A Revised Discrete Particle Swarm Optimization for Cloud Workflow Scheduling

Transcription

1 A Revsed Dscrete Partcle Swarm Optmzaton for Cloud Workflow Schedulng Zhangun Wu 1,2, Zhwe N 1, Lchuan Gu 1 1 Insttute of Intellgent Management Hefe Unversty of Technology Hefe, Chna wuzhangun@mal.hfut.edu.cn nzwgd@hfut.edu.cn gulchuan@ahan.edu.cn Xao Lu 2 2 Faculty of Informaton and Communcaton Technologes Swnburne Unversty of Technology Melbourne, Australa xlu@swn.edu.au Abstract-A cloud workflow system s a type of platform servce whch facltates the automaton of dstrbuted applcatons based on the novel cloud nfrastructure. Compared wth grd envronment, data transfer s a bg overhead for cloud workflows due to the market-orented busness model n the cloud envronments. In ths paper, a Revsed Dscrete Partcle Swarm Optmzaton (RDPSO) s proposed to schedule applcatons among cloud servces that takes both data transmsson cost and computaton cost nto account. Experment s conducted wth a set of workflow applcatons by varyng ther data communcaton costs and computaton costs accordng to a cloud prce model. Comparson s made on makespan and cost optmzaton rato and the cost savngs wth RDPSO, the standard PSO and BRS (Best Resource Selecton) algorthm. Expermental results show that the proposed RDPSO algorthm can acheve much more cost savngs and better performance on makespan and cost optmzaton. Keywords: dscrete partcle swarm optmzaton, workflow schedulng, cloud computng. I. INTRODUCTION Cloud computng s emergng as the latest dstrbuted computng paradgm and attracts ncreasng nterests of researchers n the area of Dstrbuted and Parallel Computng[1], Servce Orented Computng[2] and Software Engneerng[3]. Generally speakng, the functon of a cloud workflow system and ts role n a cloud computng envronment, s to facltate the automaton of user submtted workflow applcatons where the tasks have precedence relatonshps defned by graph-based modelng tools such as DAG (drected acyclc graph) and Petr Nets[4], or language-based modelng tools such as XPDL (XML Process Defnton Language)[17]. Among many others, one of the most mportant aspects whch dfferentate a cloud workflow system from ts other counterparts s the market-orented busness model. Such a seemed small change actually brngs sgnfcant nnovatons to conventonal computng paradgms snce they are usually based oon-busness communty models where resources are shared and free to be accessed by communty members[5]. Meanwhle, applcaton data can be hosted on dfferent storage resources at the global cloud nfrastructure. When one task needs to process data from dfferent data centers, movng the data becomes a challenge[6]. In order to effcently and cost effectvely schedule the tasks and data of applcatons among cloud servces, end user QoS-based schedulng strateges are mplemented, such as those for mnmzng makespan, mnmzng total executon cost and balancng the load of resources[7]. In ths paper, we focus on mnmzng the executon tme and the executon cost of applcatons on these resources provded by Cloud servce provders, such as Csco and Amazon. The partcle swarm method for functon optmzaton has beetroduced by Kennedy and Eberhart n[8]. The ablty of groups of some speces of anmals to work as a whole n locatng desrable postons n a gven area s smulated. It has better ablty of global searchng and has been successfully appled to many areas[9]. Ths algorthm s predomnately employed to fnd solutons for contnuous problem wthout pror nformaton. Unfortunately, workflow schedulng whch s one of a varety of NP-completes s a dscrete and very complcated optmzaton ssue. Several approaches have been developed for PSO to solve dscrete problem, such as swap operaton[10], angle modulaton[11], space transformaton[12] and prorty-based representaton [13]. Although varous dscrete PSO varants have been proposed, ther performance s generally not satsfactory when compared wth other meta-heurstcs for dscrete optmzaton [18]. More recently, set-based concept s ntroduced nto PSO to solve combnatoral optmzaton problems, such as determnng RNA secondary structure[14],travelng salesman problem (TSP) and multdmensonal knapsack problem (MKP)[15]. Ths concept has been proved to be promsng. Based on the set-based scheme, we use RDPSO to mnmze the total computaton cost of cloud workflow. The rest of ths paper s organzed as follows. Secton 2 brefly descrbes the schedulng model n workflow, and secton 3 descrbes the proposed algorthm n detal. Secton 4 shows the expermental results. Fnally, secton 5 addresses the conclusons. II. WORKFLOW TASK LEVEL SCHEDULING A. Workflow Applcaton Model A cloud workflow applcaton can commonly be modelled

2 as a Drected Acyclc Graph, denoted as ( D AG) : G ( V, A). The set of nodes V T, 1 T2,..., T n represents the tasks n the workflow applcaton; the set of arcs denotes precedence constrants and the data dependences between tasks. An arc s n the form of d, ( T, T) A where T s called the parent task of T, T s the chld task of T, d, s the data produced by T and consumed by T. We assume that a chld task cannot be executed untl all of ts parent tasks have been completed. Suppose that n tasks are to be scheduled on m servce nstances. For each task T ( 1 n) n the workflow, there are a set of canddate servce nstances 1 2 m s ( s, s,..., s ) and a set of storage stes ( 1 2 D m D D, D,..., ) avalable, where s 1 m ) represents a ( servce nstance provded by a GSP (Global Servce Provder) and m s the total number of servce nstances for T. The propertes of a servce nstance s can be represented as a group of three varables ( s g, s t, s c), n whch g stands for the GSP of s whle s t and c denote the executon tme and cost of s, respectvely. s s Fgure 1. A workflow wth 9 tasks Fgure 2. Servce nstances and data storage Fg. 1 shows a workflow applcaton wth 9 tasks, n whch the each task can be mplemented by four servce nstances. Fg. 2 shows the four servce nstances and the data storage, they are fully connected and symmetrc. B. Task level schedulng Obectves The task level schedulng manly conssts of the followng three steps: 1) Obtan the QoS constrants (n ths paper QoS constrants refer to makespan and cost. These are varyng to the user s specfc qualty preference and ther budget) for each ndvdual tasks. 2) Optmze the task-servce assgnments. In cloud data centers, the underlyng resources are vrtualzed and can be created dynamcally to sut the needs of dfferent cloud applcatons. 3) Implement the optmal schedulng plan. Based on the above three steps, a task level schedulng plan s mplemented among the cloud data centers to carry out the workflow executon wth satsfactory QoS. Meanwhle, the overall runnng cost of the cloud workflow system has also been mnmzed. There are several obectves can be measured for the mappng of workflow tasks to dstrbuted servce. In the cloud computng envronment, computaton cost s usually the frst prorty of user s concern. In ths paper, we focus not only on mnmzng the total executon cost but also on mnmzng the total makespan of the workflow applcaton. Therefore, the maor goal for our task level schedulng s to decrease the computaton cost on the condton of satsfyng the deadlne of cloud workflow applcaton by dynamcally optmzng the Task-to-Resource assgnment. Let T be the total makespan of the servce s S, T total (M ) be the total makespan (the overall completon tme) of the workflow applcaton. It s the maxmum of all the servces makespan. That s T M ) max( ) (1) total ( T s Let C exe (M ) be the total executon cost of the workflow schedulng M, C trans (M ) s the total data transmsson cost of the workflow schedulng M, C total (M) be the total computaton cost of the workflow schedulng M. The computaton cost of a schedulng conssts of the executon cost and the data transfer cost. Ctotal ( M) Cexe( M) Ctrans ( M) (2) The prce for transferrng basc data unt (e.g. per Mb) between two servces and the prce for computaton of basc tme unt (e.g. per hour) are gven by the servce provders. The cost of communcaton s applcable only when two tasks have data dependency between them. Usually, there s no data transfer charge wthn the same regon of the same servce provder. The obectve functon of ths paper can be defned as Mnmze( Ttotal ( M) Ctotal ( M)) (3) Equaton 3 ensures that all the tasks are not mapped to a sngle servce. Relatvely heavy cost wll be requred to ntally dstrbute tasks to all resources. Subsequent mnmzaton of the overall cost ensures that the total cost s mnmal even after ntal dstrbuton. For a gven assgnment M, the total cost C total (M ) for a servce s the sum of executon cost.

3 III. A. Partcle Swarm Optmzer THE PROPOSED ALGORITHM The orgnal PSO algorthm was nspred by the socal behavor of bologcal organsms. Suppose that the searchng space s D-dmensonal wth N randomly ntalzed partcles n t. Each partcle s represented by a D-dmensonal vector X (=1, 2 d) whch stands for ts locaton (x 1, x 2, x n ) n space and t s also regarded as a potental soluton. The poston of the best ndvdual of the whole swarm s noted as the global best poston P g, and the ftness of the global best poston s noted as the global best ftness F g. Then the velocty of partcle and ts new poston wll be updated accordng to the followng two equatons: n n vd ( wvd c1r1 ( pd xd ) c2r2 ( pgd xd )) (4) n xd xd vd (5) Where, d=1,2,,d; =1,2,,N; n=1,2,,ter max (ter max s the allowed largest teraton step); w s called nerta weght; c 1 and c 2 are two postve constants called acceleraton coeffcents; s a constrcton factor, whch s used to lmt the maxmum velocty; r 1 and r 2 are two random numbers unformly from the nterval [0, 1]. B. The Revsed Dscrete Swarm Model The concept of partcle swarm s orgnally desgned to fnd solutons for contnuous optmzaton problems wthout pror nformaton. To solve the workflow schedulng problem, a revsed dscrete verson of PSO (RDPSO) based on the concept of set-based s adopted n ths paper. Smlar to conventonal PSO, the key ssue of DPSO s to defne the poston and velocty of partcle as well as to defne ther operaton rules and the equaton of moton accordng to the features of dscrete varables. For the sake of clarty, varables and the rules of DPSO for solvng workflow schedulng can be depcted n defntons. In general, a mappng of workflow can be defned by a set of pars M [ T, S ]( [1, m], [1, n]). m s the number of tasks to be scheduled and n s the number of servces avalable n the cloud envronment. Defnton 1: A poston s a feasble soluton to the schedulng problem and conssts of a set of <task, servce> pars. Each par means a mappng that task s mapped onto a servce.it also ndcate that the poston of each partcle satsfes the precedence constrant between actvtes. Defnton 2: A velocty s a set wth possbltes. V { e / e) e E}, E s the set of <task, servce> pars. p ( e) [0,1], t shows the possblty of the task mappng to the servce. Defnton 3: Subtracton between two partcle postons, named as x 1 and x 2, s defned as a set of pars whch exst n x 1 but not n x 2.Ths operator also know as relatve complement or set theoretc dfference between two sets. Defnton 4: Multplcaton between random real number ' and velocty s defned as cv { e / p ( e) e E}. ', f c* e) p ( e) c* e), otherwse Defnton5: Addton of two veloctes s defned as reservaton of the larger one. V1 V2 { e / max( p1 ( e), p2( e)) e E} Defnton 6: New poston generaton s defned as a constructve procedure. The constrants between tasks must be taketo account. The <task, servce> pars n the new X can come from gbest, pbest, prevous poston or other feasble pars. RDPSO based task level Schedulng 01 swarm ntalzaton wth GRASP; 02 calculate pbest and gbest; 03 whle(stop crteron s not meted) 04 calculate V p and V g ; 05 construct the new poston x 1 ; 1: select pars from P V ) e e/ e) V ( ; 2: f x s not completed, select pars from x ; 3: else f x s not completed, select pars from other feasble pars; 06 calculate ftness value; 07 update pbest and gbest; 08 end whle; 09 return gbest; Frst, the algorthm starts wth swarm ntalzaton usng GRASP (greedy randomzed adaptve search procedure) to ensure each partcle n the ntal swarm s a feasble and effcent soluton. Then, compute the potental exemplars, pbest and gbest, for partcles to learn from whle they are movng. The stop condton can be the user s QoS requrements, such as deadlne, the budget for computaton cost or data transfer cost. The partcle s new poston generaton procedure has three steps: 1) select elements from the promsng set of pars wth larger probablty, that s, the partcle learns from gbest and pbest; 2) due to the dscrete property of schedulng, there are usually not enough feasble pars n gbest to generate new poston, so the partcle wll learn from ts prevous poston; 3) all the unmapped tasks should choose resources from other feasble pars. Ftness functon can be defned accordng to the obectves mentoned n 2.2. Fnally, gbest wll be return as optmal soluton.

4 IV. EVLUATION In ths secton we descrbe the expermental settngs, algorthm settngs, the expermental results and dscussons. A. Envronment and algorthm settngs Assume all tasks are executed on the Amazon Elastc Compute Cloud ( all the data are stored n Amazon Smple Storage Servce and data transmssons are fulflled through the Amazon Cloud Front. And assume that Servce 1 and 2 to be n US, Servce 3 n Euro and Servce 4 n APAC. Due to the varyng prce of servce, n the followng smulaton, the prce at ths moment s adopted. Cost of executon of T on Servce s $0.17 per hour (resources for hgh-cpu, on-demand nstance medum nstances, Lnux Usage). Taskcost = Tasktme * Prce. Data communcaton unt cost matrx s show Table 1. Each task has owput/output data and the sum of all data n the matrx vares accordng to the data sze we test ( M). TABLE I. COST MATRIX OF DATA COMMUNICATION ($/MB/SECOND) S 1 S 2 S 3 S 4 S S S S TABLE II. DATA INPUT/OUTPUT FOR EACH TASK (MB) T 2 T 3 T 4 T 5 T 6 T 7 T 8 T 9 nput output As for workflow, the number of total tasks ranges from 50 to 300 ncludng both workflow and non-workflow actvtes. The number of workflow segments ncrease accordngly from 5 to 50. The number of resources s constraned n the range of 3 to 20. QoS constrants ncludng tme constrant and cost constrant for each task are defned as follows: tme constrant s defned as the mean duraton plus 1.28* varance and cost constrant s defned as the trple of the correspondng tme constrant. The makespan of a workflow s defned as the latest fnshed tme on all the vrtual machnes and the total cost of a workflow s defned as the sum of task duratons multply the prces of ther allocated vrtual machnes. These settngs are much smlar to the settngs n[16]. As for RDPSO, the settngs for parameters are: Populaton sze, n=50; the constrcton factor 0.73; c1=c2= 2.0; Maxmum ftness evaluatons, me=3000; Refreshng gap, m=7; Inerta weght, wt = (1: me) * (0.7/me); Pc= *(exp (10(-1)/ (ps-1))-1)/ (exp (10)-1). B. Results and Analyss Frst, we vared the sze of total data processed by the workflow depcted n Fg.1 n the range from 64M to 2G. The total costs for dfferent data sze are compared. The data n table 3 are the computaton cost of the workflow wth the ncrease n the total data processed by the workflow. The cost obtaned by RDPSO or PSO based task-servce mappng ncreases much lower than the BRS algorthm. The man reason for two PSOs to perform better than the BRS s the way that they take communcaton costs of all the tasks, ncludng dependences between them nto account. However, the BRS algorthm calculates the cost for a sngle task at a tme, whch does not consder the mappng of other tasks n the workflow. These results n PSO based algorthm gvng lower cost of executon as compared wth BRS based algorthm. On the other hand, PSO based algorthm only consders ready tasks durng schedulng teraton and cannot get the global optmal soluton. So, RDPSO get better cost value than PSO based algorthm. TABLE III. TOTAL COST FOR DIFFERENT SIZE OF DATA Data sze(m) RDPSO PSO BRS In order to further study the optmzaton ablty among the mentoned three algorthms, more complex workflow applcatons are nvolved. Fg 3 plots the total makespan optmzaton rato of the three algorthms. From Fg 3, we can see that BRS can get around 2% optmzaton rato, PSO can acheve from 6% to 8% optmzaton rato, RDPSO can get from 10% to 17% optmzaton rato on the whole makespan. PSO does not take makespato account when t evolves; RDPSO takes not only computaton cost but also whole makespato account when t evolves. When user s requrement s specfed, complete the workflow applcaton wth the requrement constrant s very mportant, so RDPSO s more applcable n cloud envronment than PSO. We also compared the total computaton cost optmzaton rato by varyng the tasks number. The result s plotted n Fg 4. From Fg 4, we can see that both PSO and RDPSO can acheve relatvely large optmzaton rato. These two algorthms take cost nto account whle they are searchng the optmal solutons. BRS only blndly choose the best servce.

5 ACKNOWLEDGMENT The authors would lke to thank the anonymous revewers for ther valuable comments whch are helpful to mprove the presentaton of the manuscrpt. Ths work s partally supported by the Natonal Natural Scence Foundaton of Chna proect (Grant No ). Fgure 3. Fgure 4. The total makespan optmzaton rato The total computaton cost optmzaton rato On the other hand, the concluson we can draw from Fg. 4 s that when the task number of the workflow becomes large, RDPSO optmzaton rato ncreases relatvely dramatc. It means RDPSO can acheve lower cost for executng the workflow. Take an example, when the task number s 250, RDPSO can get more than 9% cost reducton whle PSO only get 6% cost reducton. So, when schedule the large scale workflow applcato cloud computng envronment, RDPSO s more promsng than PSO. V. CONCLUSION REMARKS Ths paper presents a revsed dscrete partcle swarm optmzaton algorthm to optmze the schedules of workflow applcato cloud computng envronment. In ths algorthm, the canddate soluton s presented by the set of task-servce pars, each partcle not only learns from dfferent exemplars, but also learns the other feasble pars for dfferent dmensons. The constructve poston buldng procedure guarantees each poston s feasble. Ths scheme greatly reduces the search space and enhances the algorthm performance. Based on the smulaton results, the new algorthm yelds outstandng performance on schedulng workflow applcatons n cloud envronment. REFERENCES [1] B. Raghavan, et al., "Cloud control wth dstrbuted rate lmtng," Proc. SIGCOMM 07, pp , Kyoto, Japan, [2] D. Ardagna and B. Pernc, "Adaptve servce composto flexble processes," IEEE Transactons on Software Engneerng, pp , [3] K. Bhattacharya, et al., "ICSE Cloud 09: Frst nternatonal workshop on software engneerng challenges for Cloud Computng," Proc. 31st Internatonal Conference on Software Engneerng - Companon Volume,. (ICSE-Companon 2009), pp [4] W. Van der Aalst and K. Van Hee, Workflow management: models, methods, and systems: The MIT press, [5] I. Foster, Zhao Yong, I. Racu, and S. Lu, "Cloud Computng and Grd Computng 360-Degree Compared", Proc. Grd Computng Envronments workshop, GCE '08, pp. 1-10, [6] D. Yuan, et al., "A data placement strategy n scentfc cloud workflows," Future Generaton Computer Systems, pp [7] S. Pandey, et al., "A Partcle Swarm Optmzaton-Based Heurstc for Schedulng Workflow Applcatons n Cloud Computng Envronments," n Advanced Informaton Networkng and Applcatons (AINA), 24th IEEE Internatonal Conference on, pp ,2010. [8] J. Kennedy and R. Eberhart, "Partcle swarm optmzaton," Pro. The IEEE Internatonal Conference on Neural Networks, pp , Perth, Australa, [9] D. Bratton and J. Kennedy, "Defnng a Standard for Partcle Swarm Optmzaton," n Swarm Intellgence Symposum, SIS IEEE, 2007, pp [10] M. Clerc, "Dscrete Partcle Swarm Optmzaton, llustrated by the Travelng Salesman Problem," New optmzaton technques n engneerng(sprnger), [11] G. Pampara, et al., "Combnng partcle swarm optmsaton wth angle modulaton to solve bnary problems," Proc.The IEEE Congress on Evolutonary Computaton, pp , vol.1,2005. [12] D. Sha and C. Hsu, "A hybrd partcle swarm optmzaton for ob shop schedulng problem," Computers & Industral Engneerng, pp , vol. 51,2006. [13] J. Grobler, et al., "Metaheurstcs for the mult-obectve FJSP wth sequence-dependent set-up tmes, auxlary resources and machne down tme," Annals of Operatons Research, pp. 1-32, [14] M. Neethlng and A. P. Engelbrecht, "Determnng RNA Secondary Structure usng Set-based Partcle Swarm Optmzaton," IEEE Congress on Evolutonary Computaton, BC, Canada,pp , [15] C. We-Neng, et al., "A Novel Set-Based Partcle Swarm Optmzaton Method for Dscrete Optmzaton Problems," IEEE Transactons on Evolutonary Computaton,, vol. 14, pp , [16] Z. Wu, et al., "A Market-Orented Herarchcal Schedulng Strategy n Cloud Workflow Systems," Journal of Supercomputng, Specal ssue on Advances n Network&Parallel Comptg, to be appeared,2010. [17] J. Yu and R. Buyya, "A Taxonomy of Workflow Management Systems for Grd Computng," Journal of Grd Computng, no. 3, pp , [18] X. Lu, J. Chen, Z. Wu, Z. N, D. Yuan, Y. Yang, Handlng Recoverable Temporal Volatons n Scentfc Workflow Systems: A Workflow Reschedulng Based Strategy. Proc. of 10th IEEE/ACM Internatonal Symposum on Cluster, Cloud and Grd Computng (CCGrd2010), pages , Melbourne, Australa, May 2010.