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簡介：中文中文59005900字出處出處HUNOLDHUNOLDS,S,LEPPINGLEPPINGJJEVOLUTIONARYEVOLUTIONARYSCHEDULINGSCHEDULINGOFOFPARALLELPARALLELTASKSTASKSGRAPHSGRAPHSONTOONTOHOMOGENEOUSHOMOGENEOUSCLUSTERSJCLUSTERSJ20113443522011344352同類集群上并行任務(wù)圖的進(jìn)化調(diào)度同類集群上并行任務(wù)圖的進(jìn)化調(diào)度SASCHAHUNOLD，JOACHIMLEPPING摘要當(dāng)并行程序組合成較大的應(yīng)用程序時(shí)，任務(wù)圖（PTGS）出現(xiàn)，例如，科學(xué)工作流。調(diào)度這些PTGS到集群上是一個(gè)具有挑戰(zhàn)性的問題，是由于可塑性任務(wù)產(chǎn)生的并行性的附加開銷。大多數(shù)算法是基于這樣的假設(shè)并行任務(wù)的執(zhí)行時(shí)間隨著處理器的數(shù)量增加而增加。但是，這假設(shè)并不完全通用，因?yàn)槿绻幚砥鞯臄?shù)目是多的內(nèi)部使用的塊大小，并行程序的性能經(jīng)常表現(xiàn)的更好。在這篇文章中，我們介紹了EMTS算法靜態(tài)調(diào)度PTGS到集群上。我們應(yīng)用一種漸進(jìn)式的方法確定每個(gè)任務(wù)分配處理器。進(jìn)化調(diào)度策略保證了EMTS可以用于任何底層模型，用于預(yù)測可塑性任務(wù)的執(zhí)行時(shí)間?？梢钥焖僬业浇鉀Q方案的目的，EMTS考慮其它啟發(fā)式結(jié)果（例如，HCPA，MCPA）作為起始解決方案。實(shí)驗(yàn)結(jié)果表明，EMTS顯著減少PTGS的完成時(shí)間，相比其它啟發(fā)式兩個(gè)非單調(diào)和單調(diào)遞減模式。關(guān)鍵詞任務(wù)調(diào)度；并行任務(wù)；進(jìn)化算法；集群1概述科學(xué)工作流是并行任務(wù)圖的一個(gè)重要類型，并在計(jì)算網(wǎng)格上處理。許多科學(xué)工作流僅僅包含幾個(gè)并行任務(wù)。然而，正如CIRNE等人所說，提交給就是那集群的并行任務(wù)幾乎98是可塑性的。一個(gè)可塑性的任務(wù)的處理器的數(shù)量在執(zhí)行之前被確定，并且執(zhí)行期間保持不變。如果這些并行任務(wù)結(jié)合起來，并且任務(wù)圖（PTGS）出現(xiàn)。幾種算法可以表示為PTGS，如STRASSEN的矩陣乘法和快速傅里葉變換（FFT）。一個(gè)PTG的節(jié)點(diǎn)表示計(jì)算，邊表示數(shù)據(jù)或控制的以來。執(zhí)行PTG導(dǎo)致混合并行時(shí)間調(diào)度，因?yàn)楣?jié)點(diǎn)以一種數(shù)據(jù)并行的方式實(shí)現(xiàn)，獨(dú)立的任務(wù)可以同時(shí)執(zhí)行。讓我們以兩種矩陣的大小考察SCALAPACK并行矩陣乘法例程DGEMM的執(zhí)行時(shí)間，我們就可以看到，執(zhí)行時(shí)間不單調(diào)遞減，但大多數(shù)的調(diào)度算法假設(shè)單調(diào)遞減的執(zhí)行時(shí)間模型。因此，施加一個(gè)非單調(diào)遞減模型會(huì)導(dǎo)致這些算法低效的執(zhí)行。出于這個(gè)原因，我們專注于這個(gè)問題的進(jìn)化算法，我們引入算法EMTS，其可以再任意的執(zhí)行時(shí)間模型中使用。我們發(fā)現(xiàn)，EMTS相比于其他啟發(fā)式算法，23問題聲明盡我們所知，可塑性的任務(wù)PTGS調(diào)度算法是在假設(shè)一個(gè)任務(wù)的執(zhí)行時(shí)間隨處理器數(shù)量的增加而增加的基礎(chǔ)上。在這篇文章中，我們解決了如何克服這種限制的問題?？梢约僭O(shè)另一種啟發(fā)式方法，將采取一個(gè)事實(shí)，即增加一個(gè)分配也可以增加執(zhí)行時(shí)間。然而，該算法設(shè)計(jì)者會(huì)找到一個(gè)更好的大小分配。由于分配和映射步驟高度依賴于彼此，加上K個(gè)處理器，分配可能會(huì)降低相應(yīng)的任務(wù)的并行執(zhí)行時(shí)間，但是它可能同時(shí)增加整體完工時(shí)間。因此，我們希望找到一個(gè)啟發(fā)式方法，這個(gè)調(diào)度問題是獨(dú)立用來描述并行任務(wù)的運(yùn)行時(shí)間模型。為此，我們采用進(jìn)化搜索策略，但不能保證這可能克服陷入局部最優(yōu)解的問題。進(jìn)化搜索策略的主要優(yōu)點(diǎn)是（1）他們可以應(yīng)付大問題；（2）他們能夠應(yīng)用于未知搜索空間而無需得知其結(jié)構(gòu)的精確的數(shù)學(xué)模型；（3）他們能夠優(yōu)化在搜索空間開始的任意位置。缺點(diǎn)是，進(jìn)化方法傾向于慢慢收斂到最佳值，以及一個(gè)通常為沒有度量如何接近當(dāng)前結(jié)果是最佳的解決方案。雖然意識到這些特性，我們要設(shè)計(jì)一個(gè)進(jìn)化算法用于此調(diào)度問題，提供了用于計(jì)算的解決方案，并由此產(chǎn)生完工時(shí)間之間的良好平衡。由于我們通?？梢越灰讜r(shí)間的解決方案質(zhì)量，我們專注于一個(gè)特定的時(shí)間限制。3EMTS算法在本節(jié)中提出的算法是基于應(yīng)用和平臺的模型，這是在第二章提出的，在本文中，一個(gè)同構(gòu)的集群包括相同類型的計(jì)算節(jié)點(diǎn)，也就是說，相同的處理器和存儲(chǔ)器大小。此外，任務(wù)之間的通信成本沒有考慮。如果通訊或數(shù)據(jù)分布是必要的，他們需要被包含在并行任務(wù)的執(zhí)行時(shí)間模型里。31設(shè)計(jì)算法進(jìn)化可塑性任務(wù)調(diào)度算法（EMTS）利用兩個(gè)步驟解決調(diào)度問題。在第一步驟中，每個(gè)任務(wù)的分配被計(jì)算出來，而在第二步驟中，分配被映射到系統(tǒng)的處理器上。311映射方法由于并行任務(wù)的執(zhí)行時(shí)間模型對映射步驟沒有影響，我們先限定EMTS的映射函數(shù)，由于映射功能也要適應(yīng)計(jì)算所有個(gè)體，應(yīng)該盡可能地快。

簡介：EVOLUTIONARYSCHEDULINGOFPARALLELTASKSGRAPHSONTOHOMOGENEOUSCLUSTERSSASCHAHUNOLDLIGLABORATORYGRENOBLE,FRANCESASCHAHUNOLDIMAGFRJOACHIMLEPPINGROBOTICSRESEARCHINSTITUTETUDORTMUNDUNIVERSITY,GERMANYJOACHIMLEPPINGUDOEDUABSTRACTPARALLELTASKGRAPHSPTGSARISEWHENPARALLELPROGRAMSARECOMBINEDTOLARGERAPPLICATIONS,EG,SCIENTIFICWORKFLOWSSCHEDULINGTHESEPTGSONTOCLUSTERSISACHALLENGINGPROBLEMDUETOTHEADDITIONALDEGREEOFPARALLELISMSTEMMINGFROMMOLDABLETASKSMOSTALGORITHMSAREBASEDONTHEASSUMPTIONTHATTHEEXECUTIONTIMEOFAPARALLELTASKISMONOTONICALLYDECREASINGASTHENUMBEROFPROCESSORSINCREASESBUTTHISASSUMPTIONDOESNOTHOLDINPRACTICESINCEPARALLELPROGRAMSOFTENPERFORMBETTERIFTHENUMBEROFPROCESSORSISAMULTIPLEOFINTERNALLYUSEDBLOCKSIZESINTHISARTICLE,WEINTRODUCETHEEVOLUTIONARYMOLDABLETASKSCHEDULINGEMTSALGORITHMFORSCHEDULINGSTATICPTGSONTOHOMOGENEOUSCLUSTERSWEAPPLYANEVOLUTIONARYAPPROACHTODETERMINETHEPROCESSORALLOCATIONOFEACHTASKTHEEVOLUTIONARYSTRATEGYENSURESTHATEMTSCANBEUSEDWITHANYUNDERLYINGMODELFORPREDICTINGTHEEXECUTIONTIMEOFMOLDABLETASKSWITHTHEPURPOSEOFFINDINGSOLUTIONSQUICKLY,EMTSCONSIDERSRESULTSOFOTHERHEURISTICSEG,HCPA,MCPAASSTARTINGSOLUTIONSTHEEXPERIMENTALRESULTSSHOWTHATEMTSSIGNIFICANTLYREDUCESTHEMAKESPANOFPTGSCOMPAREDTOOTHERHEURISTICSFORBOTHNONMONOTONICALLYANDMONOTONICALLYDECREASINGMODELSKEYWORDSTASKSCHEDULINGPARALLELTASKSTASKGRAPHSEVOLUTIONARYALGORITHMCLUSTERIINTRODUCTIONSCIENTIFICWORKFLOWSAREANIMPORTANTTYPEOFPARALLELTASKGRAPHSANDAREOFTENPROCESSEDONCOMPUTATIONALGRIDSMANYSCIENTIFICWORKFLOWSCONTAINONLYAFEWPARALLELTASKSYET,ASCIRNEETALSTATED,ALMOST98OFPARALLELJOBSSUBMITTEDTOCOMPUTATIONALCLUSTERSAREMOLDABLE1THENUMBEROFPROCESSORSOFAMOLDABLETASKISDETERMINEDBEFOREITSEXECUTIONANDSTAYSUNCHANGEDDURINGEXECUTION2IFTHESEPARALLELTASKSARECOMBINED,APARALLELTASKGRAPHPTGARISESSEVERALALGORITHMSCANBEEXPRESSEDASPTGSSUCHASSTRASSEN’SMATRIXMULTIPLICATIONORTHEFASTFOURIERTRANSFORMATIONFFT3THENODESOFAPTGDENOTETHECOMPUTATIONSANDTHEEDGESDENOTEDATAORCONTROLDEPENDENCIESEXECUTINGAPTGLEADSTOAMIXEDPARALLELSCHEDULEASNODESAREIMPLEMENTEDINADATAPARALLELWAYANDINDEPENDENTTASKSCANBEEXECUTEDCONCURRENTLYLETUSEXAMINETHEEXECUTIONTIMEOFTHEPARALLELMATRIXMULTIPLICATIONROUTINEPDGEMMFROMSCALAPACK4FORTWOMATRIXSIZES,WHICHISSHOWNINFIGURE1ASWECANSEE,THEEXECUTIONTIMEISNOTMONOTONICALLYDECREASING,BUTMOSTSCHEDULINGALGORITHMSASSUMEAMONOTONICALLYDECREASINGMODELOFTHEEXECUTIONTIMEFORCOMPUTINGTHESCHEDULEHENCE,APPLYINGANONMONOTONICALLYDECREASINGMODELCANLEADTOINEFFICIENTDECISIONSOFTHESEALGORITHMSFORTHATREASON,WEFOCUSONTHEQUESTIONWHETHERANEVOLUTIONARYALGORITHMEAFORSCHEDULINGPTGSCANCOPEWITHIRREGULARITIESINTHEEXECUTIONTIMEMODELFORPARALLELTASKSWEINTRODUCETHEALGORITHMEMTS,WHICHCANBEUSEDWITHANARBITRARYEXECUTIONTIMEMODELWESHOWTHATEMTS,WHENCOMPAREDTOOTHERHEURISTICS,PRODUCESBETTERSCHEDULESWITHRESPECTTOTHEMAKESPANOBJECTIVETHISHOLDSFORNONMONOTONICALLYANDMONOTONICALLYDECREASINGEXECUTIONTIMEMODELSTHEPAPERISORGANIZEDASFOLLOWSSECTIONIIDETAILSTHEPROBLEMANDDISCUSSESRELATEDAPPROACHESINSECTIONIIITHEEVOLUTIONARYMETHODEMTSISPRESENTEDTHEMETHODOLOGYANDTHESETUPOFTHEEXPERIMENTSISDESCRIBEDINSECTIONIVTHEEXPERIMENTALRESULTSAREDISCUSSEDINSECTIONVANDSECTIONVIDRAWSCONCLUSIONSIIPROBLEMDESCRIPTIONANDRELATEDWORKAAPPLICATIONANDPLATFORMMODELAPTGMIXEDPARALLELAPPLICATIONCANBEREPRESENTEDBYADIRECTEDACYCLICGRAPHDAGGV,E,WHEREV{VI|I1,,V}ISASETOFNODESTHATREPRESENTTHETASKSANDE{EI,J|I,J∈{1,,V}{1,,V}}ISASETOFEDGESREPRESENTINGTASKINTERDEPENDENCIESAPTGCANBEEXECUTEDONPIDENTICALPROCESSORSINTERCONNECTEDBYANETWORK,SOTHATEACHPAIROFPROCESSORSCANCOMMUNICATEITISASSUMEDTHATTHEPARALLELTASKSAREMOLDABLE,IE,EXECUTABLEBYANARBITRARYNUMBEROFPROCESSORS1≤P≤P002005010020NUMBEROFPROCESSORSTIMES1024281632015020025NUMBEROFPROCESSORS2048162432FIGURE1PDGEMMTIMINGSONTHECRAYXT4OFLBNL2011IEEEINTERNATIONALCONFERENCEONCLUSTERCOMPUTING9780769545165/112600?2011IEEEDOI101109/CLUSTER201145344PROBLEMOFBEINGTRAPPEDINLOCALOPTIMA,BUTWHICHCANNOTBEGUARANTEEDTHEMAINADVANTAGESOFEVOLUTIONARYSEARCHSTRATEGIESARE1THEYCANCOPEWITHLARGEPROBLEMINSTANCES2THEYCANBEAPPLIEDTOANUNKNOWNSEARCHSPACEWITHOUTHAVINGAPRECISEMATHEMATICALMODELOFITSSTRUCTURE3THEYARECAPABLEOFOPTIMIZINGASOLUTIONSTARTINGANYWHEREINSEARCHSPACETHEDOWNSIDEISTHATEVOLUTIONARYAPPROACHESTENDTOCONVERGESLOWLYTOTHEOPTIMUM,ANDONEHASUSUALLYNOMEASUREOFHOWCLOSETHECURRENTRESULTISTOTHEOPTIMALSOLUTIONWHILEBEINGAWAREOFTHESEPROPERTIES,WEWANTTODESIGNANEVOLUTIONARYALGORITHMFORTHISSCHEDULINGPROBLEMTHATPROVIDESAGOODTRADEOFFBETWEENTHETIMEUSEDTOCOMPUTETHESOLUTIONANDTHERESULTINGMAKESPANSINCEWECANUSUALLYTRADETIMEFORSOLUTIONQUALITY,WEFOCUSONAGIVENTIMECONSTRAINTIIIALGORITHMEMTSTHEALGORITHMPRESENTEDINTHISSECTIONISBASEDONTHEAPPLICATIONANDPLATFORMMODELSPTG,WHICHWEREINTRODUCEDINSECTIONIIAINTHECONTEXTOFTHISARTICLE,AHOMOGENEOUSCLUSTERCOMPRISESTHESAMETYPEOFCOMPUTATIONALNODES,IE,THESAMEPROCESSORANDTHESAMEAMOUNTOFMEMORYINADDITION,COMMUNICATIONCOSTSBETWEENTASKSARENOTCONSIDEREDIFCOMMUNICATIONORDATAREDISTRIBUTIONSARENECESSARY,THEYNEEDTOBEINCLUDEDINTHEEXECUTIONTIMEMODELOFTHEPARALLELTASKSADESIGNINGTHEALGORITHMTHEEVOLUTIONARYMOLDABLETASKSCHEDULINGEMTSUTILIZESATWOSTEPAPPROACHFORSOLVINGTHESCHEDULINGPROBLEMINTHEFIRSTSTEP,THEALLOCATIONSOFEACHTASKARECOMPUTEDWHILEINTHESECONDSTEP,THEALLOCATIONSAREMAPPEDONTOTHEPROCESSORSOFTHESYSTEMMAPPINGFUNCTIONASTHEEXECUTIONTIMEMODELOFPARALLELTASKSHASNOINFLUENCEONTHEMAPPINGSTEP,WESTARTWITHDEFININGTHEMAPPINGFUNCTIONOFEMTSSINCETHEMAPPINGFUNCTIONALSOEVALUATESTHEFITNESSOFALLINDIVIDUALS,ITSHOULDBEASFASTASPOSSIBLEANDPRODUCESHORTSCHEDULESPREVIOUSWORKSHOWEDTHATALISTSCHEDULINGAPPROACHLEADSTOEFFICIENTSCHEDULES9INTHELISTSCHEDULINGALGORITHMUSEDBYEMTS,THEREADYNODESARESORTEDBYDECREASINGBOTTOMLEVELANDEACHREADYNODEVISMAPPEDTOTHEFIRSTPROCESSORSETTHATCONTAINSSVAVAILABLEPROCESSORS1THEFITNESSLEVELOFASETOFALLOCATIONSISDEFINEDASTHERESULTINGMAKESPANOFTHEPTGASMALLERMAKESPANCORRESPONDSTOABETTERFITNESSOFANEA’SINDIVIDUALALLOCATIONFUNCTIONTHEEAMODIFIESTHEPROCESSORALLOCATIONSOFTASKSANDITSGOALISTOFINDTHERIGHTALLOCATIONFOREACHTASKSOTHATTHERESULTINGFITNESSISOPTIMIZEDTHESETOFALLOCATIONSISENCODEDASINDIVIDUALIFORATASK1SVISTHEALLOCATIONSIZEOFNODEV,ANDTHEBOTTOMLEVELBLVISTHELENGTHOFTHELONGESTPATHFROMANODEVTOTHESINKOFTHEPTGINCLUDINGITSOWNEXECUTIONTIMEFIGURE2ENCODINGOFINDIVIDUALSTHEALLOCATIONSVIOFNODEVIISSTOREDATPOSITIONIVIOFPTGGJTHEINDIVIDUALIJIHOLDSTHENUMBEROFPROCESSORSALLOCATEDTOVIATPOSITIONITHUS,IJISVIFOR1≤I≤V,WHERESVIDENOTESTHECURRENTALLOCATIONOFTASKVIFIGURE2ILLUSTRATESTHISENCODINGOFTHEALLOCATIONSOFAPTGTHEDEPICTEDPTGCONTAINSFIVENODESANDEACHNODEPOSSESSESAPROCESSORALLOCATION,EG,THREEPROCESSORSAREALLOCATEDTONODE1ANINDIVIDUALISTHECOLLECTIONOFALLALLOCATIONSOFAPTGSO,THENUMBEROFPROCESSORSOFNODE1ISSTOREDATTHEFIRSTPOSITIONOFTHEINDIVIDUALTHEEAMODIFIESTHEINDIVIDUALSRANDOMLYTOOPTIMIZETHESCHEDULETHUS,THEOBJECTIVEFUNCTIONCANBEDEFINEDASFOLLOWSFORAGIVENPTGGANDFITNESSFUNCTIONFS→R,THEEATRIESTOFINDASETOFALLOCATIONSS{SV0,,SVV}THATMINIMIZESFIFWECONSIDERPTGSOFABOUT100TASKSANDAPLATFORMWITHHUNDREDSOFPROCESSORS,THESEARCHSPACETOFINDTHEBESTSOLUTIONS?ISENORMOUSNONETHELESS,EMTSMAYFINDANSWHICHISCLOSERTOS?THANTHESOLUTIONSPRODUCEDBYOTHERHEURISTICSTHISLEADSTOTWOMAINQUESTIONS1WHERESHOULDTHEEASTARTSEARCHINGORTOPUTITINANOTHERWAY,HOWSHOULDTHEORIGINALINDIVIDUALSBEINITIALIZED2HOWTOPRODUCENEWINDIVIDUALSFROMEXISTINGONESBRETRIEVINGSTARTINGSOLUTIONSTOOBTAINSTARTINGSOLUTIONS,EMTSMAKESUSEOFRESULTSPRODUCEDBYOTHERHEURISTICSINTHEPRESENTWORK,WEEXECUTETHEALLOCATIONFUNCTIONSOFMCPA11ANDHCPA10ANDENCODETHEIRRESULTSASINDIVIDUALSINTHEINITIALPOPULATIONTHESEALLOCATIONFUNCTIONSWERECHOSENBECAUSETHEYPRODUCESUFFICIENTLYGOODSOLUTIONSINASHORTAMOUNTOFTIMEADDITIONALLY,WEDESIGNEDANOTHERHEURISTICTOCREATEASTARTINGINDIVIDUALFIRST,THEBOTTOMLEVELOFEACHTASKISCOMPUTEDASSUMINGTHATEACHTASKISALLOCATEDTOONEPROCESSORHAVINGTHEBOTTOMLEVEL,EMTSDETERMINESTHECRITICALPATHOFTHEPTGTHEIDEAISTOASSIGNALLPROCESSORSOFTHESYSTEMTONODESONTHECRITICALPATHSINCESEVERALNODESONAPRECEDENCELEVELHAVESIMILAROREQUALCRITICALITYBOTTOMLEVEL,WECONSIDERSEVERALALMOSTCRITICALPATHSTOMAKETHISHEURISTICEFFECTIVEHENCE,WESEPARATETHENODESBYPRECEDENCELEVELDEPTHOFTHENODESFROMTHE346

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