A Hybrid Meta-Heuristic Algorithm for Job Scheduling on Computational Grids

Transcription

1 verson 203. Informatca 37 (203) A Hybrd Meta-Heurstc Algorthm for Job Schedulng on Computatonal Grds Zahra Pooranan Department of Computer Engneerng, Dezful Branch, Islamc Azad Unversty, Dezful, Iran Emal: Zahra.Pooranan@gmal.com Mohammad Shojafar Department of Informaton Engneerng, Electroncs and Telecommuncaton (DIET), Sapenza Unversty of Rome, Va Eudossana 8, 0084, Rome, Italy E-mal: Shojafar@det.unroma.t Reza Tavol Department of Mathematcs, Islamc Azad Unversty, Chalous Branch (IAUC)7 Shahrvar Ave., P.O. Box , Chalous, Iran Emal: r.tavol@gmal.com Mukesh Snghal Computer Scence & Engneerng, Unversty of Calforna, Merced, CA S&E 296, USA E-mal: msnghal@ucmerced.edu Ajth Abraham Machne Intellgence Research Labs (MIR Labs), Scentfc Network for Innovaton and Research Excellence, P.O. Box 2259, Auburn, WA , USA E-mal: Ajth.Abraham@eee.org Keywords: Grd Computng, Genetc Algorthm, Gravtatonal Emulaton Local Search (GELS), Independent Task Schedulng. Receved: 25 Aprl 203 The dynamc nature of grd resources and the demands of users produce complexty n the grd schedulng problem that cannot be addressed by determnstc algorthms wth polynomal complexty. One of the best methods for grd schedulng s the genetc algorthm (GA); the smple and parallel features of ths algorthm make t applcable to several optmzaton problems. A GA searches the problem space globally and s unable to search locally. Therefore, scholars have nvestgated combnng GAs wth other heurstc methods to resolve the local search problem. Ths s the focus of the present contrbuton, where we have developed a new hybrd schedulng algorthm that combnes a GA and the gravtatonal emulaton local search (GELS) algorthm denotes GGA. The noteworthy feature of the proposed optmal scheduler s that t decreases runtme and the number of submtted tasks whose deadlnes are mssed. A comparson of the performance of our proposed jont optmal scheduler to smlar methods shows that t produces more optmal computaton tme. Povzetek: V tem prspevku smo predlagal nov skupn Umetn algortem, k se uporablja v razporejanje Mreža za neodvsne naloge. Ta prstop je bl prezkušen v več numerčnh n računske prmere. Introducton Grd computng has emerged as a new approach for solvng large-scale problems n scentfc, engneerng, and commercal felds []. A decdng factor n grd computng desgn s the purpose for whch t wll be used. Desgn goals can be dvded nto three major groups: ncreasng the effcency of an applcaton, mprovng data access, and ncreasng and mprovng servces. Grd systems can be classfed accordng to these objectves as, respectvely, grd computng systems, data grds, and servce grds. Further, grd-computng systems can be classfed nto two man categores: dstrbuted supercomputng and hghthroughput grds [2]. Data grds provde a platform for assemblng new databases from dstrbuted data sources such as dgtal lbrares or provders data warehouses. Although grd computng also needs to provde data servces, the major dfference between a data grd and grd computng s that

2 502 Informatca 37 (203) xxx yyy Z. Pooranan et al. the former provdes a specal platform to manage data storage and access for applcatons, whle n grd computng, the applcatons themselves must mplement the storage management schema. An example use for data grds s data mnng that gathers nformaton from varous sources. Two organzatons that are workng on developng large-scale data collectons are the European data grd and Globus [2]. Systems n a servce grd provde servces that cannot be provded wth a sngle machne [3]. Most research n grd computng falls under one of these classfcatons (data, computng, and servce grds). Among exstng uses of grds, grd computng s the most prevalent. By utlzng the processng power of CPUs durng ther dle perods, grd computng can be several tmes faster than what a sngle computer can acheve today. Therefore, acceptable task schedulng for resources plays a crucal role n grds, especally schedulng computng resources for tasks. The man goal of most schedulers s to fnd a balance between executon cost and the runtme for tasks. Ths means that gven a deadlne for completng executon, the runnng costs are kept low, or gven a fxed cost for executon; the necessary tme to perform the tasks wll be mnmzed. Generally, there are three methods for schedulng:. Manual schedulng. The user dvdes the tasks between dfferent resources. 2. Applcaton-mode schedulng. Applcatons perform the schedulng, wth each applcaton defnng the resources, such as MPI programs, requred for ts executon. A lst of machnes that have MPI programs s gven to the user at runtme. 3. Schedulng that s ndependent of applcatons, such as schedulng by a grd broker. Ths method s much more approprate for grd schedulng. For task processng and task analyss, applcatons delver ther requrements to the broker, based on the qualty of servce requred for ther tasks. We should note that the resources for grd task schedulng are dstrbuted n varous locatons. One or more resources are selected for runnng a task, whch s then sent to those resources. The grd scheduler has no ownershp or control over resources. Rather, tasks are delvered to local resource managers (LRMs) for executon. After that, the LRMs control the runnng status and executon of the tasks they have receved. The frst phase of grd task schedulng s resource dscovery, whch generates a lst of potental resources. The second phase ncludes gatherng nformaton about these resources and choosng the best set of resources matchng the applcaton s requrements. In the thrd phase, the task s executed, whch nvolves fle stagng and cleanup [4]. Grd systems consst of heterogeneous resources, manageral systems, polces, and applcatons wth dfferent requrements. Snce these resources are heterogeneous and dstrbuted and are used n common, grd effcency s hghly dependent on an effectve and effcent desgn for ts scheduler. Grd schedulng s consdered to be an NP-hard problem. Determnstc algorthms do not have the necessary effcency for solvng ths problem. Therefore, much research has been drected toward heurstc methods. Most of these methods attempt to mnmze makespan. Many heurstc algorthms have recently been suggested for task schedulng n grd computng, ncludng herarchcal stochastc Petr net schedulers (HSPNs) [5-8], genetc algorthms (GAs) [9], the group leaders optmzaton algorthm (GLOA) [0], smulated annealng (SA) [], the queen bee method [2], and the tabu search (TS) [3] and others [29-37]. Among these, GAs provde the best heurstc method because they are nherently parallel and can search several aspects of a problem space smultaneously. Snce the convergence of a GA s slow for global optmzaton and has been proved to be unstable n dfferent mplementatons, the effcency of GAs can be mproved by combnng them wth other algorthms such as GPSO [4] that t combnes GELS method wth PSO. Ths research combnes a GA and the gravtatonal emulaton local search (GELS) algorthm. GA s are weak for local searches and strong for global searches. Conversely, GELS s a local search algorthm that mtates gravtatonal attracton and s therefore strong for local searches and weak for global searches. Combnng the benefts of these two algorthms can solve the grd-schedulng problem. Ths paper presents a statc schedulng algorthm for schedulng ndependent tasks n a grd system. Statc schedulng means that all necessary data about tasks, resources, and the number of resources should be specfed before executon. The advantage of statc schedulng s that no overhead s exerted on the system. In addton to decreasng makespan, our proposed algorthm consders qualty of servce (QOS) to mnmze the number of tasks that mss ther deadlnes. The remander of ths paper s organzed as follows. Secton 2 brefly descrbes prevous related work and the ntellgent GA and the GELS algorthm, respectvely. Secton 3 descrbes the task-schedulng problem. Secton 4 presents our proposed algorthm n detal. Secton 5 compares our proposed algorthm wth several smlar algorthms, and Secton 6 presents our conclusons and future research drectons. 2 Related Work In the followng Secton, we provde an overvew of Genetc algorthm and GELS algorthm and explan varous methods, whch descrbe dfferent hybrd, and jont method that appled for schedulng n grd computng. 2. Genetc algorthms GAs were frst proposed n 975 by John Holland et al. [5] at Mchgan Unversty. In optmzaton methods, a GA or optmzaton nspred by nature s consdered to be the most natural evaluaton method. A GA selects the most sutable strngs from organzed stochastc nformaton that s searched and gathered by humans. In each generaton, a new set of strngs s produced based

3 A Jont Meta-Heurstc Algorthm Appled n Job Schedulng... Informatca 37 (203) on artfcal strngs wth the help of the most sutable bts and elements among the old elements. The new set s tested stochastcally, and ts strength or ftness level s evaluated. The general form of a GA s as follows: Fgure. Genetc algorthm 2.2 Gravtatonal Emulaton Local Search In 995, Voudours and hs colleagues [6] proposed the Guded Local Search (GLS) algorthm for searchng n a search space wth an NP-hard soluton. In 2004, Vebster [7] presented GLS as a strong algorthm, the GELS algorthm. GELS mmcs gravtatonal attracton for searchng wthn a search space. Each response has dfferent neghbors that can be grouped based on problem-dependent crtera. The neghbors obtaned n each neghbor group are called a dmenson. A prmary velocty s defned for each dmenson, and a dmenson wth a greater prmary velocty s more responsve for the problem. The GELS algorthm accounts for gravtatonal force n the responses n a search space through two methods. In the frst method, a response s selected from the local neghbor space of the current response and the gravtatonal force between these two responses s calculated. In the second method, the gravtatonal force s calculated usng all of the neghbor responses n a neghbor space of the current response rather than beng lmted to one response. GELS also mplements movement nto the search space wth two methods. The frst method allows movement from the current response toward the response to the current response n local neghbor spaces. The second method allows movement toward responses outsde of the current response local neghbor spaces n addton to the neghbor responses of the current response. Each of these movement methods can be used n combnaton wth each gravtaton force calculaton method, so that there are four models for the GELS algorthm. In 2007, Blachandar [8] used the GELS algorthm to solve the Travelng Salesman Problem and compared t wth other algorthms such as hll clmbng and SA. The results showed that whenever the sze of a problem s small, all algorthms perform roughly the same, but whenever the sze of the problem s large, the GELS algorthm obtans better results than the other algorthms. The algorthm begns wth a prmary response and a prmary velocty vector that conssts of a prmary velocty specfed by the user or randomly generated. After the prmary velocty vector has been examned, the responsve dmenson wth the greatest prmary velocty among the neghbor dmensons s selected for movement (select and obtan neghbor response). The algorthm uses a ponter object that can move wthn the search space. Ths object always refers to the response wth the most weght. In the frst teraton of the algorthm usng the frst method, a dmenson s selected for obtanng a neghbor response from the current response and a canddate response s selected from the local neghbor space of the current response n terms of ths dmenson. The gravtatonal force between the current and canddate responses s calculated and then added to the prmary velocty of the dmenson from whch the canddate response was obtaned. Ths s called the updated prmary velocty. In the next teraton, the prmary velocty vector s examned and a new movement drecton s selected for contnung the response search. Each teraton of the algorthm usng the second method s generally smlar to the frst method except that nstead of calculatng gravtatonal force and updatng the prmary velocty vector for just one canddate response n the current dmenson, gravtatonal force s calculated and the prmary velocty updated for each canddate response n the current dmenson. In ths algorthm, the gravtatonal force between two enttes s calculated usng Equaton (): G(CU CA) f = 2 R where CA and CU are the canddate response and current response, respectvely; G s the constant 6.672; and R s the neghbor radus of two parameters n the search space. R may be constant or can change ntellgently n each teraton. The algorthm termnates when one of the followng happens: ether the prmary velocty for all equal response dmensons (all elements of the prmary velocty vector) are equal to zero or the maxmum number of teratons of the algorthm has been reached [9]. Another parameter used n ths algorthm s the maxmum prmary velocty. Ths parameter s the maxmum value that can be used n the prmary velocty vector. The prmary velocty vector s used to select the movement drecton for obtanng a neghbor, and ths parameter prevents the move from ncreasng the prmary velocty vector elements beyond a certan lmt. In [20], the authors tred to optmze the convergence speed of a GA wth two changng ponts n the standard GA. After executng the crossover acton, f the ftness value of the produced populaton s less than the average ftness or the best ndvdual of the populaton, secondary preferental hybrdzaton or mutaton s also used after the prmary mutaton acton. Cruz-Chávez [2] proposed a hybrd genetc/annealng evolutonary algorthm for the ndependent task schedulng problem. The man purpose of ths algorthm was to fnd the soluton that mnmzes the total runtme. GAs are weak for local searches, whle SA s powerful for local searches. The authors combned these two ()

4 504 Informatca 37 (203) xxx yyy Z. Pooranan et al. methods to use both ther abltes to search the problem space. The GA ncludes a stochastc populaton generator, an eltsm selecton operator, and mutatons and crossovers wth the help of SA. Based on the ftness functon, the selecton operator selects the best half of the chromosomes n the populaton, the crossover s performed, and new chldren are produced for the next generaton. Usng a crossover leads to complete searches of the problem space. The teraton operaton used as a mutaton produces an optmzed populaton, and a better populaton s found durng the SA searchng teraton. Ths process s repeated for each generaton. It should be noted that thermal smulaton technques are performed on populatons of ndvduals who have been run off. In [22], some modfcatons of GAs are proposed to mprove schedulng effcency. These changes consst of the combnaton of the greedy algorthms, modfed crtcal path (MCP) [23] and duplcaton schedulng heurstc (DSH) [24], wth a GA to mnmze the start tme for tasks untl, n the end, makespan s mnmzed. The algorthm also uses dle processor tme. The algorthm has two ftness functons. The frst functon searches for chromosomes wth the shortest makespan and the second functon are desgned to fnd the most approprate chromosomes wth respect to load balance. In [25], a GA s presented n whch chaotc varables are used nstead of random varables for chromosome producton. Ths leads to a dstrbuton of solutons over the entre search space and avods local mnma, so that the best solutons and productons are obtaned n a shorter tme. In [26], a GA s combned wth the hll-clmbng algorthm to repar chromosomes. Ths work modfes nvald ndvduals n each generaton untl they become vald ndvduals n a new populaton. In [27], the GELS algorthm s used for resource reservaton and ndependent task schedulng, so that n the objectve functon, f one resource can t execute a task wthn ts specfed deadlne, the task s allocated to another resource for executon. Smulaton results show that ths algorthm decreases makespan compared to GAs. In prevous methods, a decrease of the entre executon tme was consdered, whle the number of tasks mssng ther deadlnes and the load balance problem were not also consdered. Our proposed algorthm tres to consder these three parameters smultaneously. Also, because a GA s weak n local searches, our proposed algorthm combnes t wth a local search algorthm to address ths weakness. A combnaton of a GA and GELS s used because GELS searches the problem space well and fnds better solutons compared to other local search algorthms such as hll-clmbng and SA. 3 Schedulng Problem Descrpton The schedulng problem for ndependent tasks s an NPhard problem that conssts of N tasks and M machnes. Each task should be consdered to be processed by each of the M machnes, so that the makespan s mnmzed. However, ths only consders one of the QOS parameters, the tme constrant, and gnores the cost. Therefore, we have ntroduced a deadlne for every task such that each task should complete ts executon before ts deadlne. Each task can be executed on only one resource and s not stopped before ts executon s complete. We use the expected tme to compute the ETC matrx model descrbed n [28]. Snce our proposed schedulng algorthm s statc, we assume that the expected executon tme for each task on each resource j has already been determned and has been set n the ETC matrx at ETC[,j]. Also, the ready tme (Ready [j]) for each machne j ndcates when j has fnshed ts prevous task. The makespan s equal to the maxmum complete tme Completon_Tme[,j] (Equaton 2): makespan=max(completon_tme[,j]) { N, j M} Completon_Tme[,j] s the tme at whch task ends on resource j and s calculated accordng to Equaton (3): Completon_Tme[,j]=Ready[j]+ETC[,j] The purpose of schedulng s to assgn tasks to resources so that the fnal makespan and the number of tasks that mss ther deadlnes are mnmzed. 4 The Proposed Method (GGA) The effcency of genetc algorthms s hghly dependent on how the chromosomes are represented. Here we use a smple method for representng chromosomes, n order to smplfy the work of the crossover and mutaton operators. Natural numbers are used for encodng the chromosomes. The numbers nsde the genes are random numbers between and M. The chromosome lengths are assumed to be task numbers. Fgure 2 shows an example of the chromosome representaton. For example, n the fgure, task 4 or T4 executes on Resource 2.. T T2 T4 T Fgure 2. Chromosome representaton Intal Populaton: The ntal populaton s created randomly. A source s selected randomly untl the task beng consdered s executed on t. Each of the chromosomes produced s assumed to be a dmenson of the problem (n fact, the problem s dmensons are just the neghbourng solutons that are obtaned by changng the current soluton). An ntal random velocty s gven to each of the problem s dmensons, rangng between one and the maxmum velocty. Frst Ftness Functon: The basc purpose of task schedulng s to mnmze makespan. Ths s the total tme requred untl all of the nput tasks complete ther executon. It should be noted that ths tme should always be less than or equal to the maxmum deadlne among all the tasks. In our proposed method for task schedulng, a (2) (3)

5 A Jont Meta-Heurstc Algorthm Appled n Job Schedulng... Informatca 37 (203) soluton s more approprate f n addton to decreasng makespan, t mnmzes the number of tasks that mss ther deadlnes. Equaton (4) calculates the frst ftness functon for each chromosome: Ft (ch) = + makespan(ch ) mss_task* MD where mss_task s the number of tasks that have mssed ther deadlnes n chromosome ch and MD s the maxmum deadlne for all tasks. As the equaton shows, when the makespan and the number of tasks mssng ther deadlnes are smaller, the ftness functon value s greater, ndcatng the more promsng chromosomes. Second Ftness functon: Wth respect to the basc purpose of task schedulng, mnmzng makespan, several chromosomes may be found that have smlar makespans but don t all balance the load among ther resources. Hence, the second ftness functon consders ths factor after obtanng solutons wth smlar makespans, to fnd the most approprate soluton wth respect to load balance. If the executon tme for resource R j s E_tme[R j ], the average executon tme (avg) for all resources s as shown n Equaton (5): avg = num_resources j = (4) E_tme[R j ] num_resources (5) where num_resources s the number of resources. The load balance for resource, Cpu_LB, can then be calculated wth Equaton (6): Cpu_LB = makespan/avg Equaton (7) shows the second ftness functon that consders the load balance: (6) Ft 2 (ch) = (7) Cpu_LB Select an Operaton: Before the mutaton and crossover operators apply, the selecton phase s frst executed. In our proposed algorthm, we use the GELS algorthm nstead of tradtonal genetc operators such as tournament, eltsm, etc. These operators provde the possblty of creatng the best solutons n each generaton, but the GELS algorthm s used to select solutons because one chromosome may not ntally have a good ftness value but turn out to be better after the mutaton and crossover operatons. Usng the GELS algorthm, the two chromosomes that have a greater prmary velocty are selected. Crossover Operator: Our proposed algorthm uses a two- pont crossover operator. Two ponts are selected randomly from chromosomes from the prevous phase. Then all of the genes wthn these two ponts of the frst and second chromosomes are removed. Mutaton Operator: A pont on each chromosome from the prevous phase s randomly selected and then changed to a random number between and M. Force Calculaton: After applyng the crossover and mutaton operatons, the gravtatonal force between the prmary chromosome and the produced chromosome are calculated as n Equaton (8). Then the gravtatonal force s added to the velocty of that dmenson. Ths leads to no copyng n the canddate populaton, f the produced chromosomes have worse ftness values than the prmary chromosomes. Ft (Canddate_ch ) 2 Force = * R Ft (Current_ch R 2 Termnatng Condtons: The algorthm termnates when the prmary velocty s equal to zero for all dmensons or the maxmum number of algorthm teratons has been reached. Algorthm shows the GGA pseudocode. Algorthm GGA Algorthm (pseudocode) Input: Tasks Populatons; Output: Scheduled tasks based on Ft and Ft2; : Generate K chromosomes to ntalze the populaton 2: Velocty_Vector [..K]=Intal velocty for each Dmenson (); 3: Whle (<=max_teraton and Velocty_Vector[...] 0) { 4: /* select current_ch and current_ch 2 such that the velocty s larger and generate two offsprng, canddate_ch and canddate_ch 2, by crossover and mutaton*/ 5: If (Ft (canddate_ch ) > Ft (current_ch ) ) current_ch = canddate_ch ; 6: If (Ft (canddate_ch 2 )> Ft (current_ch 2 )) current_ch 2 = canddate_ch 2 ; 7: Calculate gravtatonal force between canddate_ch and canddate_ch 2 usng Equaton (8) 8: Update Velocty_Vector for each dmenson by gravtatonal force of chromosome; 9: }// end whle 0: If many chromosomes wth same Ft exst Select Best chromosome usng Ft 2 ; 4. Expermental Results The GGA algorthm was mplemented usng Java software runnng under the Wn XP operatng system on a 2.66GHZ CPU wth 4GB RAM. In our proposed algorthm, we assumed that the crossover rate CR = 0.98 and the mutaton rate MR = The contents of the prmary velocty vector for the chromosomes were randomly assgned. The results of smulatons comparng GGA wth the GELS, GA, and GSA algorthms are shown n Fgures 4, 5, and 6. ) (8)

6 506 Informatca 37 (203) xxx yyy Z. Pooranan et al. 4.2 Expermental Results Here, we have tested our work on varous tasks; Generatons and dfferent ftness functon orderly. The dagram n Fgure 3 shows a number of scheduled tasks rangng between 20 and 60 allocated to 20 resources usng the comparson algorthms. As the fgure shows, when the number of tasks ncreases, the makespan ncreases as well. The dagram shows that our proposed algorthm produces a smaller makespan than the other algorthms. fewer tasks mss ther deadlnes n the GGA algorthm than n the other algorthms. Fgure 5. Comparson of the average mssed deadlne ratos for dfferent ftness functon values and algorthms. Fgure 3. Comparson of makespans Fgure 4 compares the algorthms for varous numbers of teratons. It s clear that GGA, whch s a combnaton of a globally searchng GA and the local GELS algorthm, pays more attenton to convergence velocty and optmzaton than the other algorthms, snce unlke SA, the GELS algorthm doesn t have an absolute probablty state. Fgure 4. Comparson of evolutonary process for the dfferent algorthms Fgure 5 compares the algorthms wth respect to the percentage of tasks that mss ther deadlnes. In ths dagram, the ftness value s plotted aganst the rate of tasks mssng deadlnes. As the dagram shows, whenever the ftness value ncreases, the rate of tasks mssng deadlnes decreases. Ths means that the number of tasks mssng deadlnes decreases as a result of the completon of ther makespan. The fgure shows that 5 Conclusons Ths paper presented an algorthm for solvng the grd task schedulng problem through a combnaton of a GA, whch s a global search algorthm, and the GELS algorthm, whch searches locally. The algorthm ams at mnmzng makespan as well as the number of tasks that mss ther deadlnes. Local search algorthms such as hll clmbng and SA always move to the solutons that have a better ftness functon value, and they search the problem space randomly. Although the GELS algorthm shares the specal behavour of greedy algorthms, t doesn t always move drectly to a soluton wth a better ftness functon value but rather works by examnng exstng solutons. Although the GELS algorthm uses some random elements, t doesn t always move among them n the same way, whch s why t doesn t stop wth locally optmal solutons. By combnng the advantages of the GELS algorthm and GAs, both the convergence velocty and the GA s dentfcaton of an optmal response are mproved. We compared our proposed algorthm to other algorthms, and our smulaton results showed that GGA produces smaller makespans than the other algorthms and also mnmzes the number of tasks that mss ther deadlnes. References [] J. Kołodze and F. Xhafa, Meetng securty and user behavor requrements n Grd schedulng, Smulaton Modelng Practce and Theory vol. 9, no., pp , 20. [2] W.T. Sullvan, D. Werthmer, S. Bowyer, J. Cobb, D. Gedye and D. Anderson, A new major SETI project based on Project SERENDIP data and personal computers, n Proc. of the Ffth Internatonal Conference on Boastronomy, no. 6, 997. [3] I. Foster, C. Kesselman, J. Nck and S. Tuecke, the Physology of the Grd: An Open Grd Servces Archtecture for Dstrbuted Systems Integraton, Computer, 35 (6), pp. -4, 2002.

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