A Time-driven Data Placement Strategy for a Scientific Workflow Combining Edge Computing and Cloud Computing

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1 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 A Tme-drven Data Placement Strategy for a Scentfc Workflow Combnng Edge Computng and Cloud Computng Bng Ln, Fangnng Zhu, Janshan Zhang, Jaqng Chen, Xng Chen, Neal N. Xong, Jame Lloret Maur Abstract Compared to tradtonal dstrbuted computng envronments such as grds, cloud computng provdes a more cost-effectve way to deploy scentfc workflows. Each task of a scentfc workflow requres several large datasets that are located n dfferent datacenters from the cloud computng envronment, resultng n serous data transmsson delays. Edge computng reduces the data transmsson delays and supports the fxed storng manner for scentfc workflow prvate datasets, but there s a bottleneck n ts storage capacty. It s a challenge to combne the advantages of both edge computng and cloud computng to ratonalze the data placement of scentfc workflow, and optmze the data transmsson tme across dfferent datacenters. Tradtonal data placement strateges mantan load balancng wth a gven number of datacenters, whch results n a large data transmsson tme. In ths study, a self-adaptve dscrete partcle swarm optmzaton algorthm wth genetc algorthm operators (GA-DPSO) was proposed to optmze the data transmsson tme when placng data for a scentfc workflow. Ths approach consdered the characterstcs of data placement combnng edge computng and cloud computng. In addton, t consdered the mpact factors mpactng transmsson delay, such as the bandwdth between datacenters, the number of edge datacenters, and the storage capacty of edge datacenters. The crossover operator and mutaton operator of the genetc algorthm were adopted to avod the premature convergence of the tradtonal partcle swarm optmzaton algorthm, whch enhanced the dversty of populaton evoluton and effectvely reduced the data transmsson tme. The expermental results show that the data placement strategy based on GA-DPSO can effectvely reduce the data transmsson tme durng workflow executon combnng edge computng and cloud computng. Index Terms Edge computng, Cloud computng, Data placement, data transmsson tme, scentfc workflow Xng Chen and Neal N. Xong are both the correspondng authors. Ths work was supported by the Natonal Key R&D Program of Chna under Grant No. 218YFB148, and the Talent Program of Fujan Provnce for Dstngushed Young Scholars n Hgher Educaton. B. Ln and J. Zhang s wth College of Physcs and Energy, Fujan Normal Unversty, Fujan Provncal Key Laboratory of Quantum Manpulaton and New Energy Materals, Fuzhou,35117, Chna. The Fujan Provncal Engneerng Technology Research Center of Solar Energy Converson and Energy Storage, Fuzhou,35117, Chna. The Fujan Provncal Collaboratve Innovaton Center for Optoelectronc Semconductors and Effcent Devces, Xa-men, 3615, Chna. E-mal: WheelLX@163.com, zhangjs512@163.com X. Chen, F. Zhu and J. Chen are wth the College of Mathematcs and Computer Scence, Fuzhou Unversty, Fuzhou, 35117, Chna. E-mal: chenxng@fzu.edu.cn, @qq.com, @qq.com. Neal N. Xong s wth the Department of Mathematcs and Computer Scence, Northeastern State Unversty, OK, USA. E-mal: xongnaxue@gmal.com. Jame L. Maur s wth the Integrated Management Coastal Research Insttute, Unverstat Polte cnca de Vale nca, Span. E-mal: jlloret@dcom.upv.es S I. INTRODUCTION CIENTIFIC applcatons are usually data- and computatonntensve, and they are composed of hundreds of nterrelated tasks. Workflow models have been an effectve way to represent complcated scentfc applcatons, whch are wdely used n many scentfc felds, such as astronomy [1], physcs [2], and bonformatcs [3]. The complex structure and large datasets n a scentfc workflow result n strct requrements on the storage capacty of the deployment envronment. Grds and other tradtonal dstrbuted computng envronments are typcally bult for specfc scentfc research wth low-level resource sharng. A scentfc workflow deployed n such envronments wll result n more wasted resources. Cloud computng [4,5] vrtualzes resources n dfferent geographc locatons nto a resource pool through vrtualzaton technology. The resource pool s made avalable to end-users n a pay-as-you-go manner. Its hgh effcency, flexblty, scalablty, and customzable features provde a more cost-effcent way to deploy scentfc workflows [6]. Cloud computng resources are usually deployed at the remote end, and the scentfc workflow has large-scale datasets nteracton, resultng n serous data transmsson delays [7]. Edge computng resources are usually deployed n the near end, whch can reduce the data transmsson delays and have an effect on prvate datasets protecton [8]. Due to the lmted resources, t s mpossble to store all the datasets requred and generated by a scentfc workflow n edge computng. Combnng the advantages of both edge computng and cloud computng to ratonalze the data placement of a scentfc workflow s an effcent way to reduce data transmsson delays. Cloud computng ensures the resource supply and mantans the qualty of servce under the condtons of a drastcally fluctuatng workload. Edge computng guarantee the securty of prvacy datasets for a scentfc workflow [9]. Data placement strateges for a scentfc workflow combnng edge computng and cloud computng have become a popular topc [1]. In the feld of emergency management, a low-delay data transmsson s requred for a scentfc workflow deployed combnng edge computng and cloud computng [11]. However, the prvate datasets that are stored n a fxed manner lead to a large amount of data movement across datacenters durng the workflow executon. There s a large contradcton between the large amount

2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 2 of data movement and the lmted bandwdth between datacenters, resultng n serous data transmsson delays. Therefore, t s mportant to propose a reasonable data placement strategy for a scentfc workflow combnng edge computng and cloud computng. The detaled requrements of a good strategy data placement are as follows: (1) The scentfc workflow has a complex structure and large datasets. Therefore, the data placement strategy should ensure hgh coheson wthn a datacenter and low couplng between dfferent datacenters, whch reduces the data transmsson tme across datacenters combnng edge computng and cloud computng. (2) For securty reasons, prvate datasets should be stored n edge datacenters. Because the storage capacty of edge datacenters s lmted, some datasets must be transmtted across dfferent datacenters. It s a challenge to place the datasets wth low latency un-der the condtons of the lmted bandwdth and fxed prvate datasets. Tradtonal data placement strateges for a scentfc workflow manly adopted clusterng [12,13] and evolutonary algorthms [14,15]. The clusterng algorthms mantaned load balancng and effectve resource utlzaton among multple datacenters. To guarantee low-delay data transmsson combnng edge computng and cloud computng, a data placement strategy for a scentfc workflow requres hgh coheson wthn a datacenter and low couplng between dfferent datacenters. However, the clusterng algorthms only consdered load balancng. Tradtonal evolutonary algorthms adopted the genetc algorthm (GA) [16], whose tme complexty s very hgh. Therefore, a tme-drven data placement strategy for a scentfc workflow combnng edge computng and cloud computng s stll an open ssue. In prevous works [17, 18], we addressed workflow schedulng based on the mproved partcle swarm optmzaton (PSO), whch s an evolutonary algorthm. Workflow data placement and workflow schedulng are both NP-hard problems wth many smlartes. There-fore, ths study proposed a self-adaptve dscrete PSO algorthm wth genetc algorthm operators (GA-DPSO) to reduce the data transmsson tme durng workflow executon combnng edge computng and cloud computng. Ths approach consdered the mpact factors on the transmsson delay, such as the bandwdth between datacenters, the number of edge datacenters, and the storage capacty of edge datacenters. The man contrbutons of ths study are as follows: 1. Accordng to the characterstcs of data dependences n a scentfc workflow, preprocessng for formalzng the scentfc workflow was desgned to effectvely compress the number of datasets and mprove the executon effcency of GA-DPSO. 2. The crossover and mutaton operator of the GA were adapted to avod the premature convergence of tradtonal PSO, whch enhanced the dversty of populaton evoluton and effectvely reduced the data transmsson tme. 3. A tme-drven data placement strategy based on GA- DPSO for a scentfc workflow was proposed that optmzed the data transmsson tme from a global perspectve combnng edge computng and cloud computng. Ths strategy consdered the mpact factors on the transmsson delay, such as the bandwdth between datacenters, the number of edge datacenters, and the storage capacty of edge datacenters. The remander of ths study s organzed as follows. Related work s presented n secton II. Secton III dscusses n detal the process of data placement for a scentfc workflow combnng edge computng and cloud computng, and secton IV represents the proposed GA-DPSO algorthm. In secton V, our algorthm s compared wth other state-of-the-art algorthms. Fnally, secton VI summarzes the full text and presents future work. II. RELATED WORK A data placement strategy for a scentfc workflow s crtcal to the workflow system performance. Factors such as large datasets, lmted bandwdth, and prvacy datasets stored n fxed edge datacenters have a crtcal effect on data transmsson tme. Therefore, t s of great sgnfcance to propose a feasble data placement strategy for a scentfc workflow to compress data transmsson and mprove system performance combnng edge computng and cloud computng. Current research manly focused on optmzng the number of data movement and data transmsson tme n cloud envronment. Yuan et al. [12] proposed a data placement strategy based on k-means and BEA clusterng for a scentfc workflow that effectvely reduced the number of data movements. However, t gnored the dfference n the storage capacty of each datacenter. In addton, the number of data movements dd not accurately represent the amount of data movement or actual data transmsson status. Wang et al. [19] desgned a data placement strategy based on k-means clusterng for a scentfc workflow n cloud envronments that consdered the data sze and dependency. Ths approach reduced the number of data movements usng a data replcaton mechansm, but t dd not formalze the data replcaton cost. Cu et al. [15] constructed a trpartte graph to formulate the data replca placement problem and proposed a data placement strategy based on the GA for a scentfc workflow, to reduce the number and amount of data movement n cloud envronments. However, ths work gnored the prvacy datasets n the scentfc workflow. Zheng et al. [14] proposed a three-stage data placement strategy based on the GA for a scentfc workflow n cloud envronments that consdered crucal factors such as data dependency and global load balancng across datacenters. Ths approach had a sgnfcant effect on the optmzaton of the data transmsson tme. However, t had hgh tme complexty. L et al. [13] proposed a data placement strategy based on data dependency destructon for a scentfc workflow n hybrd cloud envronments that effectvely reduced data transmsson tme across dfferent datacenters. Ths work has nfluenced the present study, yet t gnored the dfference n storage capacty across dfferent datacenters and the dfferent bandwdths between datacenters. Edge computng has recently emerged as an mportant paradgm to brng computaton and cache resources to the edge of core networks [16]. Recently, there were many studes amng at mprovng QoS n edge computng. Gang Sun et al. desgned DMRT_SL and DMRT_NSL algorthms to effcently reduce

3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3 the latency for provsonng the workflow n edge computnglke servce request, whch met the requrements of dfferent knds of servce requests [2]. Ths strategy gnored the mpact of dfferent bandwdths across multple datacenters on data placement. [21] presented a workflow-net-based mechansm for moble edge node cooperaton n fog-cloud networks to form guaranteed servce specfc overlays for faster servce delvery. By proposng an algorthm that predcts the response tme of complex event processng (CEP) servces dynamcally, [22] deployed the operators on the edge nodes wth the mnmum predcted delay to reduce the response tme. It gnored the mpact of dfferent datacenter storage capactes on the data placement. Whle some research focused on reducng energy consumpton. [23] desgned an energy-effcent computaton offloadng (EECO) scheme, whch jontly optmzed offloadng and rado resource allocaton to obtan the mnmal energy consumpton under the latency constrants. Combnng edge computng and cloud computng can solve delay mnmzaton problem effectvely. Odessa [24] was an example that could offload tasks to ether the cloud or a dedcated edge computng cloudlet. Odessa could adapt quckly to changes n scene complexty, compute resource avalablty, and network bandwdth. But t dd not make good use of the publc cloud. Both [16] and [25] consdered the characterstcs of data placement combnng edge computng and cloud computng. The former research manly focused on puttng forward a heurstc algorthm based on genetc algorthm (GA) and smulated annealng (SA) to solve a resource-constraned delay mnmzaton problem, the latter one focused on proposng a cloud asssted moble edge computng (CAME) framework to solve a capacty-constraned delay mnmzaton problem. [26] ntroduced strateges to create placement confguratons for data stream processng applcatons whose operator topologes follow seres parallel graphs, amng at mprovng the response tme. The smlarty between ther work and ours s that both the placement decsons took cloud computng and edge computng nto consderaton, but ther work focused on data stream processng. In summary, prevous studes have researched the data placement for a scentfc workflow. However, they mostly gnored crucal factors such as the lmted storage capacty of edge cloud datacenters and the dfference n bandwdths across dfferent datacenters on the data placement combnng edge computng and cloud computng. III. PROBLEM DEFINITION AND ANALYSIS The core purpose of data placement for a scentfc workflow s to acheve a mnmum data transmsson tme whle satsfyng the storage capacty constrant of each datacenter. In ths secton, we defne the concepts related to the data placement strateges for a scentfc workflow combnng edge computng and cloud computng and analyze the data transmsson tme optmzaton usng a specfc example. A. Problem Defnton The problem defnton ncludes a new hybrd envronment combnng edge computng and cloud computng, a scentfc workflow, and a data placement strategy. The hybrd envronment combnng edge computng and cloud computng DC = {DC cld, DC edg} ncludes cloud computng at the remote end and edge computng n the near end, whch both consst of multple datacenters. Cloud computng DC cld = {dc 1, dc 2,..., dc n} conssts of n datacenters, and edge computng DC edg = {dc 1, dc 2,..., dc m} conssts of m datacenters. Ths study desgns a data placement strategy. Thus, we focus on the storage capacty of each datacenter and gnore ther computng capacty. The datacenter dc (whose number s ) s expressed as dc = capacty, type, (1) where capacty represents the storage capacty of the datacenter dc, and the datasets stored n ths datacenter cannot exceed ts capacty. type = {, 1} represents the locaton that the datacenter dc belongs to. When type =, dc belongs to cloud computng, and t can only store publc datasets. When type = 1, dc belongs to edge computng, and t can store both prvate and publc datasets. The bandwdth across dfferent datacenters s expressed as follows. b b b DC b b b DC Bandwdth = (2), b b b DC 1 DC 2 DC DC b = band, type, type, (3) j j where b j represents the bandwdth between datacenters dc and dc j. band j s the measured value of bandwdth b j, where, j =1, 2,..., DC and j. The bandwdth s assumed to be known and not fluctuate. The scentfc workflow s represented by a drected acyclc graph G = (T, E, DS) [21], where T = {t 1, t 2,..., t r} denotes a set of nodes contanng r tasks, E = {e 12, e 13,..., e j} denotes the data dependences between each par of tasks, and DS = {ds 1, ds 2,..., ds n} denotes all datasets n the scentfc workflow. Each data-dependent edge e j = (t, t j) represents a data dependency between task t and task t j, where task t s the drect precursor of task t j, and task t j s the drect successor of task t. In the process of schedulng a scentfc workflow, a task cannot start untl all of ts precursors have been completed. For a task t = <IDS, ODS >, IDS s the nput datasets of t, and ODS s the output datasets of t. The relatonshp between the task set and dataset s many-to-many (that s, one data may be used by multple tasks, and one task may also requre multple nput datasets). For a dataset ds = <dsze, gt, lc, flc >, dsze represents the dataset sze, gt represents the task generatng ds usng (4), lc represents the orgnal storage locaton of ds usng (5), and flc represents the fnal placement locaton of ds., ds DS n gt =, (4) Task( ds ), ds DS gen j, ds DS flex lc =. (5) fx( ds ), ds DS fx

4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 4 Datasets can be dvded nto ntal datasets DS n and generated datasets DS gen accordng to data sources. The ntal datasets are the nput datasets of a scentfc workflow, and the generated datasets are the ntermedate datasets generated durng the scentfc workflow executon. In (4), Task(ds ) represents the task generatng the dataset ds. In addton, datasets can also be dvded nto fxed datasets DS fx (that s, prvate datasets) and flexble datasets DS flex (that s, publc datasets) accordng to ther storage locatons. Prvate datasets can only be stored n edge datacenters, and fx(ds ) represents the edge datacenter storng the prvate dataset ds. The purpose of our data placement strategy s to mnmze the data transmsson tme whle satsfyng all requrements durng workflow executon. Any task executon n a workflow must satsfy two condtons: (1) The task should be scheduled to a specfc datacenter. (2) The nput datasets requred by the task are already n the specfc datacenter. Because the tme for schedulng tasks to datacenters s much less than the tme for transmttng datasets from one datacenter to another [27, 28], ths study only focuses on the data transmsson tme. Assume that a task s scheduled to the datacenter wth a mnmum data transmsson tme after data placement for a scentfc workflow. The data placement can be defned as S = (DS, DC, Map, T total), where = represents the maps from Map { dc, ds, dc } = 1,2,..., DS k j the datasets DS to the datacenters DC. A map <dc, ds k, dc j> represents the dataset d sk transmsson from the orgnal storage locaton dc to the fnal placement locaton d cj, and the data transmsson tme s calculated as (6). T total represents the total data transmsson tme durng data placement for a scentfc workflow, whch s shown n (7). dszek Ttransfer ( dc, ds, dc ) =, (6) k j band T total DC DC DS = T transfer ( dc, ds, dc ) e, (7) k j jk = 1 j k = 1 where e jk = {, 1} represents f there s a dataset ds k transmtted from the orgnal storage locaton dc to the fnal placement locaton dc j, e jk = 1 ndcates presence, and e jk = ndcates absence. ds1 ds1 ds2 ds3 ds6 ds4 t1 t2 t3 t4 t5 ds2 ds3 (b) (a) t1 t2 t3 t4 dc1 ds5 t5 ds6 dc2 dc3 ds4 ds5 ds5 ds1 ds2 dc1 t5 j t1 t2 t3 publc datasets prvate datasets tasks data centers data dependences data transmsson Fg. 1. A sample of data placement for a scentfc workflow. The problem of tme-drven data placement strateges for a ds6 (c) ds3 t4 ds4 dc2 dc3 scentfc workflow combnng edge computng and cloud computng can be formalzed as (8). Its core purpose s to pursue a mnmum total data transmsson tme whle satsfyng the storage capacty constrant for each datacenter. Mnmze Ttotal (8) DS, subject to, ds u capacty j= 1 where u j = {, 1} ndcates whether the dataset ds j s stored n datacenter dc. u j = 1 f yes and u j = f no. B. Problem Analyss Fgure 1(a) s a sample of data placement for a scentfc workflow, whch ncludes fve tasks {t 1, t 2, t 3, t 4, t 5}, fve nput datasets {ds 1, ds 2, ds 3, ds 4, ds 5}, and an ntermedate dataset {ds 6}. These dataset szes {dsze 1, dsze 2, dsze 3, dsze 4, dsze 5, dsze 6} are {3GB, 5GB, 3GB, 3GB, 5GB, 8GB}, respectvely, and ds 4 s the prvate dataset that s only stored n edge datacenter dc 2. The nput datasets of task t 4 are {ds 3, ds 4, ds 6}, whch nclude ds 4. Therefore, task t 4 must be executed n datacenter dc 2. Smlarly, dataset ds 5 s prvate and only stored n edge datacenter dc 3. Task t 5 must be executed n datacenter dc 3. Two data placement results wth dfferent strateges are shown n Fgures 1(b) and 1(c), where dc 1 s a cloud datacenter wth unlmted storage capacty, and the other two datacenters (dc 2 and dc 3) are edge datacenters wth the same storage capacty (2 GB). The bandwdth between edge datacenters s approxmately 1 tmes faster than the bandwdth between a cloud datacenter and an edge datacenter [29]. Assume that the bandwdth {band 12, band 13, band 23} across three datacenters s {1 M/s, 2 M/s, 15 M/s}. Fgure 1(b) s the data placement result accordng to [13]. Based on the parttonng model of the dependency matrx, the publc datasets {ds 1, ds 2, ds 3} are stored n cloud datacenter dc 1, and ds 6 s stored n edge datacenter dc 2. The prvacy datasets {ds 4, ds 5} are stored n ther correspondng edge datacenters. Ths data placement result s that the number of data movements s 4, the amount of data movement s 27 GB, and the data transmsson tme s approxmately 1953 s. Fgure 1(c) s the optmal data placement result. The publc datasets {ds 1, ds 2} are stored n cloud datacenter dc 1, and the datasets {ds 3, ds 6} are stored n edge datacenter dc 3. The data placement result s that the number of data movements s 5, the amount of data movement s 3 GB, and the data transmsson tme s approxmately 123 s. Due to the consderaton of the bandwdth across dfferent datacenters, the data transmsson tme of ths strategy s sgnfcantly better than the former n [13]. The tradtonal matrx-parttonng model [12] tends to place datasets wth hgh data dependency n the same datacenter, whch effectvely reduces the amount of data movement across dfferent datacenters. However, these approaches gnore the mpact of bandwdth on the fnal data placement when pursung a short data transmsson tme. Ths study proposed a data placement strategy based on GA-DPSO, whch adaptvely placed datasets whle consderng the bandwdth between datacenters, j j

5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 5 number of edge datacenters, and storage capacty of edge datacenters. IV. DATA PLACEMENT STRATEGY BASED ON GA-DPSO For a data placement strategy S = (DS, DC, Map, T total), ts core purpose s to fnd the best map from DS to DC that has a mnmum data transmsson tme T total. It s an NP-hard problem to fnd the best map from DS to DC [3]. Therefore, we proposed a data placement strategy based on the GA-DPSO algorthm to optmze the data transmsson tme from a global perspectve combnng edge computng and cloud computng. To mprove the strategy effcency, a preprocessng of compressng datasets was performed. The preprocessng and GA-DPSO algorthm are descrbed as follows. A. Preprocessng for a scentfc workflow Algorthm 1: Merge each cut-dataset nto a new dataset procedure preprocess (G(T, E, DS)) 1: Record the out-degree and n-degree of G s datasets 2: Fnd all cut-edge datasets. 3: If there are cut-edge datasets, merge each cut-edge dataset nto a new dataset. 4: Repeat step 2 untl there s no cut-edge dataset. end procedure Algorthm 1 ntroduces the preprocessng pseudocode for a scentfc workflow that merges each cut-edge dataset nto a new one. A cut-edge dataset s one where there are two adjacent datasets (such as ds and ds j), at least one dataset s publc, and they only have one common task. The out-degree of ds s 1 and the n-degree s 1, and there s only one task between ds and ds j. The process of mergng a cut-edge dataset nto a new one s shown n Fgure 2(a). The scence workflow Epgenomcs [31] have many cut-edge datasets, and the number of datasets s compressed by more than 3% after preprocessng. Fgure 2(b) shows the structure of the Epgenomcs before and after preprocessng. GA-DPSO wll process a workflow faster wth less datasets. ds 5 t 5 ds 6 (a) (b) ds5,ds6 t 5 Fg. 2 Preprocessng for a scentfc workflow: (a) Mergng a cut-edge dataset nto a new one; (b) The structure of Epgenomcs before and after preprocessng Property 1: Preprocessng compresses the number of datasets n a scentfc workflow and mproves the executon effcency of GA-DPSO. However, t may affect the fnal data placement result. The number of datasets s compressed as shown n Fgure 2. Part B n ths secton ntroduces the problem encodng of GA- DPSO, whose dmensons are based on the number of datasets. Therefore, compressng the number of datasets reduces the codng dmenson of GA-DPSO, whch wll mprove the executon effcency. In Fgure 2(a), ds 5 and ds 6 are merged together. Ths means that ds 5 and ds 6 must be stored n the same datacenter after preprocessng. Wthout preprocessng, ds 5 and ds 6 may be stored n dfferent edge datacenters. Therefore, the preprocessng may affect the fnal result of data placement. B. GA-DOSO PSO s an evolutonary computaton technque nspred by the socal behavor of brd flocks, whch was frst presented by Kennedy and Eberhart [32]. The partcle s the most mportant concept n PSO. A partcle represents a canddate soluton that moves around n the search-space. Each partcle has ts own velocty, whch determnes ts future drecton and magntude. The movement of each partcle s determned by ts velocty and poston, and they teratvely update these usng (9) and (1). t 1 t t t t t V + = w V + c r ( pbest X ) + c r ( gbest X ), (9) X = X + V (1) t+ 1 t t+ 1. V t and X t represent the velocty and poston of the th partcle at the t th teraton, respectvely. In general, a maxmum velocty V max s defned to ensure that the partcle search-space s n the range of the soluton space. Ths velocty s affected by the personal best poston of the partcle, pbest, and the global best poston of the populaton, gbest. The nerta weght w determnes how much the prevous velocty can affect the current velocty. It has a sgnfcant mpact on the convergence of the algorthm. The two acceleraton coeffcents (that s, c 1 and c 2) represent the partcle cogntve ablty to ther personal and global best values. To enhance the randomness of searchng, the algorthm ntroduces two random numbers (r 1 and r 2) whose values are both between and 1. In addton, a ftness functon s used to evaluate the qualty of a partcle. Tradtonal PSO s used to solve the contnuous problem. The data placement problem n ths study s dscrete and requres a new problem-codng approach. For the premature convergence of tradtonal PSO, a new update strategy for partcles s needed. In addton, the parameter settng may affect the search capablty of an evolutonary algorthm. Therefore, GA-DPSO s proposed to solve the above problems. The data placement strategy based on GA-DPSO s descrbed n detal as follows. 1) Problem encodng To mprove the algorthm performance and enhance ts searchng effcency, a good encodng strategy should satsfy the followng three prncples [33]: Defnton 1 (Completeness). Each canddate soluton n the problem space can be encoded as a partcle. Defnton 2 (Non-redundancy). A canddate soluton n the problem space has only one correspondng encoded partcle.

6 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 6 Defnton 3 (Vablty). Each encoded partcle corresponds to a canddate soluton n the problem space. It s dffcult to propose an encodng strategy that satsfes the above three prncples. Inspred by [34], we adopt the dscrete encodng strategy to generate n-dmensonal canddate soluton partcles. A partcle represents a data placement soluton for a scentfc workflow combnng edge computng and cloud computng, and the th partcle n the t th teraton s shown n (11). t t t t X = ( x, x,, x ), (11) 1 2 n where n s the number of datasets after preprocessng, and each partcle s an nteger-valued vector of dmenson n. x k (k=1, 2,, n) represents the fnal placement locaton of the kth dataset n the tth teraton, whose value s the datacenter number, that s, x k = {1, 2,..., DC }. Note that the storage locaton of the prvate datasets s fxed, whch s never changed. For example, n Fgure 1, ds 4 and ds 5 can only be fxed and stored n dc 2 and dc 3, respectvely. Fgure 3 shows an encoded partcle correspondng to the data placement of Fgure 1(c). After preprocessng, the number of datasets s changed from sx to fve. The datasets ds 5 and ds6 are compressed nto a sngle dataset stored n dc 3. datasets storage locaton Fg. 3 An encoded partcle correspondng to the data placement Property 2: Our dscrete encodng strategy satsfes the nonredundancy and completeness prncples, but does not satsfy the vablty prncple. After data placement, each dataset s stored n the correspondng datacenter, whch has a correspondng datacenter number. The fnal placement locaton of a dataset can only be n a datacenter. A data placement strategy for a scentfc workflow corresponds to an n-dmensonal partcle. The value of the th dmenson n a partcle s the datacenter number that stores the th dataset. A data placement strategy only corresponds to one encoded partcle, whch satsfes the non-redundancy prncple. Each publc dataset can be stored n dfferent datacenters, and the value of correspondng dmensons n a partcle can be a dfferent datacenter number. Each data placement strategy has the correspondng encoded partcle, whch satsfes the completeness prncple. Some encoded partcles cannot be the canddate solutons for the problem space. If the fnal placement locaton of datasets n Fgure 3 s (1, 2, 2, 2, 2), then all datasets except ds 1 are stored n dc 2. The sze of datasets n dc 2 s 24 GB, whch exceeds ts storage capacty (that s, 2 GB). Therefore, the dscrete encodng strategy does not satsfy the vablty prncple. 2) Ftness functon A ftness functon evaluates the advantages and dsadvantages of a partcle. In general, a partcle wth smaller ftness has better performance [35]. The purpose of ths study s to reduce the transmsson tme of data placement for a scentfc workflow. The smaller the data transmsson tme, the better the partcle. The ftness functon s equal to the transmsson tme of a data placement strategy correspondng to a specfc partcle. However, our dscrete encodng strategy does not satsfy the vablty prncple, and the ftness functon must be defned accordng to dfferent stuatons. Defnton 4 (Feasble partcle). An encoded partcle (whch corresponds to a specfc data placement strategy) satsfes the storage capacty constrant. That s, there s no edge datacenter exceedng ts storage capacty. Defnton 5 (Infeasble partcle). An encoded partcle (whch corresponds to a specfc data placement strategy) does not satsfy the storage capacty constrant. That s, there s at le- old partcle pbest (gbest) nd 1 nd nd 1 nd 2 old partcle new partcle new partcle (a) crossover nd mutaton (b) Fg. 4 Update operaton: (a) Crossover operator for the ndvdual (socal) cognton component; (b) Mutaton operator for the nerta component ast one edge datacenter exceedng ts storage capacty. We compare the value of the ftness functon of two encoded partcles for three dfferent cases. Case 1: Both encoded partcles are feasble, and the partcle wth the smaller data transmsson tme s selected as the better one. The ftness functon s defned as follows. ftness = T total X (12) nd 1 ( ). Case 2: Both encoded partcles are nfeasble, and the partcle wth the smaller data transmsson tme s selected as the better one. An nfeasble partcle may become a feasble partcle after the update operaton, and the partcle wth the smaller data transmsson tme s more lkely to be selected. Therefore, the ftness functon s consstent wth (12). Case 3: An encoded partcle s nfeasble, and another one s feasble. There s no doubt that the feasble partcle s selected, and the ftness functon s defned as follows. DS, f, ds u capacty j j ftness = j= 1. (13) 1,else 3) Update strategy As shown n (9), tradtonal PSO ncludes three man parts: nerta, ndvdual cognton, and socal cognton. The movement of each partcle s nfluenced by ts personal best-known poston, but s also guded toward the global best-known poston n the search-space [36]. The tradtonal PSO s easy to prematurely converge nto a local optmum. To enhance the search ablty of our strategy, we adapt the crossover and mutaton operators of the GA for partcle update to explore a wder range of the soluton space. The update strategy for the th partcle at the t th teraton s descrbed as follows. t t 1 t 1 t 1 X = c C ( c C ( w M ( X ), pbest ), gbest ), (14) 2 g 1 p u

7 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 7 where C g(), C p() are both crossover operators, and M u() represents the mutaton operator. For the ndvdual cognton and socal cognton components, we adapt the crossover operator of the GA and update the correspondng parts of (9), whch s shown n (15) and (16). t t 1 t t t 1 C p( A, pbest ) r1 c1 B = c1 Cp( A, pbest ) =, (15) t A else C ( B, gbest ) r c C = c C ( B, gbest ) =, (16) t t 1 t t t 1 g g t B else where r 1 (or r 2) s a random factor between and 1. C p() (or C g()) randomly selects two ndexes n an old partcle, and replaces the segment between them wth the one n the pbest (or gbest) partcle. Fgure 4(a) llustrates the crossover operator for the ndvdual (or socal) cognton component. It randomly selects the two crossover ndexes (nd 1 and nd 2), and replaces the segment between 1 st (nd 1) ndex and 2 nd (nd 2) ndex n the old partcle wth the pbest (or gbest) partcle. Property 3: The crossover operator may change an encoded partcle from feasble to nfeasble, and vce versa. The encoded partcle (1, 1, 3, 2, 3) n Fgure 3 s feasble. Assume that the pbest partcle s (2, 3, 2, 2, 3), and the crossover ndexes are 1 st and 2 nd. Therefore, the generated encoded partcle s (2, 3, 3, 2, 3) after the crossover operator. Ths partcle places {ds 2, ds 3, ds 5, ds 6} n dc 3, and the sze of all datasets n dc 3 s 21 GB, whch exceeds the storage capacty of dc 3 (2 GB). Ths generated partcle s nfeasble. On the contrary, an nfeasble partcle (2, 3, 3, 2, 3) crossover wth the pbest partcle (2, 2, 1, 2, 3) n ndex 1 st and 2 nd. The new generated partcle (2, 2, 3, 2, 3) s feasble. For the nerta component, we adapt the mutaton operator of the GA and update the nerta part of (9), whch s shown n (17). t 1 t t 1 Mu( X ) r3 w A = w Mu ( X ) =, (17) t 1 X else where r 3 s a random factor between zero and one. Because the prvate datasets are stored n the correspondng fxed datacenters, M u() randomly selects an ndex n an old partcle, whch can only be wthn the poston of publc datasets. M u() then randomly changes ths ndex value n the range of the datacenter number. The mutaton operator selects the ndex n two cases. Case 1: The old partcle s feasble. M u() randomly changes ths ndex value n the range of the datacenter number. Case 2: The old partcle s nfeasble. M u() randomly selects one ndex of the overloaded datacenters, and then randomly changes ths ndex value n the range of the datacenter number. The encoded partcle n Fgure 3 belongs to Case 1. M u() randomly selects the ndex nd1, and then updates the value of nd1 from 3 to 2 n Fgure 4(b). Property 4: The mutaton operator may change an encoded partcle from feasble to nfeasble, and vce versa. The mutaton operator randomly selects 2 nd ndex of a feasble partcle (1, 2, 3, 2, 3) to mutate, and then generates a new nfeasble partcle (1, 3, 3, 2, 3). Ths new partcle stores {ds 2, ds 3, ds 5, ds 6} n dc 3, whose sze of datasets s 21 GB, exceedng ts storage capacty (2 GB). Alternately, t mutates an nfeasble partcle (1, 3, 3, 2, 3) n ndex 2 nd, and then generates a new feasble partcle (1, 1, 3, 2, 3). 4) A map from a partcle to a data placement Algorthm 2 s the pseudocode of mappng a partcle to a data placement for a scentfc workflow wth nputs, ncludng a scentfc workflow G = (T, E, DS), the datacenters DC, and the encoded partcle X. Frst, the current storage of all datacenters dc cur() s set to and the total data transmsson tme T total s set to (lne 1). After ntalzaton, the datasets are stored n the correspondng datacenters, and the current storage of each datacenter dc cur(x[]) s recorded. If the storage of any edge datacenter exceeds ts storage capacty, then the encoded partcle s nfeasble and returned (lne 2-7). Accordng to the task executon sequence, the task t j s placed n datacenter dc j wth a mnmal transmsson tme. If the sum (ncludng the current storage of dc j), the sze of nput datasets of task t j, and the sze of output datasets of task t j exceeds the storage capacty of dc j, then the encoded partcle s nfeasble and returned. Otherwse, the output datasets of t j are stored n the correspondng datacenters, whose current storage s updated (lnes 8-14). If the encoded partcle s feasble, we further calculate the data transmsson tme. All tasks are sequentally scanned, and the datacenters DC j that store the nput datasets IDS j of tj are dentfed. The transmsson tme Transfer j from IDS j to dc j accordng to (6) s calculated, and all related transmsson tmes are supermposed to calculate the total data transmsson tme T total (lnes 15-19). Fnally, the data placement strategy and correspondng T total are output (lne 2). 5) Parameter settngs The nerta weght w n (9) determnes the speed change, whch has an effect on the search ablty and convergence of PSO [37]. When the nerta weght w s large, the global search ablty of PSO s strong and does not easly converge; otherwse, the local search ablty of PSO s strong and converges easly. Equaton (18) s a classcal adjustment mechansm of the nerta weght [38]. In the ntal stage of PSO, more focus s placed on the global search to a wder range of soluton spaces. As the number of subsequent teratons ncreases and the search goes deeper, PSO focuses more on the local search ablty. Therefore, the value of nerta weght w decreases lnearly wth the number of teratons, where w max and w mn are the maxmum and mnmum values of w, respectvely, durng the ntalzaton phase. ters max and ters cur are the maxmum and the current number of teratons, respectvely. wmax wmn w = wmax terscur. (18) ters The nerta weght of (18) s adjusted based on the number of teratons, whch does not satsfy the nonlnear characterstcs of data placement. Therefore, an nerta weght that can adaptvely adjust the search ablty accordng to the current partcle qualty s desgned n (19). The new adjustment mechansm can adaptvely adjust ts search ablty accordng to the dfference between the current and global best partcles. t 1 t 1 w = w ( w w ) exp( d( X ) ( d( X )-1.1)), (19) max max mn max t 1 t 1 t 1 dv( X, gbest ) d( X ) =, DS (2) where dv(x t-1, gbest t-1 ) represents the number of dfferent values between the current partcle X t-1 and the global best partcle gbest t-1. When dv(x t-1, gbest t-1 ) s large (whch means

8 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 8 Algorthm 2: A map from a partcle to a data placement procedure dataplacement (G, DC, X) 1: Intalzaton: dc cur(), T total. 2: foreach ds of DS n // Determne whether there s an overloaded datacenter durng placng ntal datasets 3: dc cur(x[]) += dsze, place ds n dc X[] 4: f dc cur(x[]) > capacty X[] then 5: return ths partcle s nfeasble 6: end f 7: end for 8: for j = 1 to j = T // Determne whether there s an overloaded datacenter durng tasks executon 9: Place task t j n datacenter dc j wth mnmal data transmsson tme 1: f dc cur(j)+sum(ids j)+sum(ods j) > capacty j 11: return ths partcle s nfeasble 12: end f 13: Place the output datasets ODS j of t j n the correspondng datacenters, and update ther current storage 14: end for 15: for j = 1 to j = T // Calculate the total transmsson tme of data placement 16: Fnd the datacenters DC j storng the nput datasets IDS j of t j 17: Calculate the transmsson tme from IDS j to dc j accordng to (6) 18: T total += Transfer j 19: end for 2: Output the data placement strategy and the correspondng T total end procedure that there s a bg dfference between X t-1 and gbest t-1 ), then t must enhance the global search ablty. Therefore, the weght of w should be ncreased to ensure a larger search range and avod premature convergence. Otherwse, t must enhance the local search ablty and accelerate the convergence to fnd an optmal soluton. Accordng to the lnear ncrease (or decrease) strategy [39], the other two acceleraton coeffcents (c 1 and c 2) are defned as (21) and (22). start end start c1 c1 c1 = c1 terscur, (21) ters c Note that start 2 and c end 2 start c1 max start end start c2 c2 c2 = c2 terscur. (22) ters and end c1 max are the ntal and fnal values of c 1. are the ntal and fnal values of c 2. 6) Algorthm flowchart Fgure 5 s the GA-DPSO flowchart, whose detaled steps are descrbed as follows. Step 1: Compress the number of datasets accordng to the preprocessng for a scence workflow n part 1 n ths secton (that s, Algorthm 1). Step 2: Intalze relevant parameters of GA-DPSO such as populaton sze, maxmum teraton, nerta weght, and cogntve factors, then randomly generate the ntal populaton. Step 3: Accordng to the map from a partcle to a data placement n part 2 n ths secton (that s, Algorthm 2), calculate the ftness of each partcle based on (12) and (13). Each partcle s set as ts personal best partcle, and the partcle wth the smallest ftness s set as the global best partcle of the populaton. Step 4: Update partcles based on (14) - (17), and recalculate the ftness of each updated partcle. Start Preprocess the scentfc workflow Intalze the relevant parameters Generate the ntal populaton Calculate each partcle's ftness; select personal best partcle pbest and global best partcle gbest Update partcles based on partcle update strategy Recalculate the ftness of each updated partcle No End Yes Satsfy stop condton? Update gbest Yes ftness<gbest? Update pbest Yes ftness<pbest? Fg. 5 GA-DPSO flowchart Step 5: If the ftness of the updated partcle s smaller than ts personal best partcle, then set the updated partcle as ts own personal best partcle. Otherwse, go to Step 7. Step 6: If the ftness of the updated partcle s smaller than the global best partcle, then set the updated partcle as the global best partcle. Step 7: Verfy whether the stop condton s met. If t s not satsfed, then go to Step 4. Otherwse, termnate the procedure. V. EXPERIMENTAL RESULTS AND ANALYSIS We conducted all smulaton experments on a Wn8 64-bt operatng system wth an 7-75U 2.9 GHz Intel (R) Core (TM) processor and 8GB of RAM. Accordng to [38], the relevant parameters of GA-DPSO were set as follows. The sze of ntal populaton was 1, the maxmum teraton was 1, w max =.9, w mn =.4, start c1 =.9, A. Expermental setup end c1 =.2, start c2 =.9, and end c2 No No =.4. We conducted our experments usng fve types of partly synthetc workflows: CyberShake n earthquake scence, Montage n astronomy, SIPHT n bonformatcs, Epgenomcs n bogenetcs, and LIGO n gravtatonal physcs. These were all nvestgated n depth by Bharath et al. [3]. Both the number of datasets and the structure n each type of scentfc workflow are dfferent. The detaled nformaton about dependency structure and nput/output datasets for each type of workflows s recorded n an XML fle 1. For each scentfc feld, there are four knds of scentfc workflows wth dfferent szes of tasks, from whch ths study selected three for our experments: small (approxmately 3 tasks), medum (approxmately 5 tasks), and large (approxmately 1 tasks). We evaluate the effect of several mpact factors on dfferent data placement strateges. Therefore, we adjust some mpact factors based on the basc experment, whose setup s descrbed as follows. The hybrd envronment conssts of four datacenters {dc 1, dc 2, dc 3, dc 4}, where dc 1 s a cloud datacenter wth unlmted storage capacty, and the other three datacenters are edge datacenters. We defne the benchmark storage capacty cap benchmark as (23), and the storage capacty of three edge datacenters 1

9 Transmsson tme Transmsson tme > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 9 12 DCO-K-means GS NGA-DPSO GA-DPSO 25 DCO-K-means GS NGA-DPSO GA-DPSO 25 DCO-K-means GS NGA-DPSO GA-DPSO Transmsson tme Workflow types (a) (b) (c) dsze capacty = DC 1 = 1. (23) The proporton of prvate datasets n a workflow s set to 25%, and the bandwdth across dfferent datacenters s descrbed as follows (ts unt s M/s). ~ ~ Bandwdth = (24) ~ ~ B. Compettve algorthms There are certan smlartes between the hybrd cloud envronment and the envronment combnng edge computng and cloud computng [29]. To verfy the effectveness of GA-DPSO, we modfed the DCO-k-means data placement strategy [13] and the GA-based data placement strategy (GS) [15] to adapt the tme-drven data placement strateges for a scentfc workflow combnng edge computng and cloud computng. The DCO-k-means data placement strategy frst clustered the datasets accordng to the data dependency, and then dvded the datasets nto data blocks usng a matrx-parttonng model. The data dependency degree, whch represented the number of tasks that smultaneously accepted two relevant datasets as nput, played a sgnfcant role n the matrx-parttonng model. The defnton of data dependency degree gnored the factor of bandwdth whle optmzng data transmsson tme. Therefore, we redefne the data dependency degree dependency j as follows. dependency = Count( ds. T ds. T ) j j mn( dsze, dsze j), ds, ds j DS flex band( flc)( flc j) dsze, ds DS, ds DS band( flc)( flc j) dsze j, ds DS, ds DS band( flc)( flc j), ds, ds j DS fx flex j fx fx j flex, Workflow types (25) band ( flc)( flc j) Fg. 6 Data transmsson tme of dfferent strateges for three knds of workflows n basc experment: (a) Small; (b) Medum; (c) Large s 2.6 tmes that of cap benchmark. where Count(ds.T ds j.t) represents the number of tasks that DS accept both datasets ds and ds j as nput, and represents the pre-placement bandwdth between the datacenter storng ds and the one storng ds j. The new defnton of data dependency degree consders the nfluence of bandwdth whle optmzng data transmsson tme. GS prmarly used a bnary encodng strategy wth GA to optmze the number of data movements, amount of data movement, and data transmsson tme n cloud envronments. It gnored prvate datasets and placed all datasets n a cloud datacenter. To compare wth GA-DPSO, we modfed GS as follows. The fxed storage of prvate datasets was consdered wth bnary encodng. Moreover, GS consdered the bandwdth factor not only n the map from the encoded chromosome to the data placement, but also n the calculaton of the ftness functon. Fnally, to observe the effect of the preprocessng n secton IV, the NGA-DPSO algorthm wthout preprocessng s used as another comparson algorthm. C. Expermental results and analyss Workflow types GS, GA-DPSO, and NGA-DPSO belong to the meta-heurstc algorthms. Therefore, they termnate f they mantan ther orgnal value after 8 teratons n our experments. Because the data placement results wth the same meta-heurstc algorthm may be dfferent n each experment, the data transmsson tme s measured as the average of 1 repeated experments. The unt of data transmsson tme s seconds (s), and the expermental results for data transmsson tme s reduced by 1 tmes. Fgure 6 shows the data transmsson tme of dfferent data placement strateges for three knds of scentfc workflows under a basc experment. In general, GA-DPSO and NGA-DPSO have the best performance. GS s worse compared wth GA- DPSO and NGA-DPSO, and the overall performance of DCOk-means s the worst. Due to the data dependency degree of DCO-k-means beng defned based on the pre-placement bandwdth (but not the fnal bandwdth), there s a gap between the actual data placement and preconceved one. The search scope of GS s relatvely lmted durng each teraton, and t does not adaptvely adjust accordng to the performance of the current chromosome, whch results n a worse result compared wth GA-DPSO or NGA-DPSO. For Epgenomcs and Montage, NGA-DPSO s slghtly better than GA-DPSO, and the average data transmsson tme s reduced by approxmately 1.5%. Ths s manly due to the fact that the preprocessng affects the fnal

10 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Transmsson tme DCO-K-means GS NGA-DPSO GA-PSO 45. DCO-K-means GS NGA-DPSO GA-PSO 16. DCO-K-means GS NGA-DPSO GA-PSO Number of edge datacenters Number of edge datacenters Transmsson tme (a) (b) (c) Transmsson tme Number of edge datacenters 6. DCO-K-means GS NGA-DPSO GA-PSO 12 DCO-K-means GS NGA-DPSO GA-PSO 5. 1 Transmsson tme Transmsson tme (d) Fg. 7 Data transmsson tme of dfferent strateges for medum workflows wth dfferent numbers of edge datacenters: (a) CyberShake; (b) Epgenomcs; (c) LIGO; (d) Montage; (e) SIPHT data placement result (Property 1). The compressed datasets become larger, whch may no longer be stored n the orgnal edge datacenter and must be stored n another datacenter wth a larger storage capacty. The preprocessng eventually leads to a slght dfference between GA-DPSO and NGA-DPSO. Fgure 6(c) shows the data transmsson tme of dfferent strateges for large scentfc workflows under the basc experment. The strateges n Fgure 6(c) cost more data transmsson tme compared wth those n Fgures 6(a) and 6(b). Ths s manly because of the ncrease n the number and total amount of workflow datasets, whch results n more data transmsson across dfferent datacenters. For example, the number of datasets n the small, medum, and large scentfc workflow of LIGO s 47, 77, and 151, and the total sze of datasets s 2.47 TABLE I THE AVERAGE NUMBER OF ITERATION WHEN ACHIEVING GBEST FOR THE MEDIUM WORKFLOWS Algorthms CyberShake Epgenomcs LIGO Montage SIPHT GS NGA-DPSO GA-DPSO TABLE II THE AVERAGE EXECUTION TIME WHEN ACHIEVING GBEST FOR THE MEDIUM WORKFLOWS (MS). Algorthms CyberSh ake. Epgen omcs Number of edge datacenters LIGO Montage SIPHT GS NGA-DPSO GA-DPSO Number of edge datacenters (e) TB, 4.8 TB, and 7.98 TB, respectvely. It costs more tme to transmt more and larger datasets n large workflows wth the same bandwdth across dfferent datacenters. Tables 1 and 2 show the average number of teratons and average executon tme for the three meta-heurstc algorthms when achevng the optmal result for medum scentfc workflows. The average executon tme s measured n mllseconds (ms). The average number of teratons of GA-DPSO outperforms NGA-DPSO for Epgenomcs and Montage, whose number of teratons can be reduced by approxmately 1%. Ths s manly due to the preprocessng. The number of datasets of Epgenomcs s compressed from 77 to 5, whose compresson rate exceeds 35%. Through preprocessng, the number of datasets can be reduced and the encodng space for each partcle can be reduced accordngly. Therefore, the number of teratons for searchng the optmal result can be sgnfcantly reduced. Wth the compresson of the encodng space for each partcle, the executon effcency of GA-DPSO s mproved, and the executon tme of GA-DPSO s reduced accordngly. From Table 2, t can be seen that the executon tme of GA-DPSO s sgnfcantly superor to NGA-DPSO for the scentfc workflows wth hgh compresson ratos, whch also benefts from the preprocessng. Regardng the number of teratons and the executon tme, GS has the worst performance compared wth the other two meta-heurstc algorthms, whch s manly due to the encodng space of GS not beng effectvely compressed. The search scope of GS s relatvely lmted durng each teraton and does not adaptvely adjust tself accordng to the performance of the current chromosome.

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