A GENETIC ALGORITHM FOR PROCESS SCHEDULING IN DISTRIBUTED OPERATING SYSTEMS CONSIDERING LOAD BALANCING

Transcription

1 A GENETIC ALGORITHM FOR PROCESS SCHEDULING IN DISTRIBUTED OPERATING SYSTEMS CONSIDERING LOAD BALANCING M. Nkravan and M. H. Kashan Department of Electrcal Computer Islamc Azad Unversty, Shahrar Shahreqods Branch Tehran, Iran E-mal: KEY WORDS Dstrbuted systems, schedulng, genetc algorthm, smulated annealng, load balancng. ABSTRACT Ths paper presents and evaluates a new method for process schedulng n dstrbuted systems. Schedulng n dstrbuted operatng systems has a sgnfcant role n overall system performance and throughput. An effcent schedulng s vtal for system performance. The schedulng n dstrbuted systems s known as an NPcomplete problem even n the best condtons, and methods based on heurstc search have been proposed to obtan optmal and suboptmal solutons. In ths paper, usng the power of genetc algorthms we solve ths problem consderng load balancng effcently. We evaluate the performance and effcency of the proposed algorthm usng smulaton results. INTRODUCTION Schedulng n dstrbuted operatng systems s a crtcal factor n overall system effcency. A Dstrbuted Computng system (DCS) s comprsed of a set of Computers (Processors) connected to each other by communcaton networks. Process schedulng n a dstrbuted operatng system can be stated as allocatng processes to processors so that total executon tme wll be mnmzed, utlzaton of processors wll be maxmzed, and load balancng wll be maxmzed. Process schedulng n a dstrbuted system s done n two phases: n the frst phase processes are dstrbuted on computers, and n the second processes executon order on each processor must be determned.process schedulng n dstrbuted systems has been known to be NP-complete. Several methods have been proposed to solve schedulng problem n DCS. The proposed methods can be generally classfed nto three categores: Graphtheory-based approaches [23], mathematcal modelsbased methods [24], and heurstc Technques [2, 6, 8, 2]. Heurstcs can obtan suboptmal soluton n ordnary stuatons and optmal soluton n partculars. Snce the schedulng problem has been known to be NP-complete, usng heurstc Technques can solve ths problem more effcently. Three most well-known heurstcs are the teratve mprovement algorthms [3],the probablstc optmzaton algorthms, and the constructve heurstcs. In the probablstc optmzaton group, GA-based methods [,4,5,,3,4,7] and smulated annealng [2,20] are consderable whch extensvely have been proposed n the lterature. One of the crucal aspects of the schedulng problem s load balancng. Whle recently created processes randomly arrve nto the system, some processors may be overloaded heavly whle the others are under-loaded or dle. The man objectves of load balancng are to spread load on processors equally, maxmzng processors utlzaton and mnmzng total executon tme [2]. In dynamc load balancng, processes must be dynamcally allocated to processors n arrval tme and obtan a near optmal schedule, therefore the executon of the dynamc load balancng algorthm should not take long to arrve at a decson to make rapd task assgnments. [9,5,6,9,22] have proposed schedulng algorthms consderng load balancng. A GA starts wth a generaton of ndvduals, whch are encoded as strngs known as chromosomes. A chromosome corresponds to a soluton to the problem. A certan ftness functon s used to evaluate the ftness of each ndvdual. Good ndvduals survve after selecton accordng to the ftness of ndvduals. Then the survved ndvduals reproduce offsprng through crossover and mutaton operators. Ths process terates untl termnaton condton s satsfed [0]. GA-based algorthms have emerged as powerful tools to solve NPcomplete constraned optmzaton problems, such as travelng salesman problem, job-shop schedulng and flow-shop schedulng, machne learnng, VLSI technology, genetc synthess and etc [3, 7]. In ths paper usng the power of genetc algorthms we solve ths problem consderng load balancng effcently. The proposed algorthm maps each schedule wth a chromosome that shows the executon order of all exstng processes on processors. The fttest chromosomes are selected to reproduce offsprng; chromosomes whch ther correspondng schedules have less total executon tme, better load-balance and processor utlzaton. We assume that the dstrbuted system s non-unform and non-preemptve, that s, the processors may be dfferent, and a processor completes current process before executng a new one. The load- Proceedngs 2st European Conference on Modellng and Smulaton Ivan Zelnka, Zuzana Oplatková, Alessandra Orson ECMS 2007 ISBN / ISBN (CD)

2 balancng mechansm used n ths paper only schedule processes wthout process mgraton and s centralzed. The remander of ths paper s organzed as follows: The problem descrpton and formulaton s gven n Secton 2, In Secton 3, we descrbe the proposed algorthm. Secton 4, gves the performance evaluaton of the proposed algorthm n comparson wth other smlar algorthms. Secton 5 concludes ths research. PROBLEM DESCRIPTION AND FORMULATION In order to schedule the processes n a dstrbuted system, we should know the nformaton about the nput processes and dstrbuted system tself such as : Network topology, processors speed, communcaton channels speed and so on. Snce we study a determnstc model, a dstrbuted system wth m processors, m > should be modeled as follows: P ={ p, p2, p3,..., p m } s the set of processors n the dstrbuted system. Each processor can only execute one process at each moment, a processor completes current process before executng a new one, and a process can not be moved to another processor durng executon. R s an m m matrx, where the element ruv u, v m of R, s the communcaton delay rate between pu and pv. H s an m m matrx, where the element huv u, v m of H, s the tme requred to transmt a unt of data from pu to pv. It s obvous that h uu = 0 and r uu = 0. {, 2, 3,..., n} s the set of processes to execute. A s an n m matrx, where the element a j n, j m of A, s the executon tme of process t on processor p j.in homogeneous dstrbuted systems the executon tme of an ndvdual process t on all processors s equal, that means : n a = a 2 =... = a m. D s a lnear matrx, where the element d n of D, s the data volume for process t to be transmtted, when process t s to be executed on a remote processor. F s a lnear matrx, where the element f n of F, s the target processor that s selected for process t to be executed on. C s a lnear matrx, where the element c n of C, s the processor that the process t s presented on just now. The problem of process schedulng s to assgn for each process t T a processor f P so that total executon tme wll be mnmzed, utlzaton of processors wll be maxmzed, and load balancng wll be maxmzed. In such systems there are fnte numbers of processes, each havng a process number and a executon tme and placed n a process pool from whch processes are assgned to processors. The man objectve s to fnd a schedule wth mnmum cost. The followng defntons are also needed: Defnton The processor load for each processor s the sum of processes executon tmes allocated to that processor. However, as the processors may not always be dle when a chromosome (schedule) s evaluated, the current exstng load on ndvdual processors must also be taken nto account, therefore (): Load( p ) = Defnton 2 No. of allocated processes on processor j= a j, + No. of New Assgned processes to processor. k = maxspan( T) = max Number of a k, ( Load( p )) () The length or maxspan of a schedule T s the maxmal fnshng tme of all processes or maxmum load. Also communcaton cost (CC) to spread recently created processes on processors must be computed (2,3) : CC T Pr ocessors (2) ( number of new processes ) = ( rc f + h c f = d ) (3) Defnton 3 The Processor utlzaton for each processor s obtaned by dvdng the sum of processng tmes by maxspan, and the average of processors utlzaton s obtaned by dvdng the sum of all utlzatons by number of processors (4, 5): Load ( p U p ) ( ) = max span (4) No of processors AveU = ( U ( p )) = (5) Defnton 4 Number Of Pr ocessors Number of Acceptable Processor Queues (NoAPQ): We must defne thresholds for lght and heavy load on processors. If the processes completon tme of a processor (by addng the current system load and those contrbuted by the new processes) s wthn the lght and heavy thresholds, ths processor queue wll be acceptable. If t s above the heavy threshold or below the lght-threshold, then t s unacceptable, but what s mportant s average of number of acceptable processors queues, whch s achevable by (6): AveNoAPQ = NoAPQ Number Of Pr ocessors (6)

3 Defnton 5 A Queue assocated wth every processor, shows the processes that processor has to execute. The executon order of processes on each processor s based on queues. THE PROPOSED GA-BASED ALGORITHM Genetc algorthms, as powerful and broadly applcable stochastc search and optmzaton technques, are the most wdely known types of evolutonary computaton methods today. In general, a genetc algorthm has fve basc components as follows [3]:. An encodng method, that s a genetc representaton (genotype) of solutons to the program. 2. A way to create an ntal populaton of ndvduals (chromosomes). 3. An evaluaton functon, ratng solutons n terms of ther ftness, and a selecton mechansm. 4. The genetc operators (crossover and mutaton) that alter the genetc composton of offsprng durng reproducton. 5. Values for the parameters of genetc algorthm. Genotype In the GA-Based algorthms each chromosome corresponds to a soluton to the problem. The genetc representaton of ndvduals s called Genotype. Many Genotypes have been proposed n [3].In ths paper a chromosome conssts of an array of n dgts, where n s the number of processes. Indexes show process numbers and a dgt can take any one of the..m values, whch shows the processor that the process s assgned to. If more than one process s assgned to the same processor, the left to-rght order determnes ther executon order on that processor. Intal Populaton A genetc algorthm starts wth a set of ndvduals called ntal populaton. Most GA-Based algorthms generate ntal populaton randomly. Here, each soluton s generated as follows: one of the unscheduled processes s randomly selected, and then assgned to one of the processors. The mportant pont s the processors are selected crcularly, t means that they are selected respectvely form frst to last and then come back to frst. Ths operaton s repeated untl all of processes have been assgned. An ntal populaton wth sze of POPSIZE s generated by repeatng ths method. Ftness Functon As dscussed before, the man objectve of GA s to fnd a schedule wth optmal cost whle load-balancng, processors utlzaton and cost of communcaton are consdered. We take nto account all objectves n followng equaton. The ftness functon of a Schedule T (7): ftness( T ) = ( 7 ) ( γ AveU ) ( θ AveNoAPQ) ( α max span( T )) ( β CC( T )) Whch 0 < α, β, γ, θ are control parameters to control effect of each part accordng to specal cases and ther default value s one. Ths equaton shows that a ftter soluton (Schedule) has less maxspan, less communcaton cost, hgher processor utlzaton and hgher Average number of acceptable processor queues. Selecton The selecton process used here s based on spnnng the roulette wheel, whch each chromosome n the populaton has a slot szed n proporton to ts ftness. Each tme we requre an offsprng, a smple spn of the weghted roulette wheel gves a parent chromosome. The probablty p that a parent T s selected s gven by (8): F( T ) P = POPSIZE ( 8 ) F( T ) j= j where F( T ) s the ftness of chromosome T. Crossover Crossover s generally used to exchange portons between strngs. Several crossover operators are descrbed n the lterature [0]. Crossover s not always affected, the nvocaton of the crossover depends on the probablty of the crossover Pc. We have mplemented two crossover operators. The GA uses one of them, whch s decded randomly. Sngle-Pont Crossover Ths operator randomly selects a pont, called Crossover pont, on the selected chromosomes, then swaps the bottom halves after crossover pont, ncludng the gene at the crossover pont and generate two new chromosomes called chldren. Proposed Crossover Ths operator randomly selects ponts on the selected chromosomes, then for each chld non-selected genes are taken from one parent and selected genes from the other. Mutaton Mutaton s used to change the genes n a chromosome. Mutaton replaces the value of a gene wth a new value from defned doman for that gene. Mutaton s not always affected, the nvocaton of the Mutaton depend on the probablty of the Mutaton Pm. We have mplemented two mutaton operators. The GA uses one of them, whch s decded randomly.

4 Frst Mutaton Operator Ths operator randomly selects two ponts on the selected chromosome, then generates a chromosome by swappng the genes at the selected ponts. Second Mutaton Operator The other approach s to check f any jobs could be swapped between processors whch would result n a lower make span. If we want to test every possble swap, t would be computatonally very ntensve, and n larger problems would take an unfeasble amount of tme. It also seems unreasonable to consder swappng processes on processors whch ther load s sgnfcantly below the make span, therefore we try to swap processes between overloaded and under loaded processors. Ths concept can be mplemented as follows:. Frst, select a processor, say, whch has the latest fnsh tme. 2. Second, select a processor, say p u, whch has least fnsh tme. 3. Thrd, try to transfer a process form p to p or swap a sngle par of processes between and p u that mproves the make span of both processors the most. 4. Ths procedure s repeated untl no further mprovement s possble. Replacement Strategy When genetc operators (crossover, mutaton) are appled on selected parents T, T2 two new chromosomes T' and T'' are generated. These chromosomes are added to new temporary populaton. By repeatng ths operaton a new temporary populaton wth sze of 2*POPSIZE s generated. After that ftter chromosomes are selected from current populaton and new temporary populaton, at last selected chromosomes made new populaton and algorthm restarts. Termnaton Condton We can apply multple choces for termnaton condton: Max number of generaton, algorthm convergence, equal ftness for fttest selected chromosomes n respectve teratons. The Structure of Proposed GA-Based Algorthm Our proposed GA-Based algorthm starts wth a generaton of ndvduals. A certan ftness functon s used to evaluate the ftness of each ndvdual. Good ndvduals survve after selecton accordng to the ftness of ndvduals. Then the survved ndvduals reproduce offsprng through crossover and mutaton operators. Ths process terates untl termnaton condton s satsfed. It s Consderable to say that p v v p v u parameters such as P c, P m, POPSIZE, NOGEN, α, β, γ, θ must be determned before GA s started. Fgure shows ths operaton. Procedure GA-Based algorthm; Begn ntalze P(k); {create an ntal populaton} evaluate P(k); {evaluates all ndvduals n the populaton} Repeat For = to 2*POPSIZE do Select two chromosomes as parent and parent 2 from populaton; Chld and Chld 2 Crossover( parent, parent2); Chld Mutaton ( Chld ); Chld 2 Mutaton ( Chld 2 ); Add (new temporary populaton, Chld, Chld 2 ); End For; Make (new populaton, new temporary populaton, populaton ); Populaton = new populaton; Whle (not termnaton condton); Select Best chromosome n populaton as soluton and return t; End Fgure : The Structure Of Proposed Algorthm EXPERIMENTAL RESULTS In ths secton, we have used the smulaton results to show the performance of the proposed GA-based algorthm. Current soluton technques are concentrated on schedulng tasks wth precedence constrants so our approach s not completely comparable wth them. We have mplemented more than 3000 lnes of C++ program to smulate all of the proposed algorthms. All smulaton experments are run on a Pentum III 800, 256 MB RAM, IBM PC. We have tred dfferent values of the populaton sze ( POPSIZE), mutaton Probablty (Pm ),and crossover probablty ( Pc ),to fnd whch values would steer the search towards the best soluton. The measurement of performance of these algorthms was based on three metrcs: total completon tme, average processor utlzaton and, cost of communcaton. The default parameters were vared and the results collected from test runs were used to study the effects of changng these parameters. Changng The Number of Processes We have studed the effect of ncreasng number of processes on total completon tme and average processor utlzaton. The Obtaned results are shown n Fgure 2 and, Fgure 3. A consderable pont n Fgure 3 s that when number of processes s ncreased, hgher utlzaton s obtaned. Bref justfcatons for the values used are gven below. When the values dscussed were tested base values for each of the parameters where used to help solate the performance of the parameter n

5 hand. These values were: Pc=0.9, Pm=0., POPSIZE=50, NOGEN=50, m=0 (number of processors), n= Fgure5: Average Processor Utlzaton Fgure 2: Total Completon Tme Fgure 6: Cost Of Communcaton Fgure 3: Average Processor Utlzaton Changng The Number of Generatons When the number of generatons was ncreased our proposed algorthm had a better functon. The Obtaned results are shown n Fgure 4, Fgure 5 and, Fgure 6. Whle the number of generatons was ncreased the total completon tme was reduced, t s because the qualty of the generated process assgnment mproves after each generaton. A consderable pont n these fgures s that when the number of generatons was ncreased hgher utlzaton s obtaned and, the cost of communcaton was decreased. Bref justfcatons for the values used are gven below. These values were: Pc=0.9, Pm=0., POPSIZE=00, NOGEN=50 245, m=0 (number of processors), n=300 (number of processes). Changng The Sze of Populaton Changng the sze of populaton s also consderable n terms of total completon tme, processor utlzaton and, cost of communcaton. The Obtaned results are shown n Fgure 7, Fgure 8 and, Fgure 9. Whle the sze of populaton was ncreased the total completon tme was decreased and, average processor utlzaton was ncreased. t s because that the number of the ftter chromosomes whch are able to survve was ncreased, therefore ftter offsprng may be generated and t leads to better schedules. Accordng to above results whle the sze of populaton was ncreased hgher processor utlzaton obtaned and the cost of communcaton was decreased. Bref justfcatons for the values used are gven below. Pc=0.9, Pm=0., POPSIZE=50 50, NOGEN=50, m=0 (number of processors), n=300 (number of processes). Fgure 4: Total Completon Tme Fgure 7: Total Completon Tme

6 Fgure 8: Average Processor Utlzaton CONCLUTIONS Fgure 9: Cost Of Communcaton Schedulng n dstrbuted operatng systems has a sgnfcant role n overall system performance and throughput. The schedulng n dstrbuted systems s known as an NP-complete problem even n the best condtons. We have presented and evaluated new GA- Based method to solve ths problem. Ths algorthm consders mult objectves n ts soluton evaluaton and solves the schedulng problem n a way that smultaneously mnmzes maxspan and communcaton cost, and maxmzes average processor utlzaton and load-balance. Most exstng approaches tend to focus on one of the objectves. Expermental results prove that our proposed algorthm tend to focus on all of the objectves smultaneously and optmze them. REFERENCES [] W.Yao, J.Yao, & B.L, Man Sequences Genetc Schedulng For Multprocessor Systems Usng Task Duplcaton, Internatonal Journal of Mcroprocessors and Mcrosystems, 28, 2004, [2] G.L.Park, Performance Evaluaton of a Lst Schedulng Algorthm In Dstrbuted Memory Multprocessor Systems, Internatonal Journal of Future Generaton Computer Systems 20, 2004, [3] A.T. Haghghat, K. Faez, M. Dehghan, A. Mowlae, & Y. Ghahreman, GA-based heurstc algorthms for bandwdthdelay-constraned least-cost multcast routng, Internatonal Journal of Computer Communcatons 27, 2004, 27. [4] M. Moore, An Accurate and Effcent Parallel Genetc Algorthm to Schedule Tasks on a Cluster, Proceedngs of the IEEE Internatonal Parallel and Dstrbuted Processng Symposum, [5] V. D. Martno, Sub Optmal Schedulng n a Grd usng Genetc Algorthms, Proceedngs of the IEEE Internatonal Parallel and Dstrbuted Processng Symposum, [6] C.I.Park, & T.Y.Choe, An optmal schedulng algorthm based on task duplcaton, IEEE Trans. on Computers, 5(4), 2002, [7] A.T. Haghghat, K. Faez, M. Dehghan, A. Mowlae, & Y. Ghahreman, Multcast routng wth multple constrants n hgh-speed networks based on genetc algorthms, In ICCC 2002 Conf., Inda, 2002, [8] A.Y.Zomaya, & Y.Teh, Observatons on Usng Genetc Algorthms for Dynamc Load-Balancng, IEEE Trans.On Parallel and Dstrbuted Systems, 2( 9), 200, [9] K.Quresh, and M.Hatanaka, A Practcal Approach of Task Schedulng and Load Balancng on Hetrogeneous Dstrbuted Raytracng Systems, Informaton Processng Letters 79, 200, [0] L.M.Schmtt, Fundamental Study Theory of Genetc Algorthms, Internatonal Journal of Modellng and Smulaton Theoretcal Computer Scence 259, 200, 6. [] A.Y.Zomaya, C.Ward, & B.Macey, Genetc Schedulng for Parallel Processor Systems: Comparatve Studes and Performance Issues, IEEE Trans. On Parallel and Dstrbuted Systems, 0(8), 999, [2] S. Salleh, & A.Y. Zomaya, Schedulng n Parallel Computng Systems: Fuzzy and Annealng Technques, Kluwer Academc, 999. [3] M.Ln, & L.T.Yang, Hybrd Genetc Algorthms for Schedulng Partally Ordered Tasks n a Mult-processor Envronment, Proc. of the 6 th IEEE Conf. on Real-Tme Computer Systems and Applcatons, 999, [4] Sung-Ho Woo, Sung-Bong Yang, Shn-Dug Km, Tack- Don Han, "Task schedulng n dstrbuted computng systems wth a genetc algorthm", Hgh-Performance Computng on the Informaton Superhghway, HPC-Asa '97, 997, p. 30. [5] C. Xu, & F. Lau, Load-Balancng n Parallel Computers : Theory and Practce, Kluwer Academc, 997. [6] Y. Lan, & T. Yu, A Dynamc Central Scheduler Load- Balancng Mechansm, Proc. of the 4 th IEEE Ann. Int'l Phoenx Conf. on Computers and Communcaton, 995, [7] E.S.H.Hou, N.Ansar, & H.Ren, A Genetc Algorthm for Multprocessor Schedulng, IEEE Trans. On Parallel and Dstrbuted Systems, 5(2), 994, [8] C.M.Woodsde, & G.G.Monforton, Fast Allocaton of Processes n Dstrbuted and Parallel Systems, IEEE Trans. On Parallel and Dstrbuted Systems, 4(2), 993, [9] H.C. Ln, & C.S. Raghavendra, A Dynamc Load- Balancng Polcy wth a Central Job Dspatcher (LBC), IEEE Trans. on Software Eng., 8(2), 992, [20] A.Nanda, et. al, Schedulng Drected Task Graphs on Multprocessors Usng Smulated Annealng, Proc. Int'l. Conf. On Dstrbuted Systems, 992, [2] A.K.Sarje & G.Sagar, Heurstc Model for Task Allocaton n Dstrbuted Computer Systems, Proc. of the IEE-E, 38(5), 99, [22] F. Bonom, & A. Kumar, Adaptve Optmal Load- Balancng n a Heterogeneous Multserver System wth a Central Job Scheduler, IEEE Trans. on Computers, 39(0) 990, [23] C.C.Shen, & W.H.Tsa, A Graph Matchng Approach to Optmal Task Assgnment n Dstrbuted Computng Usng a Mnmax Crteron, IEEE Trans. On Computers, 34(3), 985, [24] P.Y.R.Ma, E.Y.S.Lee, & J.Tsuchya, A Task Allocaton Model for Dstrbuted Computng Systems, IEEE Trans. On Computers, 3(), 982, [25] T.C.Hu, combnatoral algorthms (Addson-Wesley, 982).