Analyss of Partcle Swarm Optmzaton and Genetc Algorthm based on Tas Schedulng n Cloud Computng Envronment Frederc Nzanywayngoma School of Computer and Communcaton Engneerng Unversty of Scence and Technology Bejng Bejng, Chna Prof Yang Yang School of Computer and Communcaton Engneerng Unversty of Scence and Technology Bejng Bejng, Chna Abstract Snce the begnnng of cloud computng technology, tas schedulng problem has never been an easy wor Because of ts NP-complete problem nature, a large number of tas schedulng technques have been suggested by dfferent researchers to solve ths complcated optmzaton problem It s found worth to employ heurstcs methods to get optmal or to arrve at near-optmal solutons In ths wor, a combnaton of two heurstcs algorthms was proposed: partcle swarm optmzaton (PSO) and genetc algorthm (GA) Frstly, we lst pros and cons of each algorthm and express ts best nterest to maxmze the resource utlzaton Secondly, we conduct a performance comparson approach based on two most crtcal objectve functons of tas schedulng problems whch are executon tme and computaton cost of tass n cloud computng Thrdly, we compare our results wth other exstng heurstcs algorthms from the lteratures The expermental results was examned wth benchmar functons and results showed that the partcle swarm optmzaton (PSO) performs better than genetc algorthm (GA) but they both present a smlarty because of ther populaton based search methods The results also showed that the proposed hybrd models outperform the standard PSO and reduces dramatcally the executon tme and lower the processng cost on the computng resources Keywords Executon Tme; Tas Schedulng Algorthms; Partcle Swarms (PSO); Genetc Algorthm (GA); Vrtual Machnes (VMs) I INTRODUCTION Cloud computng[] s the delvery of computer servces and resources ncludng networs, data storage space, computer processng power, specalzed corporate and user applcatons over the nternet Cloud computng models allow cloud users to use software and hardware that are managed by cloud provders wthout nowng whch servers are n use to delver servce or nowng ther exact physcal locatons where ther data are stored The cloud provders provde servces that can be grouped nto three models: Software as a Servce (SaaS), Platform as a Servce (PaaS), and Infrastructure as a Servce (IaaS) Servce s a very mportant concept n cloud computng envronments Servce s used to llustrate the detals of a resource wthn the cloud Cloud servces and resources are Ths research was sponsored by the Student Fnancng Agency of Rwanda and Natonal Scence Foundaton of Chna (Grant Nos 60508, 6743, 63703, 647033, and 637009, Fundamental Research Funds for the Central Unverstes [FRF-TP-4-045A]) regstered wthn one or more cloud Informaton Servers The cloud users s the requests to the schedulng tas manager Then after the schedulng tas manager receves the servce requests from the users tracs the avalable actve resources to assgn the servces The servces are executed depng on the tas schedulng strateges A servce requests may be any onlne fle storage, onlne busness applcatons, socal meda stes, any software access and executon or any data processng We defne a tas as a request for a tas of the contracted applcaton that may requre a defned amount of resources and the creaton of a vrtual machne to support the applcaton Schedulng s the matter of assgnng tass to machne to acheve ther wor It s used to decde whch of the outstandng requests s to be allocated resources A tas schedulng s defned as a set of rules that decde the tass to be executed at a partcular tme[] Schedulng s a challengng problem n cloud computng envronment As mentoned n [3, 4] tas schedulng s NPcomplete problem that requres heurstc methods The wor[5] presents a partcle swarm optmzaton (PSO) based heurstc method to schedule tass n Cloud resources that taes nto consderaton both executon tme and computng cost Other three exstng basc heurstc methods nspred from nature for cloud computng such as Genetc Algorthm(GA), Smulated Annealng(SA) and Tabu Search(TS) heurstcs for cloud tas schedulng were presented n several wors[6, 7],[8, 9], and[0] PSO wors well n solvng global optmal problems and t has a good ablty of global searchng and was appled n other areas le neural networ, system analyss, desgn, robotcs, and so on Ths wor uses a comparson approach between two nature nspred heurstc methods, PSO and GAs algorthms appled n tas schedulng to mnmze the two parameters mentoned above smultaneously Another notable advantage of PSO and GA s that they perform better n problems for whch the searchng space s complex - those where the objectve functon s dscontnuous, changes over tme, or has many local optma[] PSO and GA have both characterstcs of explorng smultaneously dfferent parts of the soluton space, area less prone to converge to these local optma GA and PSO are flexble to handle constrants whch may be mplemented more easly, when comparng to the `standard' optmzaton technques PSO s a populaton consstng of varous partcles, wth each partcle representng a soluton 9 P age
A Genetc Algorthm s a search technque to fnd solutons to optmzaton and search problems One of the frst references to t was made by Holland (975) It uses concepts nspred from bologcal evoluton such as nhertance, selecton, crossover and mutaton The comparson between GA and PSO shows that PSO presents more focused search ablty than GA PSO taes more emphass on explotaton than exploraton PSO concentrates the search around a promsng area n order to refne a canddate soluton and explores dfferent regon of the search space to locate a good optmum Both PSO and GA dep on good ntal postonng of the partcles n the soluton space[] Wth ther explotaton and exploraton, the partcles fly through the problem space and get two reasonng capabltes: the memory of the best poston (pbest) and memory of the neghborhood s best poston (gbest)[3, 4] The same as n cloud systems, each tas runs on vrtual machne where the resources are dstrbuted vrtually le the way partcle swarm moves through problem space mantan useful nformaton of ther local poston and global poston The poston of partcle deps on the velocty and should be updated each tme the partcle moves from one pont to the next poston Assumng that the tass are totally dfferent and are depent as partcles move n swarm and all tass need to use resources such as CPU, memory, bandwdth, to be accomplshed and they must be measured n terms of cost The more accurate costs, the more the profts are[5] Our man am n ths study s to mnmze the executon tme and computaton cost Snce the tradtonal approaches used n optmzaton provded can t be applcable n cloud computng or present weanesses, modern heurstc based algorthms were developed and have been proven to be sutable for tas schedulng Ths paper nvolves varous sectons descrbng genetc algorthm(ga) and partcle swarm optmzaton(pso) and t s organzed as follows: In secton I, we ntroduced PSO and GA algorthms and lsted ther pros and cons; n secton II, we cted the related wor, n secton III, we conducted a comparson method to compare two based heurstc algorthms: PSO, GA, and we proposed PSO-GA; n secton IV, we dscussed and modeled tas schedulng problem by a tas graph; n secton V, we outlned the expermental set up, parameter settngs, and benchmar functons used to measure the performance between PSO and GA; fnally, secton VI contans the concluson of the paper II RELATED WORK Snce cloud resources are heterogeneous, depent, and present a lot of capabltes, tas schedulng problem becomes NP-complete problem We defne NP-complete problems as computatonal problems whch are normally hard to be solved n real world such as vertex cover, napsac, or travelng salesman problems and whch have the property that they can be solved n polynomal tme f and only f all other NPcomplete problems can also be solved n polynomal tme by maxmzng or mnmzng some values[6] NP-hard problems are ndspensable n practcal applcatons to develop heurstc method to provde ways to measure, analyze, compare and ncrease the system performance[7] As purpose of tas schedulng algorthm n cloud system s to get optmal tasprocessor assgnment and mnmze applcaton completon tme and the total cost, t s our vewpont that we explore how PSO and GA wor and how they can be appled to tas schedulng problems from the ndvdual partcle s pont of vew to the chromosome n all the searchng space PSO approach can solve the tas schedulng problems Therefore, we lst other approaches to solve schedulng problems[5] such as GA [8], Smulated annealng[9], tabu search[0], and ant colony [9] The wor[0]studed the comparson of partcle swarm optmzaton and the genetc algorthm n the mprovement of power system and stablty L Zhang et al[] has compared GA and PSO n tmes of mnmum completon tme Other comparson of partcle swarm optmzaton and the genetc algorthm can be found n [] It was found that PSO s comparable to the Genetc Algorthm (GA) so that these two heurstcs are populatonbased search methods[] A comparatve study of DE, PSO was also ntroduced n[5] wth objectve of examnng whch algorthm outperform better among all others on a large and dverse set of problems III PARTICLE SWARM OPTIMIZATION (PSO) VERSUS GENETIC ALGORITHM (GA) A Basc prncples and mplementaton of Partcle Swarm Optmzaton PSO was frstly ntroduced by J Kennedy through smulaton of a smplfed socal model to the optmzer PSO has found wdespread applcaton n two man component methodologes: one n artfcal lfe and another one based to brd flocng, fshes schoolng, and swarm theory As mentoned n [3], the advantages of usng PSO n tas schedulng are as the followng: a PSO algorthm can mantan useful nformaton about characterstcs of the envronment; PSO as characterzed by ts fast convergence behavor, has an n-bult ablty to adjust to a dynamc envronment; PSO s effectve for locatng and tracng optma n both statc and dynamc envronments The partcle swarm optmzer has been found to be fast n solvng nonlnear, non-dfferentable, multmodal problems[4] PSO ntroduces a method for optmzaton of contnuous non-lnear functons Other advantages of PSO wth optmzaton algorthms are that PSO present a smple mathematcal operaton wth less parameters, and s nexpensve n terms of both memory and speed requrements PSO have no overlappng and mutaton calculaton[] The dsadvantages of PSO algorthms are cted n[3]as the followng: ()The method suffers from the partal optmsm, whch causes the less exact at the regulaton of ts speed and the drecton ()The method cannot wor out the problems of scatterng and optmzaton (3)The method cannot wor out the problems of non-coordnate system, such as the soluton to the energy feld and the movng rules of the partcles n the energy feld Every sngle soluton s a brd n the searchng space called a "partcle" and all partcles possess postons and veloctes The partcles fly through the problem space by followng the current optmum partcles Each tme a partcle moves from one bn to another In the whole searchng space, all partcles dep on the value of the chosen optmzaton functon and have the followng nformaton: poston and the speed The Fg below represents the 0 P age
tradtonal Partcle Swarm Optmzer n multprocessor envronment Fg Two tradtonal neghbourhood topologes In order to acheve good optmzaton, each partcle n the searchng space moves wth two nformaton: poston and velocty We have two nds of tradtonal topologes n fgure: () Rng topology to represent local best poston and full mesh topology to represent the global best poston All partcles have postons and veloctes The th partcle s represented wth the followng elements: x the current partcle postons; v the veloctes vector, the current best poston pbest and global postons gbest c and c are the acceleraton coeffcents, r and r are two random vectors whch can tae any value between 0 and The ntalzaton process s gven n the followng formula 0 x 0 v = x x = mn mn + rand( x ) max xmn + rand( xmax xmn ) t 0 At ntal poston partcles poston wll be x then all partcles move towards the optmal pont wth the velocty At the tme +, there must be an update of all partcles wth partcle objectve or ftness value for the next teraton PSO s descrbed by the below equatons: v Rng (Local Best) = ωv + c rand ( pbest x ) + crand ( gbest x + + + x = x + v t Where v s the velocty of the th partcle at the th teraton; ω s the nerta factor; c and c are the acceleraton constants (cogntve and socal); rand and rand are the random numbers between 0 and ; for =, ; current poston of the th partcle at the s the best poston for the th partcle and th teraton; x s the pbest gbest represents the partcle poston or global poston To acheve a hgh performance, we set the nerta weght as ya ymax ( ω ) ω = ω + ω start e Full Mesh (Global Best) ) ωstart and ω are the startng and ng nerta values We set ther values to 065 and 0 respectvely y and ymax represent the current and maxmum teraton number whch we set to 00 and a s an nteger constant number B Basc prncples and mplementaton of tas schedulng based on Genetc Algorthms A GA s among the evolutonary algorthms whch mmc the process of natural selecton used to solve optmal and search problems[5] It generates solutons to optmzaton problems usng natural evoluton methods We present dfferent genetc algorthm operators as follows: ) Encodng and ntalzaton In genetc algorthm tas schedulng-based, the ntal populaton of canddate solutons s randomly generated The chromosome sequence represents a varety of tass Every tas s consdered as a gene The chromosome s encoded usng permutaton encodng The length of chromosome s the same as the length of the nput tass To start, the ntal populaton s generated randomly usng random generator functon of chromosomes Some resource nformaton such as CPU, number of tass, the sze of populaton s needed to create the ntal populaton TABLE I A SAMPLE CHROMOSOME OF 5 TASKS 3 5 4 Table shows a sample chromosome of 5 tass wth ther tas allocatons: tass{,3} are assgned to resource, tas { } s assgned to resource, and tass{ 5,4} are assgned to resource 3 ) Ftness functon The ftness functon s the evaluaton functon to gude the search space For tas schedulng based on genetc algorthm n cloud computng, the ftness functon s based on executon tme, computaton cost and measures the qualty of the soluton and determnes f the genetc materal wll be transmtted from parent to offsprng It helps to transform the objectve functon value n a measure of relatve ftness[6] ( x) g( f (x)) F = The objectve functon f and g are two functons whch result to relatve ftness f s used to measure how the ndvduals have performed n the problem doman and g transforms the value of the objectve functon f to a negatve number f ( x ), where N F( x ) = nd represent the N nd f ( x ) populaton sze and = x s the phenotypc value of ndvdual 3) Crossover Crossover operator s used to vary the programmng of the chromosomes from one generaton to the next P age
4) Mutaton The mutaton operaton expands the search space by decreasng the executon tme based on mutaton probablty and generates the offsprng wth dfferent assgnment Pm s the probablty of mutaton It s not greater n nature and durng our matlab smulaton of results; the probabltes of mutaton are randomly gven by computer C Comparson of genetc algorthms and partcle swarm optmzaton In ths secton, we compare PSO and GA As both algorthms ntroduce the bascs of evolutonary computng, Intalzaton of populaton PSO shares many smlartes technques wth GAs n partcular [7] GA and PSO are both heurstc algorthms and are used n optmzaton problems to fnd soluton to a gven objectve functon by usng dfferent technques and computatonal effort Fg represents the flow chart of GA (a) and PSO algorthm (b) GA begns wth a populaton of random chromosomes to present a better soluton to the problem At each step, the GA taes ndvduals from the current populaton to be parents and uses them to produce the chldren for the next generaton GA uses operators such as crossover and mutaton GAs and PSO can both be appled n pattern dscovery, sgnal processng, neural networs, cloud computng, manufacturng, power Electroncs to control power System such as schedulng power flow, provdng voltage support, lmtng short-crcut, etc[7, 8] Yes Evaluate the ftness functon Stop Condton =true? No Select parent Output results (a) Begn Intalzaton the swarm X wth random solutons Reproducton //The pseudocode of the proposed PSO&GA algorthm Set the partcle dmensonal accordng to the ready tass Intalze the partcle swarm poston X and velocty V randomly, Repeat for each partcle =,,,P do f f(x )>f(pest ) then //Calculate the ftness value pbest =X ; f (f(pbest)>f(gbest) then gbest =pbest ; for each partcle =,,,P do update the velocty matrx //update the velocty of each partcle update the poston matrx //update the poston of each partcle Untl stoppng condton s true// GA vs PSO Schedulng algorthms Evaluate the ftness functon of each partcle Update poston and velocty to the new poston Evaluatng termnaton No Yes Termnate checng (b) Fg Flow chart of genetc algorthm (a) and PSO algorthm (b) P age
The pseudocode of the average computaton cost for all resources Calculate average computaton cost of all tass n all compute resources Calculate average communcaton cost between resources Set tas node weght as average computaton cost Set edge weght to the sze of the transferred between tass Compute //a set of all tass Repeat for allready tass do Assgn tass to avalable resources accordng to PSO's soluton for Dspatch all the mapped tass Wat for pollng_tme Update the ready tas lst Update the average cost of communcaton between resources Compute Untl there are unscheduled tass IV TASK SCHEDULING IN CLOUD COMPUTING USING HYBRID GA-PSO MODEL The tas schedulng am [3] s to assgn ncomng tass to the avalable resources Accordng to the schedulng strateges used, the tas schedulng algorthms can sgnfcantly affect the effcency of the whole system In ths paper, we are usng hybrd PSO and GA models to solve a tas schedulng problem n cloud computng As a result, the frst tas whch s the most useful s to now how to model the problem as a set of ndvduals In order to model the tas schedulng problem, suppose that the number of swarm partcles correspond wth a set of tas numbers Then we denote n as the number of tass and m the number of avalable heterogeneous computng resources The objectve to model the schedulng problem s to fnd the best resource utlzaton Here the ftness of a partcle s measured wth executon tme and communcaton cost to all tass In ths paper, tas schedulng problem s modeled by a tas graph Frstly, usng tas graph model, tass are represented by nodes and edges represent the depences between tass Let G = ( V, E) be a graph wth V = { t, t,, t n } as a set of tass nodes/vertces, and E s a set of drected edges between two tass t and t The graph n Fgure 3 starts wth root node and s wth node The node wth no parent s called an entry node or root node and a node wth no chld s called an ext node or node A tas t s called the entry tas and t n the ext tas of the graph We calculate the communcaton cost accordng to the amount of data to be transmtted between resources and the avalable bandwdth between the resources If we suppose that n tass are submtted from the tas schedule manager to the avalable resources, and we suppose that those tass are depent to each other wth nter-tas data depences and they are nonpreemptve; and also f we assume that the number of the tass s less than the number of avalable resources, we wll rely on the frst come-frst-served rule Otherwse we wll adopt other schedulng schemes where the number of tass s greater than the number of resources From Fg3 below, tas 5 cannot start ts executon untl tas and tas 4 complete ther executons t e e 3 e 34 Fg 3 Tas graph wth 5 tass Secondly, mappng the set of tass to the avalable heterogeneous resources, we can compute the completon tme of the tass To map a set of resources, consder m number of avalable heterogeneous computng resources, and b j the bandwdth between resources as t s shown n Fgure 3 Then calculate the avalable bandwdth B = ( b j ) for the avalable NxN resource Fg4 shows that a tas can be executed randomly by the avalable resources after fndng that there are a fnte number of possble mappngs from a collecton T = { t, t,, t n } to a collecton M = { r, r,, r m } and a large number of par of tas and resource t t t n t e 4 t 3 e5 Fg 4 Mappng of the tas to avalable resources We consder a dscrete-tme model wth a collecton M of machnes ndexed from,,, m Tass come n wth a tagged random mappng number and each tas s assocated t 4 e 45 r r r m t 5 3 P age
wth m number of avalable resources and they are floced together accordng to ther ndces n an ncreasngly order nto a vector m {, r < r < rm } ( r r,, rm ) {,,, } V M < and executon tme equals to the raton of the worload and computaton ablty of the resource r ET T = { t n j = m R = { r j E { e, j j t r n }represents a set of n tass j m } represents a set of m resources = j m, j m } represents a matrx of communcaton tmes of tas on resource t number of resources r j The communcaton cost of edges s defned as enm f t s a predecessor of t j and j bj CTj = otherwse 0 enm represents the quantty of data to be transmtted between two resources and j s representng the ln communcaton speed between two resources If e nm = 0, that means that both tass t and t j are assgned on the same resource V EXPERIMENTAL RESULTS AND STATISTICAL ANALYSIS A Smulaton envronment To compare the performance of PSO and GA algorthms, we tae nto consderaton varous parameters such as number of tass, number of processors, swarm sze, populaton sze, number of chromosomes, and number of teraton The algorthms are smulated wth java language runnng and n matlab on Intel(R) dual-core(tm)5-4590 CPU@330GHz, 400GB nstalled memory on wndows 7 Ultmate servce par and NetBeans IDE 80 Table gves a summary of PSO&GA parameters Frstly, genetc algorthms wll run wth the followng parameters: the populaton sze, crossover probablty, mutaton probablty, b and maxmum number of teraton Secondly, the partcle swarm optmzaton wll run wth the followng parameters: number of partcle (Swarm sze), maxmum veloctyv max, the neghborhoods best found solutons c = c = 0, number of teratons=[ 0 n] wth n stands for the number of nodes, and nerta weght The nerta weght wll decrease lnearly over tme up to 0 TABLE II GA parameters PSO parameters SUMMARY OF () PSO PARAMETERS () GA PARAMETERS Populaton sze 60 Crossover probablty 07 Mutaton probablty 00 Number of teratons 00 Populaton sze 60 ω 065 C C Number of teratons 00 B Smulaton Result and analyss In ths wor, hybrd PSO-GA algorthms are used to solve tas schedulng problem n cloud computng, and a comprehensve performance based on benchmar functons has been conducted We appled Schaffer and Acley benchmar functons showed n Table III below to assess the performance of the algorthms We chose the ranges of ther searchng space and ther dmensons We ran 00 test computatons randomly on a couple of test functons The combned PSO-GA algorthm performs well for all test functons as t s represented n Fg5 and Fg 6 and t can easly fnd the global mnma n 00 runs better than PSO or GA Names Schaffer Acley TABLE III Functons 05 sn x BENCHMARK FUNCTIONS + y 05 +, 00 x 00 ( 0 + 000( x + y ) 0exp 0 D x exp D D D d cos d + d = d = Fg 5 Acley functon ( Πx ) + 0 e 4 P age
Fg 6 Schaffer functon VI CONCLUSION In ths study, heurstc algorthms were compared based on tas schedulng problems and based on two QoS (qualty of servce) parameters The man purpose of the wor s to use comparson approach to determne the effcency of GA and PSO The study found that PSO and GA are smlar n fndng the global optmal soluton because they all utlze the ftness value to evaluate the populaton and also they all update the populaton The crterons consdered to major the performance are executon tme and processng cost In ths study, we explored how PSO/GA wor and apply them to solve NPcomplete problems of tas schedulng n cloud computng based on executon tme and processng cost Usng these two algorthms, the results show that the genetc algorthm (GA) presents hgh global searchng ablty but has poor computaton effcency, and poor optmzaton speed compared to ts counterpart PSO presents good advantages n convergence speed, n fndng global optmal, and n smplcty ablty Therefore, we conclude by sayng that whle usng PSO algorthms the cloud computng resources can easly notce resources dscovery, resources matchng, and tas executon The results show that the combnaton of these two algorthms can reduce dramatcally the tas executon tme, and reduce the computaton cost on the avalable resources In the future wor, better results wll be provded by mprovng our soluton usng PSO combned wth other meta-heurstc technques(e Smulated Annealng(SA), Tabu Search(TS), etc) REFERENCES [] Bash, T, et al A New Meta-heurstc PSO Algorthm for Resource Constrant Project Schedulng Problem n Proceedngs of Seventh Internatonal Conference on Bo-Inspred Computng: Theores and Applcatons (BIC-TA 0) 03 Sprnger [] Dubey, S and S Agrawal, QoS drven tas schedulng n cloud computng Internatonal Journal of Computer Applcatons Technology and Research, 03 (5): p 595>< meta name= [3] Chen, Z-G, et al Deadlne constraned cloud computng resources schedulng for cost optmzaton based on dynamc objectve genetc algorthm n 05 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