multiobjectiveoptimizationofcloudmanufacturingservice...

Research ArticleMultiobjective Optimization of Cloud Manufacturing ServiceComposition with Improved Particle SwarmOptimization Algorithm

Yongxiang Li 12 Xifan Yao 2 and Min Liu2

1School of Mechanical Engineering Guizhou University of Engineering Science Bijie 551700 Guizhou China2School of Mechanical amp Automotive Engineering South China University of Technology Guangzhou 510640 Guangdong China

Correspondence should be addressed to Xifan Yao mexfyaoscuteducn

Received 7 March 2020 Revised 4 August 2020 Accepted 25 September 2020 Published 14 October 2020

Academic Editor Agathoklis Giaralis

Copyright copy 2020 Yongxiang Li et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Aiming at the problems of low search efficiency and inaccurate optimization of existing service composition optimizationmethods a new multiobjective optimization model of cloud manufacturing service composition was constructed which tookservice matching degree composition synergy degree cloud entropy execution time and execution cost as optimization ob-jectives and an improved particle swarm optimization algorithm (IPSOA) was proposed In the IPSOA the integer encodingmethod was used for particle encoding+e inertia coefficient and two acceleration coefficients were improved by introducing thenormal cloudmodel sine function and cosine function+e global search ability of IPSOA in the early stage was improved and itsprematurity was restrained to form amore comprehensive solution space In the later stage IPSOA focused on the local fine searchand improved the optimization precision Taking automatic guided forklift manufacturing task as an example the correctness ofthe proposed multiobjective optimization model of cloud manufacturing service composition and the effectiveness of its solutionalgorithm were verified +e performance of IPSOA was analyzed and compared with standard genetic algorithm (SGA) andtraditional particle swarm optimization (PSO) Under the same conditions IPSOA had a faster convergence speed than PSO andSGA and had better performance than PSO

1 Introduction

In todayrsquos world the trend of manufacturing globalizationdiversification of consumer demand and shortening ofproduct marketization cycle has brought great challenges totraditional manufacturing enterprises It is difficult for asingle enterprise to meet all the customersrsquo needs and it isalso difficult for a single enterprise to possess all themanufacturing resources needed for product manufactur-ing In order to effectively overcome the shortcomings of thetraditional production mode cloud manufacturing hasdeveloped rapidly in the past ten years Based on the idea ofcentralized use of decentralized resources and servingdecentralized users with centralized resources [1] cloudmanufacturing is a new service-oriented demand-drivenon-demand payment efficient and low consumption andknowledge-based networked manufacturing mode [2]

Cloud manufacturing is developed on the basis of cloudcomputing technology It integrates service-oriented tech-nology Internet technology communication technologymodern logistics technology Internet of +ings technologyhigh-performance computing and artificial intelligencetechnology to virtualize and servitize all kinds ofmanufacturing resources and manufacturing capabilities ofresource providers so as to achieve unified and centralizedintelligent management and operation Furthermore it canprovide timely safe high-quality and low-cost cloudmanufacturing services for resource users [3]

A single manufacturing cloud service is often difficult tomeet the userrsquos needs A complex manufacturing require-ment needs to combine multiple fine-grained simple cloudservices into coarse-grained complex cloud services Com-plex cloud services are implemented in distributed het-erogeneous and autonomous environments to accomplish

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 9186023 17 pageshttpsdoiorg10115520209186023

manufacturing tasks which are highly uncertain and dy-namic Optimal selection of cloud manufacturing services isone of the key technologies of cloud manufacturing and animportant part of service management of cloudmanufacturing platform [4] +e advantages and disad-vantages of cloud manufacturing service composition modeland its solution methods affect the rapid and efficient use ofmanufacturing resources in cloud manufacturing environ-ment It has become a hot issue in the field of cloudmanufacturing research In this paper we study themathematical model of multiple influence factors in cloudmanufacturing service composition and the service com-position optimization algorithm

+e remaining chapters of this paper are arranged asfollows Section 2 comprehensively analyzes the researchwork done by domestic and foreign scholars on cloudmanufacturing service composition optimization Section 3gives the definitions and calculation methods of cloud en-tropy service matching degree composition synergy degreeexecution time and execution cost Section 4 proposes theIPSOA algorithm Section 5 analyzes and verifies the per-formance of the proposed optimization algorithm throughapplication example and Section 6 summarizes the wholepaper and puts forward the future work

2 Literature Review

In recent years many scholars have used genetic algorithmbee colony algorithm particle swarm optimization algo-rithm and other methods to study the modeling and op-timization of cloud manufacturing service composition Forexample +ekinen and Panchal [5] regarded resource al-location in cloud environment as a two-way matchingproblem Four kinds of two-way matchingmechanisms wereclassified from individual rationality stability antistrategyconsistency monotony and Pareto efficiency includingdeferred acceptance top trading cycle Munkres and firstcome first service+rough Delphi research on the attributesof cloud service quality Lang et al [6] determined thatservice function legality contract geographical locationand flexibility were the highest service quality evaluationcriteria for cloud service selection Raileanu et al [7]combined energy consumption with product scheduling andresource allocation and proposed a design method of highavailability production management system based on cloudHelo and Hao [8] proposed a dynamic optimization modelof production planning and control based on cloud for sheetmetal processing and developed a scheduling prototypesystem based on the genetic algorithm Chen and Wang [9]proposed a classified artificial neural network ensemblemethod to predict the time required to simulate cloudmanufacturing tasks K-means was used to classify thesimulated manufacturing cloud tasks For each task cate-gory an artificial neural network was constructed to predictthe time required for manufacturing cloud tasks in thecategory Namjoo and Keramati [10] used resource-basedtheory and Dematel method to study the causality betweenthe dimensions and attributes of composite service elasticityin cloud manufacturing Souza et al [11] studied the

distributed service layout strategy in mixed fog-cloud sce-narios and proposed a concurrent service execution schemeBrant and Sundaram [12] carried out the application ex-periment of manufacturing cloud Under the condition ofmanufacturing cloud the micrometal materials weremanufactured by indoor electrochemical deposition tech-nology +e horizontal deposition parameters were opti-mized based on the deposition resolution and themanufacturing data were saved in the cloud for users to useon demand Based on the formal description of cloudmanufacturing resource allocation problemWang et al [13]constructed a multiobjective resource allocation model withminimizing cost and time and optimizing quality +emultiobjective optimization problem was transformed into asingle-objective optimization problem by the classicalweighted summation method and solved by the maximuminheritance method Zhou and Yao [14] proposed a mul-tipopulation parallel adaptive differential artificial bee col-ony algorithm to optimize the selection of NP-hard forcomposite cloud manufacturing services A number ofparallel subpopulations were used Each subpopulationevolved according to different mutation strategies borrowedfrom differential evolution +e control parameter of eachmutation strategy was adjusted independently to generatedisturbed food sources for foraging Li et al [15] studied self-governing cloud manufacturing service composition andoptimization selection and proposed a fuzzy soft decisionmethod based on volatility analysis Li and Yao [16] con-structed cloud manufacturing service description modelinteraction scenario model and composition process formalmodel based on process algebra extended process algebrasemantics to describe service quality information andproposed an intelligent service composition method basedon extended process algebra Tao et al [17] designed a cloudmanufacturing service supply-demand matching simulatorbased on hypernetwork which could compare servicematching results and scheduling algorithm performanceZhang et al [18] studied a fuzzy QoS-aware manufacturingservice composition method based on the extended polli-nation algorithm Yang et al [19] proposed a dynamicservice selection method within multiple manufacturingcloud systems aiming to apply the Internet of +ings real-time sensors big data and event-driven dynamic serviceselection Chen et al [20] proposed a method called QoS-aware web service composition to help cloud demanders forservice composition based on a multiobjective model andprovided an efficient-dominance multiobjective evolution-ary algorithm to fulfill the service composition model +ehuge and ever-increasing number of web service providersin the cloud had the same manufacturing functions yet theypossessed different QoS indexes [21] +erefore mostscholars conducted their research based on quality of serviceA number of indexes such as cost time and reliability wereutilized to form the overall objective functions in order toselect the best possible composition for a specific task [22]Quality of service could be described as a set of key per-formance index used to assess the quality of servicescomposed in a cloud manufacturing system Availabilityreliability cost time geographical position and

2 Mathematical Problems in Engineering

technological capability were among the key indicatorsapplied by researchers in service composition issues Aimingat the problem of optimal selection of manufacturing servicecomposition Que et al [23] proposed a new manufacturers-to-users model for cloud manufacturing established acomprehensive mathematical evaluation model with fourkey service quality perception indicators (ie time costreliability and capability) and solved the model by usinginformation entropy immune genetic algorithm Huanget al [24] combined genetic algorithm with particle swarmoptimization proposed a hybrid genetic particle swarmoptimization algorithm based on teaching and learningintroduced learning mechanism into genetic algorithm andenabled the descendants of genetic algorithm to learn thecharacteristics of elite chromosomes from double memorylearning in the evolutionary process +e algorithm wassearched for solutions in two subpopulations of geneticalgorithm module and particle swarm optimization moduleand exchanged information simultaneously Zhao et al [25]proposed a SPEA2 algorithm based on adaptive selectionevolutionary operator to solve multiobjective optimizationproblem In the evolutionary process the simulated binarycrossover operator polynomial mutation operator anddifferential evolution operator could be selected adaptivelyaccording to the contribution of operators Zhang et al [26]proposed an extended teaching and learning optimizationalgorithm for parallel optimization of distributedmanufacturing resource allocation Xu and Cai [27] pro-posed an efficient global optimization algorithm based onmultidata for automobile body design +e general com-puting technology based on graphics processing unit and thehybrid parallel computing method was used to improve thesolving efficiency

+e above literature mainly considers time and cost astwo quality factors adopts the basic idea of transforming themultiobjective optimization problem of manufacturingcloud service composition optimization into a single-ob-jective optimization problem and uses traditional matureoptimization algorithm to solve it indirectly [28] Howeverthese traditional solutions have obvious defects or defi-ciencies which are mainly reflected as follows firstly theabovementioned studies mainly focus on the optimization ofservice quality parameters such as execution cost and timebut the impact of composition complexity collaborationmatching property and other nonfunctional service qualityparameters in service composition is less considered sec-ondly the selection of weight coefficients has strong sub-jectivity and the optimization results are greatly influencedby the subjective factors In the cloud manufacturing en-vironment each cloud service executing agent is in a certainsocial relationship not an idealized ldquorigid bodyrdquo In themanufacturing process different cloud manufacturing ser-vices carry out different data exchange information trans-mission and material transportation +ey are constrainedby each other in the manufacturing life cycle process and inwhich cooperation and competition coexist+e relationshipbetween cloud manufacturing services and manufacturingtasks and the relationship between services directly affect theefficiency of service composition in performing

manufacturing tasks In cloud manufacturing environmentcustomized product manufacturing to meet individual needsis a common process which often requires collaborativeparticipation of customers and service providers Cloudmanufacturing service composition not only needs to meetthe requirements of traditional product delivery period andmanufacturing costs but also the matching degree betweenmanufacturing tasks and cloud services the synergy degreebetween cloud manufacturing services in the manufacturingprocess and the service composition complexity All of themhave significant impacts on the completion of customizedproduct manufacturing tasks +erefore it is necessary toimprove the traditional optimization algorithm explore newefficient cloud service composition optimization methodsand take service matching degree composition synergydegree and service composition complexity as optimizationfactors to study cloud manufacturing service compositionoptimization

In the process of service composition all manufacturingsubtasks decomposed according to customerrsquosmanufacturing needs must be allocated to one or morecorresponding cloud services to complete +e optimizationobjectives of the optimal cloud manufacturing servicecomposition scheme such as service matching degreecomposition synergy degree cloud entropy execution timeand cost should be as close as possible to the ideal valuesBased on the basic rules the cloud manufacturing servicecomposition optimization modeling particle swarm opti-mization algorithm improvement and its application arestudied in the following research

3 Mathematical Modeling of CloudManufacturing Service Composition

31 Service Composition Problem Description In cloudmanufacturing a complex manufacturing task needs to bedecomposed into several simple manufacturing subtasks tocomplete in most cases By searching for simple cloudservices matching each manufacturing subtask in the cloudmanufacturing service platform for composition and op-timization the complex cloud service with coarse granu-larity is constructed to achieve the complex manufacturingtask requirements If a complex manufacturing task J canbe decomposed into m manufacturing subtasks and it canbe expressed as J J1 J2 Jj Jmminus 1 Jm where Jj is the j-thmanufacturing subtask of the complex manufacturing taskJ j 1 2 3 middot middot middot m For each manufacturing subtask thecorresponding candidate manufacturing cloud services aresearched in the cloud resource pool to form the candidatemanufacturing cloud service set Sj of the j-thmanufacturing subtask +e j-th cloud service set can beexpressed as Sj S1j S2j Sbij

where bi denotes thenumber of cloud services contained in the j-th cloud serviceset and Sbij

denotes the bi-th cloud service in the j-th cloudservice set +e total number of cloud services in n cloudservice sets S1 S2 Sj Sn is N 1113936

nj1 bj +e cloud

manufacturing service composition process is shown inFigure 1 [29]

Mathematical Problems in Engineering 3

32 Computation of Execution Time and Execution CostMinimum time and minimum cost are two basic principles inthe operation of a companyrsquos business In the research field ofcloud manufacturing service composition service executiontime and execution cost are important indicators for perfor-mance evaluation of cloud manufacturing service compositionschemes According to the characteristics of manufacturingresources in cloud manufacturing environment service exe-cution time and execution cost are defined as follows

Execution time (ET) is the response time for cloudmanufacturing service to manufacturing task Because cloudmanufacturing service involves both online and offline factorsand its execution time is longer than that of ordinary webservice Moreover the influence of logistics time in hetero-geneous cloud manufacturing environment often becomes thebottleneck of the whole manufacturing process +erefore it isnecessary to take logistics time into consideration of servicequality To sum up the value of execution time is equal to thesumof the processing time of cloudmanufacturing services thetime required for auxiliary work (such as equipment main-tenance and workpiece clamping) and the time consumed formaterial transportation during service execution namely

ET Tprocessing + Tauxiliary + Tlogistics (1)

where ET is the execution time Tprocessing is the processingtime Tauxiliary is the auxiliary time and Tlogistics is the lo-gistics time

Execution cost (EC) is the cost that service users pay forusing the cloud manufacturing service +e value of exe-cution cost is equal to the sum of manufacturing cloudservice charges identified by service providers payment formaterial transportation in the service execution and third-party service fees charged by cloud platform namely

EC Cservice + Clogistics + Cplatform (2)

where EC is the execution cost Cservice is the cloud servicecost Clogistics is the logistics cost and Cplatform is the platformcost

+e types of cloud manufacturing service compositioninclude sequence composition parallel composition choicecomposition and cycle composition as shown in Figure 2[30] In the sequence composition different services areexecuted sequentially according to their order in the servicecomposition As shown in Figure 2(a) the two services S1and S2 in the composition constitute an orderly serial chainand service S2 can be executed only after service S1 has beenexecuted In the parallel composition the two services S1 andS2 are executed concurrently as shown in Figure 2(b) Forkis the beginning transition of service operation in the parallel

Manufacturing subtasks

Service sets

Services

J1

J2

J3

J4

J5

J6

JjJ7

S1

S2 S4

S3

S31

S42 S14

S23 S17

S26

S35 Sij

S5

S6

S7

Sj

Manufacturing taskJ

Figure 1 Cloud manufacturing service composition process [29]


composition and join is the end transition Only when S1and S2 are all executed can the end transition join betriggered In the choice composition as shown inFigure 2(c) one of the services is selected As long as theselected service is successfully executed the choice com-position is successfully executed Decision is the beginningtransition of service operation of choice composition andmerge is the end transition Figure 2(d) shows the cyclecomposition where service S1 is repeatedly executed Cycleis a cyclic operator Cycle(k)S1 indicates that service S1 isrepeatedly executed k times Under different compositionmodes the execution time and cost of cloud manufacturingservice composition are different as shown in Table 1 [30]

Screening candidate services according to service exe-cution time and execution cost is an important work in cloudmanufacturing service composition However it is notenough to screen candidate services only according to thetwo indicators In order to fully reflect the service quality ofcandidate cloud manufacturing services and service com-position this paper takes execution time execution costservice matching degree composition synergy degree andcloud entropy as five quality evaluation criteria of servicecomposition and then carries out cloud manufacturingservice composition model construction algorithm im-provement and case analysis

33 Service Matching Degree Modeling Service matchingdegree (MD) is a quantitative measure of the matchingbetween cloud manufacturing services and allocatedmanufacturing tasks Service matching degree reflects therequest-response relationship between cloud services andmanufacturing tasks +e main factors affecting servicematching degree are the idleness of manufacturing re-sources equipment status comprehensive manufacturingcapability service reputation cumulative times of cloudmanufacturing services performing similar manufacturingtasks active degree of cloud manufacturing services anddistance between manufacturing resources mapped by cloud

manufacturing services and service objects According to thecharacteristics of different factors the factors affectingservice matching can be summarized as technical factorhunger factor and distance factor

331 Technical Factor Technical factor (TF) refers toevaluating the technical level of a cloud manufacturingservice to accomplish a manufacturing task based on cu-mulative times of cloud manufacturing services performingsimilar manufacturing tasks service reputation serviceexecution rate service activity and equipment performancein the past period of time It is described by the rank vectorTFij = [0 01 02 03 middot middot middot 09 1] in which TFij represents thetechnical capability measurement of the i-th service thatperforms the j-th task 1le ileN 1lejlem +e technical ca-pability of N cloud services that perform m manufacturingtasks can be described by Ntimesm technical matrix TF =(TFij)N times m

332 Hunger Factor One of the outstanding contributionsof cloud manufacturing is to activate idle manufacturingresources +e idle rate of manufacturing resources refers tothe ratio of the number of available manufacturing resourcesunused for manufacturing tasks to the total number ofmanufacturing resources According to the idle rate ofmanufacturing resources mapped by cloud manufacturingservices the desire level of the cloud manufacturing servicesto undertake and complete manufacturing tasks can beevaluated which is described as hunger factor HFij HFijrepresents the hunger degree of the i-th service to undertakeand complete the j-th task 1leileN 1le jlem +e range ofHFij is [0 1] +e higher the idle rate of manufacturingresources mapped by cloud manufacturing services themore hungry and thirsty for accepting manufacturing tasksand the bigger the hunger factor on the contrary the smallerthe hunger factor+e value of hunger factor can be obtainedby calculating the idle rate of manufacturing resources andthe hunger factor matrix is HF (HFij)Ntimesm

S1Starte1 e2 e3

EndS2

(a)

S1

S2e1

e2

e3

e4

e5

e6Start End

Fork Join

(b)

S1

S2e1

e2

e3

e4

e5

e6Start End

Decision Merge

(c)

S1e1 e2

Start End

k

Cycle

(d)

Figure 2 Schematic diagrams of four main types of service composition [30] (a) sequence composition (b) parallel composition (c) choicecomposition (d) cycle composition


333 Distance Factor Cloud manufacturing services aremore complicated than ordinary web services due to theinfluence of offline factors in the execution process Spatialdistance often becomes a constraint in the execution processof cloud manufacturing services Generally small spatialdistance is beneficial to the execution of cloudmanufacturing services while large spatial distance is notconducive to the execution of cloud manufacturing servicesDistance factor is introduced to describe the impact of therelative distance between manufacturing resources mappedby cloud manufacturing services and service users on theexecution of cloud manufacturing services It is expressed asDFij 1le ileN 1le jlem DFij represents the distance factorbetween the manufacturing resources mapped by the i-thcloud manufacturing service and the j-th service users +erange of DFij is [0 1] +e smaller the relative distance thelarger the distance factor on the contrary the smaller thedistance factor For example if the distance between cloudmanufacturing resources and cloud service users is 300 kmthen DFij 04 if the distance is 50 km then DFij 08 if thedistance is less than 1 km then DFij 1 similarly othercorresponding distance factors can be obtained

In summary service matching degree matrix can becalculated as follows

MD

MD11 MD12 middot middot middot MD1mminus 1 MD1m

MD21 middot middot middot middot middot middot middot middot middot MD2m

middot middot middot middot middot middot MDij middot middot middot middot middot middot

MDNminus 11 middot middot middot middot middot middot middot middot middot MDNminus 1m

MDN1 MDN2 middot middot middot MDNmminus 1 MDNm

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(3)

where MDij represents the matching degree of the i-thservice to the j-th task MDij αtimesTFij + βtimesHFij + c timesDFij1leileN 1le jlem α β and c are the weight coefficientsEvery influencing factor has different importance to servicematching degree and the three influencing factors can begiven different weight coefficients +e sum of the weightcoefficients of the three factors is equal to 1 ie α+ β+ c 1which is helpful for calculating service matching degree andevaluating the importance of the three factors

34 Composition Synergy Degree Modeling Compositionsynergy degree (SD) represents the collaboration levelamong cloud manufacturing services that are composed toperform a complicated manufacturing task Compositionsynergy degree reflects the collaborative relationship be-tween two cloud manufacturing services in service com-position In service composition the more convenient theinformation exchange between cloud manufacturing ser-vices and the smoother the material transportation theshorter the time for them to cooperate to completemanufacturing tasks and the higher the composition syn-ergy degree between cloud manufacturing services on thecontrary the lower the composition synergy degree [31]With low composition synergy degree there are seriousobstacles to information exchange and material trans-portation between cloud manufacturing services which candelay product delivery and increase execution cost +ecomposition synergy degree of cloudmanufacturing servicesis directly reflected in execution time +e compositionsynergy degree can be evaluated by calculating the timetaken by cloud manufacturing services to completemanufacturing tasks For example the composition synergydegree between services Si and Sj used to complete tasks Jiand Jj is calculated as follows

SDij Ti + Tj

Tij

(4)

where Ti is the time taken by service Si to complete task Jiindependently Tj is the time taken by Sj to complete Jjindependently and Tij is the total time taken by two servicesSi and Sj to synergically perform two tasks Ji and Jj +erelationship structure between tasks affects the calculation ofexecution time +ere are mainly parallel sequential andinteractive coupling relationships among manufacturingtasks It is relatively easy to calculate the total execution timeof complex manufacturing tasks composed of independentmanufacturing subtasks However the calculation of thetotal execution time of complex manufacturing tasks withinteractive coupling relationship is rather complicated +ecalculation for Tij in different cases is listed in the followingequation

Table 1 Calculation of execution time and cost for different types of service composition [30]

No Composition types Execution time Execution cost1 Sequence composition ETsequence 1113936ET(Si) ECsequence 1113936EC(Si)

2 Parallel composition ETparallel Max(ET(Si)) ECparallel 1113936EC(Si)

3 Choice composition ETchoice 1113936(θi middot ET(Si)) ECchoice 1113936(θi middot EC(Si))

4 Cycle composition ETcycle k middot ET(Si) ECcycle k middot EC(Si)

Note θi is the probability that the i-th service in the choice composition is selected and 1113936 θi 1 If the i-th service must not be selected then θi 0 If the i-thservice must be selected then θi 1 and the probability of other services being selected is 0 k denotes the cycle number


Tij

max Ti Tj1113960 1113961 if manufacturing tasks Ji and Jj are parallel and independent with each other

Ti + Tj if manufacturing tasks Ji and Jj are sequential and independent with each other

Ti + Tj + 2ζ ijTi middot Tj

1113969 if there is an interactive coupling relationship between tasks Ji and Jj

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(5)

where ζ ij is the interactive coupling coefficient and its rangeis [minus 1 1]+e higher the previous cooperation frequency andthe better the smoothness of service interaction and materialtransportation the smaller the ζ ij value on the contrary thebigger the ζ ij value Tij max[Ti Tj] is the total completiontime calculation formula when manufacturing tasks Ji and Jjare independent and in the parallel relationship Tij Ti +

Tj is the total completion time calculation formula whenmanufacturing tasks Ji and Jj are independent and in thesequence relationship Tij Ti + Tj + 2ζ ij

Ti middot Tj

1113969is a for-

mula for calculating the total completion time ofmanufacturing tasks Ji and Jj when they are in the interactivecoupling relationship It is based on the electromagneticcoupling principle in physics Because of the interactivecoupling relationship between manufacturing tasks Ji and Jjthe completion process of two subtasks depends on eachother and influences each other +e interactive couplingcoefficient ζ ij transforms the qualitative relationship of in-terdependence and mutual influence into a quantitative onewhich is helpful for a clearer analysis of the characteristicsand rules of the relationship [32]

+us the composition synergy degree matrix of cloudmanufacturing service can be constructed as follows

SD

SD11 SD12 SD13 middot middot middot SD1Nminus 1 SD1N

SD21 SD22 middot middot middot middot middot middot middot middot middot SD2N

SD31 middot middot middot middot middot middot middot middot middot middot middot middot middot middot middot

middot middot middot middot middot middot middot middot middot SDij middot middot middot middot middot middot

SDNminus 11 middot middot middot middot middot middot middot middot middot middot middot middot SDNminus 1N

SDN1 SDN2 middot middot middot middot middot middot SDNNminus 1 SDNN

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(6)

where SDij represents the composition synergy degree of thei-th cloud manufacturing service to the j-th cloudmanufacturing service in service composition

35 Cloud Entropy Modeling Simple and orderly servicecomposition structure has greater certainty to completemanufacturing tasks successfully Complex and disorderedcloud manufacturing service composition structure is proneto failure and the probability of successfully completingmanufacturing tasks is small Entropy originated fromthermodynamic research and has been widely recognizedand accepted by the scientific community since it gainedgreat development in information theory Different cloud

manufacturing services have different continuous workingtimes maintenance times and logistics times when per-forming manufacturing tasks +e process of cloudmanufacturing services completing manufacturing tasks atone time is obviously simpler than that of dividing them intomultiple stages to complete +e quantification level ofcomplexity and orderliness of cloud manufacturing servicecomposition can be expressed by cloud entropy (CE) +ecloud entropy of the i-th cloud manufacturing service tocomplete corresponding manufacturing task can be calcu-lated as follows [33]

CEi minus 1113944

Qi

j1

STij

TTi

lnSTij

TTi

(7)

where CEi is the cloud entropy of the i-th cloudmanufacturing service STij is the duration of the i-th cloudmanufacturing service in the j-th state TTi is the total time ofthe i-th service for completing the corresponding task andQi is the total state number of the i-th service for completingthe task+e cloud entropy of a cloud manufacturing servicecomposition is equal to the sum of cloud entropy of all cloudmanufacturing services in the service composition schemeCloud entropy is used to measure the composition com-plexity Its calculation formula is shown in equation (8) [33]+e smaller the cloud entropy is the more orderly andsimpler the cloud manufacturing service composition is andthe higher the reliability is

CE minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

(8)

where N is the total service number in the service compo-sition and CE is the cloud entropy of cloud manufacturingservice composition

36 Multiobjective Optimization Model for ServiceComposition +e ultimate goal of cloud manufacturingservice composition is to select the best cloud services tocomplete all of the usersrsquo manufacturing tasks +e resultingservice composition scheme should meet the constraints ofexecution time and execution cost and make the cloudmanufacturing service composition have the highest com-position synergy degree the biggest composition matchingdegree the smallest cloud entropy the smallest executiontime and the smallest execution cost Cloud manufacturingservice composition is a multiobjective optimization prob-lem and its mathematical model is constructed as follows


maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N

q1SDpq middot ξpj middot ξqk1113872 1113873 (10)

minY3 minCE min minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)

minY4 min ET min max T1 T2 T3 Tmminus 1 Tm( 1113857( 1113857 (12)

minY5 minEC min 1113944m

j1ECj min 1113944

m

j11113944

N

i1Ti middot wi middot ξij1113872 1113873 (13)

stmax T1 T2 T3 middot middot middot Tmminus 1 Tm( 1113857leET0 (14)

1113944

m

j1ECj 1113944

m

j11113944

N

i1Ti middot wi middot ξij1113872 1113873leEC0 (15)

1113944

N

i1ξij ge 1 (16)

ξij 1 if the j-thmanufacturing task is allocated to the i-th cloudmanufacturing service0 otherwise

1113896 (17)

where wi represents the unit time cost and ECj representsthe execution cost of the j-th manufacturing taskEquations (9)ndash(13) are objective functions in whichequation (9) maximizes the total service matching degreeequation (10) maximizes the total composition synergydegree and equations (11)ndash(13) represent the minimumvalues of the total cloud entropy execution time andexecution cost of service composition respectivelyEquations (14)ndash(16) are constraints in which equation(14) stipulates that the maximum execution time of mmanufacturing tasks cannot exceed the threshold timeET0 Equation (15) stipulates that the maximum executioncost of m manufacturing tasks cannot exceed thethreshold cost EC0 Equation (16) stipulates that every taskmust be allocated to one or more cloud services forexecution

4 Improved Particle SwarmOptimization Algorithm

+e cloud manufacturing service composition problem is aNP-hard problem of multiobjective collaborative optimi-zation +e traditional particle swarm optimization algo-rithm is easy to premature and fall into local extremumand it is difficult to adapt to complex nonlinear optimi-zation problem+erefore its optimization quality needs tobe improved +is paper introduces the normal cloudmodel [34] to improve the inertia coefficient and

acceleration coefficient of the traditional particle swarmoptimization algorithm balances the global explorationand local development ability of the algorithm and designsan improved particle swarm optimization algorithm(IPSOA) to solve the cloud manufacturing service com-position mathematical model +e algorithm process isshown in Figure 3

41 Particle Encoding Method +e mapping relationshipbetween particle position vector and service compositionscheme is established by the integer encoding method Incloud manufacturing environment if a multifunctionalrequirement task is decomposed into m subtasks and eachsubtask is allocated to a candidate cloud service to performthen the service composition used by the complexmanufacturing task is composed of m single resource cloudservices A cloud service composition is represented as anm-dimensional particle +e particle dimension is ParDimm+e j-th dimension of the particle represents the j-th subtaskJj of the complex manufacturing task and the task Jj cor-responds to a cloud service set Sj which contains multiplecandidate cloud services for the task Jj +e value of the j-thdimension represents the candidate cloud service numberselected by the task Jj Assuming that the particle swarmconsists of R particles the position and velocity of the i-thparticle can be represented by an m-dimensional vector asfollows


xi xi1 xi2 xi3 middot middot middot xim1113872 1113873 i 1 2 3 R (18)

vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)

where xij and vij represent the position and velocity ofthe j-th dimension of the i-th particle respectively +eposition xij of the particle represents the candidatecloud service number selected by the task Jj in theprocess of service composition Figure 4 shows thecorresponding relationship between particle and servicecomposition

BPi and BGi represent the historical optimal position ofthe i-th particle (ie individual extremum) and the globaloptimum position of the whole particle swarm (ie globalextremum) respectively Both of them can be represented byan m-dimensional vector as follows

BPi BPi1BPi2BPi3 BPim1113872 1113873 i 1 2 3 R

(20)

BG BG1BG2BG3 BGm( 1113857 (21)

where BPij represents the optimal position of the i-thparticle in the j-th dimension and BG represents the optimalservice composition selected by the manufacturing task setJ (J1 J2 J3 Jm)

In the first iteration of the algorithm the particle Pi inthe particle swarm is randomly generated and assigned toBPi and the particle with the optimal fitness value isassigned to BG In each subsequent iteration BPi and BG areupdated according to particle fitness values When themaximum iteration number is reached the algorithm isterminated and cloud manufacturing service compositionwith the optimal comprehensive service quality is obtained

42 Velocity and Position Updating Method +e formulasfor particle velocity and position updating are as follows

v(t+1)ij ψ middot v

(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)

where ψ represents the inertia coefficient t represents thecurrent number of iterations i represents the particlenumber j represents the j-th dimension of the particle c1and c2 represent the acceleration coefficient and r

(t)1 and r

(t)2

are random numbers distributed in [0 1] +e right side ofequation (22) consists of three parts ψ middot v

(t)ij is the mo-

mentum part of the particle which reflects the inertia of theparticle motion and indicates that the particle has thetendency to maintain its previous velocity c1 middot r

(t)1 middot (BP

(t)ij minus

x(t)ij ) is the part of the particlersquos self-recognition which

reflects the memory of the particles own historical

Random initialization of the particle swarm

Calculate the particle fitness values of the swarm and calculate the maximum minimum and average fitness values

For each particle compare its fitness valuewith individual extremum and update and save

its historical optimal individual extremum

For each particle compare its fitness valuewith global extremum and update and save the

historical optimal global extremum

Update the velocity and position of the particles

Update the algorithm iteration generation t = t + 1

Calculate cloud entropy service matchingdegree composition synergy degreeexecution time and execution cost

Generation gt Maxgen

End the algorithm and output the optimization

results

Yes

No

Calculate particle entropy ParEnt expected value ExpVal andhyper entropy HypEnt and provide different particles with

different inertia and acceleration coefficients

Figure 3 Flow chart of IPSOA

3 4 2 1 3 1

Service sets

Particle

Tasks

S11 S12 S13 S15 hellip

hellip

hellip

hellip

hellip

hellip

hellip

hellip

helliphelliphelliphelliphelliphellip hellip

S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services

Figure 4 +e corresponding relationship between particle andservice composition


experience and indicates that the particle has the tendencyto approach its best historical position c2 middot r

(t)2 middot (BG(t)

j minus

x(t)ij ) is the social consciousness part of the particle which

reflects the collective historical experience of cooperationand knowledge sharing among particles and indicates thatthe particle tends to approach the best historical position ofgroup or neighborhood

43 Inertia Coefficient Setting Inertia coefficient is one of themost important parameters in the particle swarm optimiza-tion algorithm A bigger inertia coefficient can improve theglobal search ability of the algorithm and avoid prematureconvergence because of falling into local extremum A smallerinertia coefficient can help to achieve accurate search in anarea and improve convergence accuracy In order to avoidfalling into local extremum and improve the diversity ofparticles the normal cloud model is introduced to improvethe inertia and acceleration coefficients of the traditionalparticle swarm optimization algorithm and a nonlinear in-ertia coefficient is set up to balance the global exploration andlocal development ability of the particle swarm optimizationalgorithm Normal cloud model is a set of random numberswhich follow the normal distribution law and has a stabletendency It is described by four main parameters expectedvalue ExpVal particle entropy ParEnt standard deviationStaDev and hyperentropy HypEnt +e improved inertiacoefficient is calculated as follows [34]

ψ

η1eminus (fminus ExpVal)22(StaDev)2

fgef

η2 ψmax minusf minus fmin

fmax minus fminψmax minus ψmin( 11138571113890 1113891 fltf

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)

where ExpVal=f in which f is the average fitness value ofparticles in the particle swarmStaDev= r3 times HypEnt + CloEnt in which r3 is a randomnumber distributed in [0 1] ParEnt=fmax minus fτ1 in whichτ1 is the control coefficient of particle entropyHypEnt=CloEntτ2 in which τ2 is the control coefficient ofhyperentropy ψmax is the maximum inertia coefficient of theparticle swarm ψmin is the minimum inertia coefficient ofthe particle swarm fmax is the maximum fitness value of theparticle swarm fmin is the minimum fitness value of theparticle swarm f is the average fitness value of the particleswarmf is the fitness value of the particle and η1 and η2 arethe constants in [0 1] and can be set η1 04 and η2 08From the analysis of equation (24) the inertia coefficient ψhas a larger value in the initial stage With the increase initerations the inertia coefficient gradually decreases whichmakes the algorithm change from global search in the initialstage to local fine search in the later stage

+e verticality of normal cloud model curve is controlledby particle entropy ParEnt +e average value of the normalcloud model is reflected in expected value ExpVal+e cloudparticles in the model fluctuate around ExpVal which showsthe discreteness of cloud particles +e discreteness of cloud

particles is mainly determined by the hyperentropy HypEnt+e randomness of normal cloud model increases with theincrease in HypEnt and its stability increases with the de-crease in HypEnt With the help of the normal cloud modelthe IPSOA algorithm improves the global search ability inthe initial stage restrains the premature convergence to forma more comprehensive solution space and focuses on localfine search in the later stage of the algorithm

44 Acceleration Coefficients Setting In the iteration processof IPSOA algorithm the acceleration coefficients c1 and c2determine the influence of particle self-cognition and socialcognition on particle trajectory which reflects the infor-mation exchange degree between particles in swarms andrepresent the acceleration weights of particles advancingtowards their own extremum and global extremum re-spectively +e formulas for calculating the accelerationcoefficients are as follows [35]

c1 c1start + c1end minus c1start1113872 1113873sin(ψ) (25)

c2 c2start minus c2start minus c2end1113872 1113873cos(ψ) (26)

where c1 is the self-acceleration coefficient c2 is the globalacceleration coefficient c1start and c2start are the initial valuesof acceleration coefficients c1 and c2 and c1end and c2end aretheir termination values respectively Acceleration coeffi-cients c1 and c2 are set according to equations (25) and (26)Setting larger global acceleration coefficient and smaller self-acceleration coefficient in the initial stage of the IPSOA al-gorithm the social learning ability of the particle is strongerand the self-learning ability is weaker which is beneficial tostrengthening the global search ability setting smaller globalacceleration coefficient and larger self-acceleration coefficientat the later stage of the IPSOA algorithm the self-learningability of the particle is stronger and the social learning abilityis weaker which is beneficial to local fine search and con-verges to the global optimal solution with high precision

45 Fitness Function Establishment +e multiple objectivesof cloud manufacturing service composition interact witheach other and are difficult to solve directly by generalmathematical methods However cloud service users oftenhave a clear understanding of the objectives and expectationsof cloud manufacturing service composition +e purpose ofcloud manufacturing service composition can be expressedas finding a cloud manufacturing service compositionscheme which is as close as possible to the expectations ofcloud service users under limited time limited cost andother conditions +e expectations of cloud service users aredefined as the ideal point of the objective functions of cloudmanufacturing service composition IPSOA algorithm usesthe ideal point method to design fitness function +e cri-terion for evaluating the effect of service compositionscheme is the distance between ideal point and objectivefunction values ie deviation Its calculation formula is asfollows


Dev

Yi1 minus Ylowast11113872 1113873

2+ Y

i2 minus Ylowast21113872 1113873

2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi

4 and Yi5 are the five objective function

values of cloud manufacturing service composition schemecorresponding to the i-th particle Ylowast1 Ylowast2 Ylowast3 Ylowast4 and Ylowast5 arethe optimal values of five objective functions respectivelywhich constitute the ideal point and Dev is the deviation

Dimensionless treatment is done for five objectivefunctions of cloud manufacturing service composition sothe deviation formula is changed to

Devprime

Yi1 minus Ylowast1Ylowast1

1113888 1113889

2

+Yi2 minus Ylowast2Ylowast2

1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)

where Devprime is called the relative deviation+e smaller the deviation the better the service com-

position scheme on the contrary the worse the servicecomposition scheme +ere are two main methods to de-termine the ideal point one is to calculate the optimal valuesthrough single-objective function optimization algorithm to

form the ideal point and another is to compose the idealpoint by all objective function expected values specified bycloud service users Weight coefficients are given accordingto the different importance of five objective functions +usthe fitness function of IPSOA algorithm can be designed asfollows

f(i) Γ minus

δ 1Yi1 minus Ylowast1Ylowast1

1113888 1113889

2

+ δ2Yi2 minus Ylowast2Ylowast2

1113888 1113889

2


1113888 1113889

2

+ +δ4Yi4 minus Ylowast4Ylowast4

1113888 1113889

2


1113888 1113889

2

11139741113972

(29)

where f(i) is the fitness function value of the i-th particle Γ isa sufficiently large positive number δ1 δ2 δ3 δ4 and δ5 arethe weight coefficients of the five objective functions re-spectively and 1113936

5k1 δk 1

46 IPSOA Algorithm Steps +e main steps of IPSOA al-gorithm are as follows

Step 1 initialize particle swarm including particleswarm size ParSiz position xi and velocity vi of eachparticle set the initial and end values of accelerationcoefficients c1 and c2 maximum evolutionary gener-ation MaxGen and randomly initialize the initial po-sition and initial velocity of each particle in thedefinition domain +e initial position of the particle isset as the initial individual optimal position and theposition of the particle with the best fitness in theparticle swarm is set as the initial global optimalpositionStep 2 calculate service matching degree compositionsynergy degree cloud entropy execution time andexecution costStep 3 calculate the fitness value of all the particles inthe particle swarmStep 4 for each particle compare its fitness value f(i)

with individual extremum f(BPi) If f(i)gtf(BPi)then replace f(BPi) with f(i) and BPi with Pi

Step 5 for each particle compare its fitness value f(i)

with global extremum f(BG) If f(i)gtf(BG) thenreplace f(BG) with f(i) and BG with PiStep 6 update the inertia coefficient of particlesaccording to equation (24) update the self-accelerationcoefficient and global acceleration coefficient of par-ticles according to equations (25) and (26) update thevelocity and position of particles according to equa-tions (22) and (23)Step 7 check the termination condition of the al-gorithm If the evolutionary generation reaches theset maximum value or other algorithm end condi-tions are met stop the iterative operation of thealgorithm and output the results otherwise return tostep 2

IPSOA is a parallel algorithm All the particles can bedivided into several groups [36] Each group solves theoptimization problem separately and each group is com-puted by one core of the multicore CPU ie parallelcomputing to achieve concurrent solutions

5 Application Example

Taking producing automatic guided forklift (AGF) by usingcloud manufacturing services as an example the proposedoptimization algorithm for cloud manufacturing servicecomposition is applied


+e AGF manufacturing task can be divided into sevensubtasks J1 body production J2 driving device productionJ3 working device production J4 power supply systemproduction J5 auxiliary control system production J6 maincontrol system production and J7 painting and packagingAccording to the proposed IPSOA algorithm the abovemanufacturing tasks are matched with cloud services asshown in Table 2 +e cloud service sets for manufacturingtasks J1 J2 J3 J4 J5 J6 and J7 are S1 S2 S3 S4 S5 S6 and S7respectively +e number of cloud services included in eachset is 3 2 2 3 2 4 and 2 respectively TF HF and DFrepresent technical factor hunger factor and distance factorTexe Tcon and Trep are used for execution time (hour)maximum continuous working time (hour) and repair time(hour) respectively w denotes the unit time cost (dollarhour) Taking α 04 β 03 and c 03 the servicematching degree MD can be calculated according toequation (3) +e cloud entropy CE can be calculatedaccording to equation (8)

According to equation (6) the service compositionsynergy degree matrix of the AGFmanufacturing task can becalculated as follows

SD

SD11 SD12 middot middot middot SD16 SD17

SD21 middot middot middot middot middot middot middot middot middot SD27

middot middot middot middot middot middot SD44 middot middot middot middot middot middot



⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)

where the diagonal elements of the matrix SD are all 1 andSD12 is a 3times 2 matrix which represents the compositionsynergy degree of three candidate cloud manufacturingservices of the manufacturing task J1 to two candidate cloudmanufacturing services of the manufacturing task J2 +emeaning of other elements is the same All elements ofmatrix SD are calculated as shown in Table 3

+e improved particle swarm optimization algorithm isprogrammed by using Matlab R2015a +e deadline con-straint ET0 is 480 and the cost constraint EC0 is 18000 +eparticle swarm size is ParSiz 30 +e maximum iterationgeneration is MaxGen 120 Taking Γ 100 all the weightcoefficients of the five objective functions are set to 02 ieδk 02 (k 1 2 3 4 5) According to the single-objectivefunction optimization algorithm the ideal point can beobtained ie (515 19035 7317 406 13608) +e spaceboundaries for total execution time ETsum are [0 490] +ebounds for total execution cost ECsum are [0 18500] +ebounds for total service matching degree MDsum are [0 10]+e bounds for total composition synergy degree SDsum are[0 20] +e bounds for total cloud entropy CEsum are [0 20]After 49 iterations the optimal fitness value of the particleswarm is 99928 the corresponding point (MDsum SDsumCEsum ETsum ECsum) is (447 18142 7887 406 13671) andthe particle code of the optimal service composition schemeis 2112132 +e relative deviation between the optimal so-lution and the ideal point is 0160 As shown in Figure 5 theparticle code represents the following meanings themanufacturing task J1 is allocated to the 2-nd cloud service

in cloud service set S1 task J2 to the 1-st cloud service incloud service set S2 task J3 to the 1-st cloud service in cloudservice set S3 task J4 to the 2-nd cloud service in cloudservice set S4 task J5 to the 1-st cloud service in cloud serviceset S5 task J6 to the 3-rd cloud service in cloud service set S6and task J7 to the 2-nd cloud service in cloud service set S7+e average running time of the algorithm is 1156 s and theiteration curves of its related parameters are shown inFigure 6 Figure 6(a) shows the iteration curve of the optimalparticle fitness Figure 6(b) shows the iteration curve of theservice matching degree Figure 6(c) shows the iterationcurve of the composition synergy degree Figure 6(d) showsthe iteration curve of the cloud entropy Figure 6(e) showsthe iteration curve of service composition execution timeFigure 6(f) shows the iteration curve of service compositionexecution cost and Figure 6(g) shows the iteration curve ofrelative deviation +e particle swarm tends to be stablewhen it iterates to the 49-th generation

Given the samemaximum iteration generation and particleswarm size IPSOA algorithm standard genetic algorithms(SGA) [37] and traditional particle swarm optimization al-gorithm (PSO) [35] are used to solve the same service com-position optimization problem respectively As shown inFigure 7 IPSOA converges to the optimal solution in the 49-thgeneration SGA converges in the 82-nd generation and PSOconverges to the optimal solution in the 54-th generation +ealgorithms run on a portable computer with Intel core i3-3110M CPU 24GHz main frequency and 4G memoryIPSOA takes 1156 s SGA 1905 s and PSO 1294 s as shown inTable 4+e relative deviation of IPSOA is 0160 that of SGA isalso 0160 and that of PSO is 0183+e above case analysis andexperimental results show that IPSOA has faster convergencespeed and shorter solution time than PSO and SGA formultiobjective optimization of cloud manufacturing servicecomposition and IPSOA has better performance than PSO

In the process of using IPSOA to optimize GAF cloudmanufacturing service composition service matching degreecomposition synergy degree cloud entropy execution timeand execution cost are used as the five main variables of theoptimization model +e influence of technical factor re-sources vacancy rate distance factor multiple services col-laboration level coupling relationship complexity reliabilitytime and cost of service composition are fully considered Asshown in Table 5 the service composition scheme obtained byIPSOA has better comprehensive characteristics than thegeneral methods Maximum matching degree method(MaxMDM) service composition scheme has the best servicematching degree but it has worse cloud entropy executiontime execution cost and relative deviation Maximum syn-ergy degree method (MaxSDM) service composition schemehas the best composition synergy degree but it has worsecloud entropy execution time execution cost and relativedeviation Minimum cloud entropy method (MinCEM)service composition scheme has minimum cloud entropy butits service matching degree and composition synergy degreeare smaller than that of IPSOA and it has worse executiontime execution cost and relative deviation Minimum exe-cution time method (MinETM) service composition schemehas the minimum execution time but with the increase in the


weight coefficients of service matching degree compositionsynergy degree and cloud entropy the relative deviation valueof MinETM will be bigger than that of IPSOA and itscomprehensive service quality will become worse Minimumexecution cost method (MinECM) service compositionscheme has the minimum execution cost but its servicematching degree and composition synergy degree are smallerthan that of IPSOA and it has worse execution time andrelative deviation Compared with the five service composi-tion schemes IPSOA has the smallest relative deviation andthe best comprehensive performance which helps users make

more reasonable decisions If only the execution cost andexecution time are considered in the service composition andthe influence of service matching degree combination co-ordination degree and combination entropy are not con-sidered it may lead to userrsquos wrong decision and bring adverseeffects tomanufacturing industry such as the shortcomings ofMinETM andMinECM Because the service matching degreeand composition synergy degree of the two service compo-sition schemes are very small the manufacturing servicesselected from the two service composition schemes may haveproblems of poor service quality and low service reliability

Table 2 Matching table of cloud services and manufacturing tasks

Jj J1 J2 J3 J4 J5 J6 J7Sj S1 S2 S3 S4 S5 S6 S7Sij S1 1 S2 1 S3 1 S1 2 S2 2 S1 3 S2 3 S1 4 S2 4 S3 4 S1 5 S2 5 S1 6 S2 6 S3 6 S4 6 S1 7 S2 7TF 08 02 02 06 02 04 02 08 02 04 06 06 02 04 08 04 06 08HF 09 05 08 07 04 06 03 05 04 08 03 09 06 07 05 09 09 05DF 08 1 04 1 08 08 1 04 08 1 1 08 04 08 1 04 08 1Texe 79 46 52 48 58 49 60 75 63 72 55 62 77 68 62 76 90 83Tcon 30 24 24 30 40 20 19 24 20 16 30 24 30 24 16 20 24 30Trep 3 4 1 2 1 4 2 3 2 1 1 2 2 2 3 1 2 1w 49 40 45 31 36 31 39 42 51 50 35 40 35 35 30 32 25 22MD 083 053 044 075 044 058 047 059 044 07 063 075 038 061 077 055 075 077CE 1281 0919 0991 0792 0689 1220 1316 1343 1309 1735 0765 1251 1224 1283 1691 1527 1580 1190

Table 3 Computation results of composition synergy degree

Jj J1 J2 J3 J4 J5 J6 J7Sj S1 S2 S3 S4 S5 S6 S7SD S1 1 S2 1 S3 1 S1 2 S2 2 S1 3 S2 3 S1 4 S2 4 S3 4 S1 5 S2 5 S1 6 S2 6 S3 6 S4 6 S1 7 S2 7S1 1 1000 1000 1000 0838 0771 0774 0835 0588 0770 0833 0836 0771 0588 0770 0834 0588 0770 0833S2 1 1000 1000 1000 0909 0834 0833 0910 0534 0835 0911 0909 0835 0534 0836 0910 0534 0841 0913S3 1 1000 1000 1000 0527 0589 0588 0527 0670 0589 0530 0526 0589 0671 0590 0527 0671 0597 0533S1 2 0838 0909 0527 1000 1000 0833 0910 0532 0835 0911 0909 0834 0533 0835 0834 0533 0840 0912S2 2 0771 0834 0589 1000 1000 0770 0833 0590 0769 0834 0833 0769 0591 0770 0769 0590 0773 0836S1 3 0774 0833 0588 0833 0770 1000 1000 0594 0771 0836 0834 0770 0594 0772 0834 0594 0777 0838S2 3 0835 0910 0527 0910 0833 1000 1000 0528 0833 0909 0909 0833 0528 0834 0909 0528 0836 0910S1 4 0588 0534 0670 0532 0590 0594 0528 1000 1000 1000 0529 0589 0667 0589 0527 0667 0589 0527S2 4 0770 0835 0589 0835 0769 0771 0833 1000 1000 1000 0834 0769 0589 0769 0833 0589 0772 0835S3 4 0833 0911 0530 0911 0834 0836 0909 1000 1000 1000 0910 0834 0526 0833 0909 0526 0834 0909S1 5 0836 0909 0526 0909 0833 0834 0909 0529 0834 0910 1000 1000 0530 0834 0909 0530 0837 0911S2 5 0771 0835 0589 0834 0769 0770 0833 0589 0769 0834 1000 1000 0590 0769 0833 0589 0772 0835S1 6 0588 0534 0671 0533 0591 0594 0528 0667 0589 0526 0530 0590 1000 1000 1000 1000 0589 0526S2 6 0770 0836 0590 0835 0770 0772 0834 0589 0769 0833 0834 0769 1000 1000 1000 1000 0771 0834S3 6 0834 0910 0527 0834 0769 0834 0909 0527 0833 0909 0909 0833 1000 1000 1000 1000 0836 0910S4 6 0588 0534 0671 0533 0590 0594 0528 0667 0589 0526 0530 0589 1000 1000 1000 1000 0589 0527S1 7 0770 0841 0597 0840 0773 0777 0836 0589 0772 0834 0837 0772 0589 0771 0836 0589 1000 1000S2 7 0833 0913 0533 0912 0836 0838 0910 0527 0835 0909 0911 0835 0526 0834 0910 0527 1000 1000

2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks

Figure 5 +e optimal solution of the AGF manufacturing task


Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)

Figure 6 IPSOA iteration curves (a) iteration curve of the optimal particle fitness (b) iteration curve of service matching degree (c)iteration curve of composition synergy degree (d) iteration curve of cloud entropy (e) iteration curve of execution time (f ) iteration curveof execution cost (g) iteration curve of relative deviation


which will affect the supply chain product quality deliverytime and even the survival of manufacturing enterprises Forexample when multinational manufacturing enterprises suchas ZTE and Huawei purchase parts globally based on cloudservices they need to consider factors such as servicematching degree composition synergy degree and cloudentropy rather than just considering execution time andexecution cost Unstable cooperation and low service reli-ability may hinder the normal production of products andthreaten the survival of enterprises +e impact of COVID-19has increased the weight of service matching degree com-position synergy degree and cloud entropy in the servicecomposition optimization model Enterprises need to paymore attention to these aspects when making decisions from2020 and make appropriate adjustments to adapt to therapidly changing global manufacturing environment

6 Conclusion

In order to solve the problems of low search efficiency andinaccurate optimization in existing service compositionoptimization methods the multiobjective optimization of

cloudmanufacturing service composition is discussed a newimproved particle swarm algorithm is proposed andcomprehensive service quality evaluation method is studied+e main work and contributions are summarized asfollows

(1) +e main factors affecting the performance of cloudmanufacturing service composition are studied Anew service quality model of cloud manufacturingservice composition is constructed by combining thethree new attributes of cloud entropy servicematching degree and composition synergy degreewith two traditional attributes of execution time andexecution cost which evaluates the service compo-sition performance more comprehensively

(2) +e mathematical model of cloud manufacturingservice composition optimization is establishedCloud entropy service matching degree composi-tion synergy degree execution time and executioncost are taken as five objective functions and particlefitness function is constructed by the ideal pointmethod which provides a multiobjective

9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation

Figure 7 Comparison of SGA PSO and IPSOA iteration curves

Table 4 Optimization results for the AGF manufacturing task

Algorithms Computing time (s) Convergence generation Optimization results Relative deviationSGA 1905 82 S21 S12 S13 S24 S15 S36 S27 0160PSO 1294 54 S21 S12 S13 S24 S15 S26 S27 0183IPSOA 1156 49 S21 S12 S13 S24 S15 S36 S27 0160

Table 5 Comparison of different factorsrsquo influences on service composition

Algorithms Optimization results MDsum SDsum CEsum ETsum ECsum Relative deviationIPSOA S21 S12 S13 S24 S15 S36S27 447 18142 7887 406 13671 0160MaxMDM S11 S12 S13 S34 S15 S36S27 515 18150 8675 448 16089 0284MaxSDM S21 S12 S23 S34 S15 S36 S27 462 19035 8409 426 14879 0210MinCEM S21 S22 S13 S24 S15 S16 S27 377 15919 7317 431 15106 0338MinETM S21 S12 S13 S24 S15S36 S27 447 18142 7887 406 13671 0160MinECM S21 S12 S13 S14 S15S36 S27 462 16443 7921 418 13608 0192


optimization solution for cloud manufacturing ser-vice composition optimization problem It is helpfulfor enterprises to make more reasonable decisionsand adapt to the unstable global manufacturingenvironment Especially under the influence ofCOVID-19 enterprises should consider more un-stable manufacturing factors in cloud manufacturingactivities and the weight coefficients of servicematching degree composition synergy degree andcloud entropy should be given bigger values in theservice composition optimization model

(3) An improved particle swarm optimization algorithmIPSOA is proposed +e inertia and accelerationcoefficients of the algorithm are improved by in-troducing the normal cloud model sine functionand cosine function It improves the global searchability in the initial stage of the algorithm restrainsthe premature convergence of the algorithm in orderto form a more comprehensive solution space andmakes the algorithm focus on local fine search in thelater stage so as to improve the optimization pre-cision and efficiency

(4) Taking the AGF manufacturing task as an examplethe correctness of the multiobjective service com-position optimization mathematical model and thefeasibility and effectiveness of the IPSOA algorithmare verified Case study shows that compared withthe PSO algorithm and SGA algorithm the IPSOAalgorithm has better performance faster conver-gence speed and shorter solving time for multi-objective optimization problem of cloudmanufacturing service composition

+e development of cloud manufacturing and otherrelated technologies impels manufacturing enterprises todevelop from traditional large-scale flow line productionmode to multibatch customization production from pro-duction-oriented to production-service-oriented and acti-vates all kinds of idle manufacturing resources around theworld Service quantification service granularity cloudentropy matching degree and synergy degree affect thefuture development of cloud manufacturing and will bestudied in depth in future work

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e project was supported by the National Natural ScienceFoundation of China (nos 51375168 and 5181102248) theGUES Scientific Research Foundation for Advanced Talents(no YKHZ G2018009) and the Science and Technology

Foundation of Guizhou Province (nos QKHLHZ [2014]7528 and QJHKYZ [2019]158)

References

[1] B H Li L Zhang S L Wang et al ldquoCloud manufacturing anew service-oriented networked manufacturing modelrdquoComputer Integrated Manufacturing Systems vol 1 pp 1ndash72010

[2] F V Omid andHMahmoud ldquoA platform for optimization indistributed manufacturing enterprises based on cloudmanufacturing paradigmrdquo International Journal of ComputerIntegrated Manufacturing vol 11 pp 1031ndash1054 2014

[3] M Yuan K Deng and W A ChaovalitwongseldquoManufacturing resource modeling for cloudmanufacturingrdquoInternational Journal of Intelligent Systems vol 32 no 4pp 414ndash436 2017

[4] J Lartigau X Xu L Nie and D Zhan ldquoCloud manufacturingservice composition based on QoS with geo-perspectivetransportation using an improved Artificial Bee Colony op-timisation algorithmrdquo International Journal of ProductionResearch vol 53 no 14 pp 4380ndash4404 2015

[5] J +ekinen and J H Panchal ldquoResource allocation in cloud-based design and manufacturing a mechanism design ap-proachrdquo Journal of Manufacturing Systems vol 43 pp 327ndash338 2017

[6] M Lang M Wiesche and H Krcmar ldquoCriteria for selectingcloud service providers a delphi study of quality-of-serviceattributesrdquo Information amp Management vol 55 no 6pp 746ndash758 2018

[7] S Raileanu F Anton T Borangiu et al ldquoA cloud-basedmanufacturing control system with data integration frommultiple autonomous agentsrdquo Computers in Industry vol 11pp 50ndash61 2018

[8] P Helo and Y Hao ldquoCloud manufacturing system for sheetmetal processingrdquo Production Planning amp Control vol 28no 6-8 pp 524ndash537 2017

[9] T Chen and Y-C Wang ldquoEstimating simulation workload incloud manufacturing using a classifying artificial neuralnetwork ensemble approachrdquo Robotics and Computer-Inte-grated Manufacturing vol 38 pp 42ndash51 2016

[10] M R Namjoo and A Keramati ldquoAnalysing causal depen-dencies of composite service resilience in cloudmanufacturing using resource-based theory and dematelmethodrdquo International Journal of Computer IntegratedManufacturing vol 4 pp 1ndash19 2018

[11] V B Souza X Masip-Bruin E Marın-Tordera et al ldquoTo-wards a proper service placement in combined Fog-to-Cloud(F2C) architecturesrdquo Future Generation Computer Systemsvol 87 pp 1ndash15 2018

[12] A Brant and M M Sundaram ldquoA novel system for cloud-based micro additive manufacturing of metal structuresrdquoJournal of Manufacturing Processes vol 20 pp 478ndash484 2015

[13] S Wang W Song L Kang et al ldquoManufacturing resourceallocation based on cloud manufacturingrdquo Computer Inte-grated Manufacturing Systems vol 7 pp 1396ndash1405 2012

[14] J Zhou and X Yao ldquoMulti-population parallel self-adaptivedifferential artificial bee colony algorithm with application inlarge-scale service composition for cloud manufacturingrdquoApplied Soft Computing vol 56 pp 379ndash397 2017

[15] C Li J Guan T Liu et al ldquoAn autonomy-oriented methodfor service composition and optimal selection in cloudmanufacturingrdquo International Journal of AdvancedManufacturing Technology vol 3 pp 1ndash22 2018


[16] Y X Li and X F Yao ldquoCloud manufacturing service com-position and formal verification based on extended processcalculusrdquo Advances in Mechanical Engineering vol 6 pp 1ndash16 2018

[17] F Tao J Cheng Y Cheng S Gu T Zheng and H YangldquoSDMSim a manufacturing service supply-demand matchingsimulator under cloud environmentrdquo Robotics and Computer-Integrated Manufacturing vol 45 pp 34ndash46 2017

[18] S Zhang Y Xu W Zhang et al ldquoA new fuzzy QoS-awaremanufacture service composition method using extendedflower pollination algorithmrdquo Journal of IntelligentManufacturing vol 4 pp 1ndash15 2017

[19] C Yang W Shen T Lin and X Wang ldquoIoT-enabled dy-namic service selection across multiple manufacturingcloudsrdquo Manufacturing Letters vol 7 pp 22ndash25 2016

[20] F Chen R DouM Li andHWu ldquoA flexible QoS-aware webservice composition method by multi-objective optimizationin cloud manufacturingrdquo Computers amp Industrial Engineer-ing vol 99 pp 423ndash431 2016

[21] Y Liu X Xu L Zhang L Wang and R Y ZhongldquoWorkload-based multi-task scheduling in cloudmanufacturingrdquo Robotics and Computer-IntegratedManufacturing vol 45 pp 3ndash20 2017

[22] H Bouzary and F Frank Chen ldquoService optimal selection andcomposition in cloud manufacturing a comprehensive sur-veyrdquo Fe International Journal of Advanced ManufacturingTechnology vol 97 no 1-4 pp 795ndash808 2018

[23] Y Que W Zhong H Chen et al ldquoImproved adaptive im-mune genetic algorithm for optimal QoS-aware servicecomposition selection in cloud manufacturingrdquo InternationalJournal of Advanced Manufacturing Technology vol 10pp 1ndash11 2018

[24] X Huang Z Guan and L Yang ldquoAn effective hybrid al-gorithm for multi-objective flexible job-shop schedulingproblemrdquo Advances in Mechanical Engineering vol 9pp 1ndash14 2018

[25] F Zhao W Lei W Ma Y Liu and C Zhang ldquoAn improvedSPEA2 algorithm with adaptive selection of evolutionaryoperators scheme for multiobjective optimization problemsrdquoMathematical Problems in Engineering vol 2016 pp 1ndash202016

[26] W Zhang S Zhang S Guo et al ldquoConcurrent optimal al-location of distributed manufacturing resources using ex-tended teaching-learning-based optimizationrdquo InternationalJournal of Production Research vol 3 pp 1ndash18 2016

[27] B Xu and Y Cai ldquoA multiple-data-based efficient globaloptimization algorithm and its parallel implementation forautomotive body designrdquo Advances in Mechanical Engi-neering vol 8 pp 1ndash13 2018

[28] Y Wang Z Dai W Zhang et al ldquoUrgent task-aware cloudmanufacturing service composition using two-stage bioge-ography-based optimizationrdquo International Journal of Com-puter Integrated Manufacturing vol 10 pp 1ndash14 2018

[29] W Liu Y Li and B Liu ldquoService composition in cloudmanufacturing based on adaptive mutation particle swarmoptimizationrdquo Journal of Computer Applications vol 10pp 2869ndash2874 2018

[30] Y X Li X F Yao C Xu et al ldquoCloud manufacturing servicecomposition modeling and QoS evaluation based on extendedprocess calculusrdquo Computer Integrated Manufacturing Sys-tems vol 3 pp 689ndash700 2014

[31] Y Li X Yao and M Liu ldquoCloud manufacturing servicecomposition optimization with improved genetic algorithmrdquo

Mathematical Problems in Engineering vol 2019 Article ID7194258 19 pages 2019

[32] Y Li X Yao and J Zhou ldquoMulti-objective optimization ofcloud manufacturing service composition with cloud-entropyenhanced genetic algorithmrdquo Strojniski Vestnik-Journal ofMechanical Engineering vol 62 no 10 pp 577ndash590 2016

[33] Y J Chen X F Yao and D L Xu ldquoJob shop scheduling withprofit and entropy as performance measuresrdquo Journal ofBeijing University of Technology vol 10 pp 1305ndash1311 2010

[34] C H Dai Y F Zhu W R Chen et al ldquoCloud model basedgenetic algorithm and its applicationrdquo Acta Electronic Sinicavol 7 pp 1419ndash1424 2007

[35] M Guo R Li and L Liu ldquoParticle swarm optimization al-gorithm of learning factors and time factor adjusting toweightsrdquo Application Research of Computers vol 11pp 3291ndash3294 2014

[36] N Ghadimi M Afkousi-Paqaleh and A Nouri ldquoPSO basedfuzzy stochastic long-term model for deployment of dis-tributed energy resources in distribution systems with severalobjectivesrdquo IEEE Systems Journal vol 7 no 4 pp 786ndash7962013

[37] Y J Huang X F Yao D Y Ge and Y X Li ldquoEntropy-enhanced genetic algorithm with tabu search for job shopscheduling problemsrdquo Advanced Materials Research vol 590pp 557ndash562 2012


manufacturing tasks which are highly uncertain and dy-namic Optimal selection of cloud manufacturing services isone of the key technologies of cloud manufacturing and animportant part of service management of cloudmanufacturing platform [4] +e advantages and disad-vantages of cloud manufacturing service composition modeland its solution methods affect the rapid and efficient use ofmanufacturing resources in cloud manufacturing environ-ment It has become a hot issue in the field of cloudmanufacturing research In this paper we study themathematical model of multiple influence factors in cloudmanufacturing service composition and the service com-position optimization algorithm

+e remaining chapters of this paper are arranged asfollows Section 2 comprehensively analyzes the researchwork done by domestic and foreign scholars on cloudmanufacturing service composition optimization Section 3gives the definitions and calculation methods of cloud en-tropy service matching degree composition synergy degreeexecution time and execution cost Section 4 proposes theIPSOA algorithm Section 5 analyzes and verifies the per-formance of the proposed optimization algorithm throughapplication example and Section 6 summarizes the wholepaper and puts forward the future work

2 Literature Review

In recent years many scholars have used genetic algorithmbee colony algorithm particle swarm optimization algo-rithm and other methods to study the modeling and op-timization of cloud manufacturing service composition Forexample +ekinen and Panchal [5] regarded resource al-location in cloud environment as a two-way matchingproblem Four kinds of two-way matchingmechanisms wereclassified from individual rationality stability antistrategyconsistency monotony and Pareto efficiency includingdeferred acceptance top trading cycle Munkres and firstcome first service+rough Delphi research on the attributesof cloud service quality Lang et al [6] determined thatservice function legality contract geographical locationand flexibility were the highest service quality evaluationcriteria for cloud service selection Raileanu et al [7]combined energy consumption with product scheduling andresource allocation and proposed a design method of highavailability production management system based on cloudHelo and Hao [8] proposed a dynamic optimization modelof production planning and control based on cloud for sheetmetal processing and developed a scheduling prototypesystem based on the genetic algorithm Chen and Wang [9]proposed a classified artificial neural network ensemblemethod to predict the time required to simulate cloudmanufacturing tasks K-means was used to classify thesimulated manufacturing cloud tasks For each task cate-gory an artificial neural network was constructed to predictthe time required for manufacturing cloud tasks in thecategory Namjoo and Keramati [10] used resource-basedtheory and Dematel method to study the causality betweenthe dimensions and attributes of composite service elasticityin cloud manufacturing Souza et al [11] studied the

distributed service layout strategy in mixed fog-cloud sce-narios and proposed a concurrent service execution schemeBrant and Sundaram [12] carried out the application ex-periment of manufacturing cloud Under the condition ofmanufacturing cloud the micrometal materials weremanufactured by indoor electrochemical deposition tech-nology +e horizontal deposition parameters were opti-mized based on the deposition resolution and themanufacturing data were saved in the cloud for users to useon demand Based on the formal description of cloudmanufacturing resource allocation problemWang et al [13]constructed a multiobjective resource allocation model withminimizing cost and time and optimizing quality +emultiobjective optimization problem was transformed into asingle-objective optimization problem by the classicalweighted summation method and solved by the maximuminheritance method Zhou and Yao [14] proposed a mul-tipopulation parallel adaptive differential artificial bee col-ony algorithm to optimize the selection of NP-hard forcomposite cloud manufacturing services A number ofparallel subpopulations were used Each subpopulationevolved according to different mutation strategies borrowedfrom differential evolution +e control parameter of eachmutation strategy was adjusted independently to generatedisturbed food sources for foraging Li et al [15] studied self-governing cloud manufacturing service composition andoptimization selection and proposed a fuzzy soft decisionmethod based on volatility analysis Li and Yao [16] con-structed cloud manufacturing service description modelinteraction scenario model and composition process formalmodel based on process algebra extended process algebrasemantics to describe service quality information andproposed an intelligent service composition method basedon extended process algebra Tao et al [17] designed a cloudmanufacturing service supply-demand matching simulatorbased on hypernetwork which could compare servicematching results and scheduling algorithm performanceZhang et al [18] studied a fuzzy QoS-aware manufacturingservice composition method based on the extended polli-nation algorithm Yang et al [19] proposed a dynamicservice selection method within multiple manufacturingcloud systems aiming to apply the Internet of +ings real-time sensors big data and event-driven dynamic serviceselection Chen et al [20] proposed a method called QoS-aware web service composition to help cloud demanders forservice composition based on a multiobjective model andprovided an efficient-dominance multiobjective evolution-ary algorithm to fulfill the service composition model +ehuge and ever-increasing number of web service providersin the cloud had the same manufacturing functions yet theypossessed different QoS indexes [21] +erefore mostscholars conducted their research based on quality of serviceA number of indexes such as cost time and reliability wereutilized to form the overall objective functions in order toselect the best possible composition for a specific task [22]Quality of service could be described as a set of key per-formance index used to assess the quality of servicescomposed in a cloud manufacturing system Availabilityreliability cost time geographical position and










nj1 bj +e cloud












Service sets

Services

J1

J2

J3

J4

J5

J6

JjJ7

S1

S2 S4

S3

S31

S42 S14

S23 S17

S26

S35 Sij

S5

S6

S7

Sj

Manufacturing taskJ









S1Starte1 e2 e3

EndS2

(a)

S1

S2e1

e2

e3

e4

e5

e6Start End

Fork Join

(b)

S1

S2e1

e2

e3

e4

e5

e6Start End

Decision Merge

(c)

S1e1 e2

Start End

k

Cycle

(d)





MD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(3)



SDij Ti + Tj

Tij

(4)









Tij





⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(5)



Ti middot Tj

1113969is a for-



SD







⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(6)




CEi minus 1113944

Qi

j1

STij

TTi

lnSTij

TTi

(7)


CE minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

(8)




maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N



i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)



j1ECj min 1113944

m

j11113944

N



1113944

m

j1ECj 1113944

m

j11113944

N


1113944

N

i1ξij ge 1 (16)


1113896 (17)








vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References

















































nj1 bj +e cloud












Service sets

Services

J1

J2

J3

J4

J5

J6

JjJ7

S1

S2 S4

S3

S31

S42 S14

S23 S17

S26

S35 Sij

S5

S6

S7

Sj

Manufacturing taskJ









S1Starte1 e2 e3

EndS2

(a)

S1

S2e1

e2

e3

e4

e5

e6Start End

Fork Join

(b)

S1

S2e1

e2

e3

e4

e5

e6Start End

Decision Merge

(c)

S1e1 e2

Start End

k

Cycle

(d)





MD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(3)



SDij Ti + Tj

Tij

(4)









Tij





⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(5)



Ti middot Tj

1113969is a for-



SD







⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(6)




CEi minus 1113944

Qi

j1

STij

TTi

lnSTij

TTi

(7)


CE minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

(8)




maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N



i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)



j1ECj min 1113944

m

j11113944

N



1113944

m

j1ECj 1113944

m

j11113944

N


1113944

N

i1ξij ge 1 (16)


1113896 (17)








vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References


















































Service sets

Services

J1

J2

J3

J4

J5

J6

JjJ7

S1

S2 S4

S3

S31

S42 S14

S23 S17

S26

S35 Sij

S5

S6

S7

Sj

Manufacturing taskJ









S1Starte1 e2 e3

EndS2

(a)

S1

S2e1

e2

e3

e4

e5

e6Start End

Fork Join

(b)

S1

S2e1

e2

e3

e4

e5

e6Start End

Decision Merge

(c)

S1e1 e2

Start End

k

Cycle

(d)





MD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(3)



SDij Ti + Tj

Tij

(4)









Tij





⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(5)



Ti middot Tj

1113969is a for-



SD







⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(6)




CEi minus 1113944

Qi

j1

STij

TTi

lnSTij

TTi

(7)


CE minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

(8)




maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N



i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)



j1ECj min 1113944

m

j11113944

N



1113944

m

j1ECj 1113944

m

j11113944

N


1113944

N

i1ξij ge 1 (16)


1113896 (17)








vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References















































S1Starte1 e2 e3

EndS2

(a)

S1

S2e1

e2

e3

e4

e5

e6Start End

Fork Join

(b)

S1

S2e1

e2

e3

e4

e5

e6Start End

Decision Merge

(c)

S1e1 e2

Start End

k

Cycle

(d)





MD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(3)



SDij Ti + Tj

Tij

(4)









Tij





⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(5)



Ti middot Tj

1113969is a for-



SD







⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(6)




CEi minus 1113944

Qi

j1

STij

TTi

lnSTij

TTi

(7)


CE minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

(8)




maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N



i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)



j1ECj min 1113944

m

j11113944

N



1113944

m

j1ECj 1113944

m

j11113944

N


1113944

N

i1ξij ge 1 (16)


1113896 (17)








vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References











































MD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(3)



SDij Ti + Tj

Tij

(4)









Tij





⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(5)



Ti middot Tj

1113969is a for-



SD







⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(6)




CEi minus 1113944

Qi

j1

STij

TTi

lnSTij

TTi

(7)


CE minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

(8)




maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N



i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)



j1ECj min 1113944

m

j11113944

N



1113944

m

j1ECj 1113944

m

j11113944

N


1113944

N

i1ξij ge 1 (16)


1113896 (17)








vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References









































Tij





⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(5)



Ti middot Tj

1113969is a for-



SD







⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(6)




CEi minus 1113944

Qi

j1

STij

TTi

lnSTij

TTi

(7)


CE minus 1113944N

i11113944

Qi

j1

STij

TTi

lnSTij

TTi

(8)




maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N



i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)



j1ECj min 1113944

m

j11113944

N



1113944

m

j1ECj 1113944

m

j11113944

N


1113944

N

i1ξij ge 1 (16)


1113896 (17)








vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References









































maxY1 max1113944N

i11113944

m

j1MDij middot ξij1113872 1113873 (9)

maxY2 max1113944m

j11113944

j

k11113944

N

p11113944

N



i11113944

Qi

j1

STij

TTi

lnSTij

TTi

⎛⎝ ⎞⎠ (11)



j1ECj min 1113944

m

j11113944

N



1113944

m

j1ECj 1113944

m

j11113944

N


1113944

N

i1ξij ge 1 (16)


1113896 (17)








vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References










































vi vi1 vi2 vi3 vim1113872 1113873 i 1 2 3 R (19)




(20)

BG BG1BG2BG3 BGm( 1113857 (21)





(t)ij + c1 middot r

(t)1 middot BP

(t)ij minus x

(t)ij1113872 1113873 + c2 middot r

(t)2 middot BG

(t)j minus x

(t)ij1113872 1113873

(22)

x(t+1)ij x

(t)ij + v

(t+1)ij

(23)


(t)1 and r

(t)2


(t)ij is the mo-


(t)1 middot (BP

(t)ij minus














results

Yes

No




3 4 2 1 3 1

Service sets

Particle

Tasks


hellip

hellip

hellip

hellip

hellip

hellip

hellip


S14 S1m

S21 S22 S23 S24 S25 S2m

S31 S33S32 S34 S35 S3m

S41 S42 S43 S44 S45 S4m

S51 S52 S53 S54 S55 S5m

J1

S1 S2 S3 S4 S5 Sm

J2 J3 J4 J5 Jm

Services




(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References










































(t)2 middot (BG(t)

j minus




ψ


fgef



⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(24)










Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References









































Dev


2+ Y


2+ Y


2+ Y


2+ Y


2

1113970

(27)

where Yi1 Yi

2 Yi3 Yi




Devprime


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(28)




f(i) Γ minus


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2


1113888 1113889

2

11139741113972

(29)


5k1 δk 1












SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References











































SD






⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(30)













2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References















































2 1

S21 S12 S13 S24 S15 S36 S27

1 2 1 3 2

J1 J2 J3 J4 J5 J6 J7

Services

Particle

Tasks



Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References









































Generation

999

999

9985

998

9975

Fitn

ess

0 20 40 60 80 100 120

(a)

Generation0 20 40 60 80 100 120

5

48

46

44

42

4

38

Mat

chin

g de

gree

(b)

Generation0 20 40 60 80 100 120

Syne

rgy

degr

ee

19

18

17

16

15

14

13

(c)

Generation0 20 40 60 80 100 120

Clou

d en

tropy

95

9

85

8

75

(d)

Generation0 20 40 60 80 100 120

Exec

utio

n tim

e (ho

ur)

500

480

460

440

420

400

(e)

Generation0 20 40 60 80 100 120

19

18

17

16

15

14

13

Exec

utio

n co

st (d

olla

r)

times104

(f )

Generation0 20 40 60 80 100 120

Rela

tive d

evia

tion

06

05

04

03

02

01

(g)




6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References










































6 Conclusion





9995

999

9985

998

9975Fi

tnes

s

0 20 40 60 80 100 120

SGA

IPSOAPSO

Generation











Data Availability




Acknowledgments



References













































Data Availability




Acknowledgments



References









































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