node uses Frs-Come, Frs-erved (FCF) mehod for performng he receved jobs. We assume ha each node n he grd can esmae how much me s needed o perform each servce ncludes. In addon each node ncludes a me as prevous worload whch s he me requred for performng he jobs gven o n he prevous seps. We used he ETC model o esmae he requred me for execung a job n a node. In ETC model we ae he usual assumpon ha we now he compung capacy of each resource, an esmaon or predcon of he compuaonal needs of each job, and he load of pror wor of each resource. Table shows a smple example of a se of receved jobs by GRB n a specfc me nerval and saus of avalable nodes and servces n he grd. In hs Table GRB receved 5 jobs n a me nerval and he saus of avalable nodes and resources n he grd s as follows: obs :{,,,, 5} ervces {,,, } Nodes : :{ N, N, N } obs Requremens: 5 Table A smple example of a se of jobs and grd saus Nodes saus: Prevous worload N N N 6 98

3 There are servces and nodes; N ncludes 5 me uns of prevous worload whch means ha requres 5 me uns o complee he ass already submed o. Ths node requres 8 me uns o perform, 5 me uns o perform and 75 me uns o perform. nce hs node does no nclude, s no able o perform. Therefore he requred me o perform by hs node s consdered as. In hs Table job requres servce, requres, requres, requres, and 5 requres. chedulng algorhm should be desgned n a way ha each job s allocaed o a node whch ncludes he servces requred by ha job. Assume ha C, ( {,,..., m}, j {,,..., n}) s he compleon me for performng jh job n h j node and W ( {,,..., m}) s he prevous worload of N, hen Eq. () shows he me requred for N o complee he jobs ncluded n. Accordng o he aforemenoned defnon, maespan and flowme can be esmaed usng Equaons. () and () respecvely. + W C () maespan = max{ C {,,..., m} flowme = m C = + W }, () () As menoned n he prevous secon he goal of he scheduler s o mnmze maespan and flowme smulaneously.. Parcle warm Opmzaon Parcle warm Opmzaon (PO) s a populaon based search algorhm nspred by brd flocng and fsh schoolng orgnally desgned and nroduced by Kennedy and Eberhar [9] n 995. In conras o evoluonary compuaon paradgms such as genec algorhm, a swarm s smlar o a populaon, whle a parcle s smlar o an ndvdual. The parcles fly hrough a muldmensonal search space n whch he poson of each parcle s adjused accordng o s own experence and he experence of s neghbors. PO sysem combnes local search mehods (hrough self experence) wh global search mehods (hrough neghborng experence), aempng o balance exploraon and exploaon [5]. In 997 he bnary verson of hs algorhm was presened by Kennedy and Eberhar [6] for dscree opmzaon problems. In hs mehod, each parcle s composed of D elemens, whch ndcae a poenal soluon. In order o evaluae he appropraeness of soluons a fness funcon s always used. Each parcle s consdered as a poson n a D-dmensonal space and each elemen of a parcle poson can ae he bnary value of 0 or n whch means ncluded and 0 means no ncluded. Each elemen can change from 0 o and vse versa. Also each parcle has a D-dmensonal velocy vecor he elemens of whch are n range [ V max, Vmax ]. Veloces are defned n erms of probables ha a b wll be n one sae or he oher. A he begnnng of he algorhm, a number of parcles and her velocy vecors are generaed randomly. Then n some eraon he algorhm ams a obanng he opmal or near-opmal soluons based on s predefned fness funcon. The velocy vecor s updaed n each me sep usng wo bes posons, pbes and nbes, and hen he poson of he parcles s updaed usng velocy vecors.

4 Pbes and nbes are D-dmensonal, he elemens of whch are composed of 0 and he same as parcles poson and operae as he memory of he algorhm. The personal bes poson, pbes, s he bes poson he parcle has vsed and nbes s he bes poson he parcle and s neghbors have vsed snce he frs me sep. When all of he populaon sze of he swarm s consdered as he neghbor of a parcle, nbes s called global bes (sar neghborhood opology) and f he smaller neghborhoods are defned for each parcle (e.g. rng neghborhood opology), hen nbes s called local. Equaons and 5 are used o updae he velocy and poson vecors of he parcles respecvely. V ( + ) ( = wv. ( + cr ( pbes ( X ( ) + cr ( nbes ( X ( ) () ( + ) X where, ( = ( + ) f sg( V ( ) > r 0 oherwse j (5) sg ( ) = (6) ( + exp( V ( ) ( ( + ) V + ) In () X ( s jh elemen of h parcle n h sep of he algorhm and V ( s he jh elemen of he velocy vecor of he h parcle n h sep. c and c are posve acceleraon consans whch conrol he nfluence of pbes and nbes on he search process. Also r and r are random values n range [ 0, ] sampled from a unform dsrbuon. w whch s called nera wegh was nroduced by h and Eberhar [7] as a mechansm o conrol he exploraon and exploaon ables of he swarm. Usually w sars wh large values (e.g. 0.9) whch decreases over me o smaller values so ha n he las eraon ends o a small value (e.g. 0.). r j n Eq. (5) s a random number n range [ 0, ] and Eq. (6) shows sgmod funcon.. Proposed PO Algorhm for Grd ob chedulng In hs secon we propose a verson of dscree parcle swarm opmzaon for grd job schedulng. Parcle needs o be desgned o presen a sequence of jobs n avalable grd nodes. Also he velocy has o be redefned. Deals are gven wha follows.. Poson of parcles One of he ey ssues n desgnng a successful PO algorhm s he represenaon sep whch ams a fndng an approprae mappng beween problem soluon and PO parcle. In our mehod soluons are encoded n a m n marx, called poson marx, n whch m s he number of avalable nodes a he me of schedulng and n s he number of jobs. The poson marx of each parcle has he wo followng properes: ) All he elemens of he marces have eher he value of 0 or. In oher words, f X s he poson marx of h parcles, hen:

5 X (, {0,} (,, {,,... m}, j {,,..., n} (7) ) In each column of hese marces only one elemen s and ohers are 0. In poson marx each column represens a job allocaon and each row represens allocaed jobs n a node. In each column s deermned ha a job should be performed by whch node. Assume ha X shows he poson marx of h parcle. If X (, = hen he jh job wll be performed by h node. Fgure shows a poson marx n he example menoned n Table. Ths poson marx shows ha and wll be performed n N ; and 5 wll be performed n N and wll be performed n N. 5 N N N Fg.. Poson marx.. Parcles velocy, pbes and nbes Velocy of each parcle s consdered as a In oher words f V s he velocy marx of h parcle, hen: V ( max max m n marx whose elemens are n range V max, V ]. [ max, [ V, V ] (,, {,,... m}, j {,,..., n} (8) Also Pbes and nbes are m n marces and her elemens are 0 or as poson marces. pbes represens he bes poson ha h parcle has vsed snce he frs me sep and nbes represens he bes poson ha h parcle and s neghbors have vsed from he begnnng of he algorhm. In hs paper we used sar neghborhood opology for nbes. In each me sep pbes and nbes should be updaed; frs fness value of each parcle (for example han he fness value of pbes ( pbes assocaed wh X ) s esmaed and n case s value s greaer X ), pbes s replaced wh X. For updang nbes n each neghborhood, pbess are used so ha f n neghborhood fness value of pbes s greaer han nbes, hen nbes s replaced wh pbes... Parcle updang Equaon (9) s used for updang he velocy marx and hen (0) for poson marx of each parcle. V ( + ) (, = w. V (, + cr ( pbes (, X (, ) + cr ( nbes (, X (, ) (9)

6 X ( + ) (, = ( + ) = ( + ) f ( V j V j (, ) max{ (, )}), {,,... m} 0 oherwse (0) In (9) V (, s he elemen n h row and jh column of he h velocy marx n h me sep of he algorhm and X (, denoes he elemen n h row and jh column of he h poson marx n h me sep. Eq. (0) means ha n each column of poson marx value s assgned o he elemen whose correspondng elemen n velocy marx has he max value n s correspondng column. If n a column of velocy marx here s more han one elemen wh max value, hen one of hese elemens s seleced randomly and assgned o s correspondng elemen n he poson marx... Fness evaluaon In hs paper, maespan and flowme are used o evaluae he performance of scheduler smulaneously. Because maespan and flowme values are n ncomparable ranges and he flowme has a hgher magnude order over he maespan, he value of mean flowme, flowme / m, s used o evaluae flowme where m s he number of avalable nodes. The Fness value of each soluon can be esmaed usng (). fness = ( λ. maespan + ( λ). mean _ λ [0, ] flowme), () λ n () s used o regulae he effecveness of parameers used n hs equaon. The greaer λ, more aenon s pad by he scheduler n mnmzng maespan and vse versa. The smaller maespan and flowme n (), he graer fness value, and hence a beer soluon s regarded..5. Proposed PO algorhm The pseudo code of he proposed PO algorhm s saed as follows: Creae and nalze a m n -dmensonal swarm wh P parcles repea for each parcle =,,P do f f ( X ) > f ( pbes ) hen // f( ) represen he fness funcon pbes = X ; end f f pbes ) > f ( nbes ) hen ( nbes = pbes ; end end for each parcle =,,P do updae he velocy marx usng Eq. (9) updae he poson marx usng Eq. (0) end unl soppng condon s rue; Fg.. Pseudo code of he proposed mehod

7 5. Implemenaon and Expermenal Resuls In hs econ, he proposed algorhm s compared o he mehods presened n [5]. Boh approaches were mplemened usng VC++ and run on a Penum IV. GHz PC. In he prelmnary expermen he followng ranges of parameer values were esed: λ = [0, ], c and c = [, ], w = [. 0.0], P = [0, 0], V max = [5, 50], and maxmum eraons = [ 0 m, 00 m] n whch m s he number of nodes. Based on expermenal resuls he proposed PO algorhm performs bes under he followng sengs: λ =0.5, c = c =. 5, w = , P = 8, V max = 0, and maxmum eraon = 00 m. 5.. Comparson of resuls wh he mehod proposed n [5] Abraham e al. [5] used Fuzzy dscree parcle swarm opmzaon [] for grd job schedulng. In her mehod, he poson of each parcle s presened as m n marces n whch m s he number of avalable nodes and n s he number of receved jobs. Each marx represens a poenal soluon whose elemens are n [0, ] nervals n whch he oal sum of he elemens of each column s equal o. The value of s, he elemen n h row and jh column of he poson marx, means he degree of j membershp ha he grd node N j would process he job n he feasble schedule soluon [5]. In he frs me sep of he algorhm one poson marx s generaed usng LFR-FR heursc [6] ha mnmzes he maespan and he flowme smulaneously and ohers are generaed randomly and hen n each me sep hese marces are updaed usng velocy marx whose elemens are real numbers n range [ V max, Vmax ]. Afer updang each poson marx, s normalzed n a way ha each elemen s n range [0, ] and he sum of values of each column equals and hen usng hese obaned marces schedules are generaed. In hs paper, for comparson and evaluaon of he scheduler, maespan and mean flowme are used smulaneously. A random number n he range [ 0, 500], sampled from unform dsrbuon, s assgned o he prevous worload of each node n our ess. One or more servces (a mos servces) of {,,..., } are randomly seleced for each node. The me for execung servces s randomly seleced n range [, 00] f he node has hese servces; oherwse s seleced as. For each job one servce among servces s seleced randomly as he requred servce of ha job. To mprove he effcency of our proposed mehod and he mehod presened n [5] we generae only feasble soluons n nal sep as well as each eraon/generaon. In oher words each job s allocaed o he node whch has he servce requred by ha job. If n grd here s a job ha s correspondng servce does no exs n any of he nodes, hen s allocaed node s consdered as - and hs means ha hs job s no performable n he grd a ha specfc me. In hs case, he requred me for performng he job, s no aen no accoun n fness esmaon so ha he effcency of he mehod does no fade. Nne grd saus of dfferen szes wh number of jobs, n=50, 00, 00 number of nodes, m=0, 0, 0 and number of servces, =0, 80, 60 are generaed. The sascal resuls of over 50 ndependen runs are llusraed n Table.

8 Case udy Grd saus: Number of (obs, Nodes, ervces) Table Comparson of sascal resuls beween our proposed mehod and FDPO proposed n [5] LFR-FR Number of FPO [5] Proposed DPO heursc eraons: (00 m ) maespan flowme maespan flowme maespan flowme I (50,0,0) II (00,0,80) III (00,0,60) IV (50,0,0) V (00,0,80) VI (00,0,60) VII (50,0,0) VIII (00,0,80) IX (00,0,60) As evden, he proposed mehod performs beer han he Fuzzy PO proposed n [5]. Fgures and show a comparson of CPU me requred o acheve resuls and he fness values of each mehod for dfferen case sudes as shown n Table. Tme (seconds) FPO [5] DPO (proposed) I II III IV V VI VII VIII IX Case sudy Fg.. Comparson of convergence me beween our proposed mehod and FPO [5]. Fness value (Eq.) FPO [5] DPO (proposed) I II III IV V VI VII VIII IX Case udy Fg.. Comparson of fness values beween our proposed mehod and FPO [5]. 6. Conclusons Ths paper presened a verson of Dscree Parcle warm Opmzaon (DPO) algorhm for grd job schedulng. cheduler ams a generang feasble soluons whle mnmzng maespan and flowme smulaneously. The performance of he proposed mehod was compared wh he fuzzy PO hrough carryng ou exhausve smulaon ess and dfferen sengs. Expermenal resuls show ha he proposed mehod ouperforms fuzzy PO. In he fuure, we plan o use he proposed mehod for grd job schedulng wh more qualy of servce consrans.

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