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Research ArticleJob Scheduling in Cloud Computing Using a Modified HarrisHawks Optimization and Simulated Annealing Algorithm

Ibrahim Attiya 12 Mohamed Abd Elaziz 23 and Shengwu Xiong 1

1School of Computer Science and Technology Wuhan University of Technology Wuhan China2Department of Mathematics Faculty of Science Zagazig University Zagazig Egypt3School of Computer Science and Technology Huazhong University of Science and Technology Wuhan China

Correspondence should be addressed to Shengwu Xiong xiongswwhuteducn

Received 11 November 2019 Accepted 13 February 2020 Published 11 March 2020

Academic Editor Jose Alfredo Hernandez-Perez

Copyright copy 2020 IbrahimAttiya et al0is is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In recent years cloud computing technology has attracted extensive attention from both academia and industry0e popularity ofcloud computing was originated from its ability to deliver global IT services such as core infrastructure platforms and ap-plications to cloud customers over the web Furthermore it promises on-demand services with new forms of the pricing packageHowever cloud job scheduling is still NP-complete and became more complicated due to some factors such as resourcedynamicity and on-demand consumer application requirements To fill this gap this paper presents a modified Harris hawksoptimization (HHO) algorithm based on the simulated annealing (SA) for scheduling jobs in the cloud environment In theproposed HHOSA approach SA is employed as a local search algorithm to improve the rate of convergence and quality of solutiongenerated by the standard HHO algorithm0e performance of the HHOSAmethod is compared with that of state-of-the-art jobscheduling algorithms by having them all implemented on the CloudSim toolkit Both standard and synthetic workloads areemployed to analyze the performance of the proposed HHOSA algorithm 0e obtained results demonstrate that HHOSA canachieve significant reductions in makespan of the job scheduling problem as compared to the standard HHO and other existingscheduling algorithms Moreover it converges faster when the search space becomes larger which makes it appropriate for large-scale scheduling problems

1 Introduction

Scientific computing is a promising field of study that isusually associated with large-scale computer modeling andsimulation and most often requires a massive amount ofcomputing resources [1] For instance scientific applicationsin various domains such as computational materials sciencehigh energy physics molecular modeling earth sciences andenvironmental computing involve the production of massivedatasets from simulations or large-scale experiments Henceanalyzing and disseminating these datasets among re-searchersscientists located over a wide geographic arearequires high power of computing that goes beyond thecapabilities of a single machine 0erefore given the ever-growing data produced by scientific applications and thecomplexities of the applications themselves it becomes

prohibitively slow to deploy and execute such applicationson traditional computing paradigms

To cope with the complexities and ever-increasingcomputational demand of those large-scale scientific ap-plications the concept of cloud computing is introduced Itprovides elastic and flexible resources of computing (egCPU storage memory and networks) which can be rapidlyprovisioned and released with minimal management effortor service provider interaction [2] 0ese cloud services canbe automatically as well as easily scaled up or down anddelivered to the end customers based on a pay-per-usepayment model 0e major services offered by cloud pro-viders can be classified as infrastructure as a service (IaaS)platform as a service (PaaS) and software as a service (SaaS)At the bottom of the cloud computing stack is the IaaSmodel In this model fundamental resources of the

HindawiComputational Intelligence and NeuroscienceVolume 2020 Article ID 3504642 17 pageshttpsdoiorg10115520203504642

computing such as CPU storage memory and bandwidthare offered0e next layer in the stack is PaaS PaaS provides ahigh-level integrated environment to build test deploy andhost developer-created or -acquired applications 0e SaaS isallocated at the top of the stack and it is a software deliverymodel in which applications or services are provided over theInternet so that end users can access them through a webbrowser 0is model allows users to utilize online softwareinstead of the locally installed one SaaS has now become apopular delivery model for service apps such as web mailGoogle Docs and social networking applications

0ere is a consensus in the researcher community and ITindustries that the growth in cloud computing will far exceedthat of other computing paradigms [3] 0is is due to thefollowing reasons First the cloud offers a practical solutionto solve the issue of resource lack and greatly reduces theexpenses of purchasing and maintaining the physical re-sources [4 5] Second it provides virtually infinite resourcesat different prices to properly serve different applicationrequirements in a dynamic and elastic way As a result theemphasis of computing has recently been pushed onto cloudplatforms On the contrary with the growing adoption ofcloud services (especially the IaaS model) by several insti-tutions there has been a huge amount of computing tasksthat are implemented in the cloud computing (CC) envi-ronment Since the computing resources are heterogeneousand geographically distributed there are compromises interms of communication cost system integration andsystem performance 0us in order to efficiently execute thecloud user requests and utilize the distributed resources inan appropriate way a scheduling policy needs to be in place

Indeed many algorithms have been introduced to tacklethe job scheduling problem in a CC environment In theearly stage various heuristics were developed to address jobscheduling problems which produce optimal schedule so-lutions for small-sized problems [6] However the quality ofsolutions generated by these heuristic strategies deterioratesseverely as the problem scale and the number of objectives tobe optimized increase In addition the solutions producedby these heuristic techniques depend largely on certainunderlining rules and they are generated at high operatingcost [7] In contrast metaheuristic techniques have provento be effective robust and efficient in solving a wide varietyof real-world complex optimization problems 0is can beattributed to their ability to employ a set of candidate so-lutions for the purpose of traversing the solution spacerather than using a single candidate solution as with heu-ristic techniques 0is feature of metaheuristic algorithmsmakes them outperform other optimization methods Someof the most popular metaheuristic techniques that have beenintroduced to solve the cloud job scheduling problem in-clude genetic algorithm (GA) [8] particle swarm optimi-zation (PSO) [9] ant colony optimization (ACO) [10] tabusearch [11] BAT algorithm [12] simulated annealing (SA)algorithm [13] symbiotic organisms search (SOS) [14] andcuckoo search (CS) algorithm [15] Although some of thesealgorithms have shown promising improvements in findingthe global optimal solution for the job scheduling problem inthe cloud they are all suffering from premature convergence

and difficulty to overcome local minima especially whenfaced with a large solution space [16]0ese limitations oftenlead to suboptimal job scheduling solutions which affect thesystem performance and also violate quality of service (QoS)guarantees 0is indicates that there is an urgent need fornew adaptive and efficient algorithms to find the globaloptimal solution for the cloud job scheduling problem

Recently Heidari et al [17] proposed a population-based nature-inspired optimization technique called theHarris hawks optimizer (HHO) which mimics the socialbehavior of Harrisrsquo hawks in nature It is mainly inspired bythe cooperative behavior and chasing strategy of Harrishawks 0e exploration and exploitation phases of the HHOare modeled by exploring a prey performing a surprisepounce and then attacking the intended prey 0e Harrishawks optimizer can demonstrate a variety of attackingstrategies according to the dynamic nature of circumstancesand escaping behaviors of the prey Local optima avoidanceand smooth transition from exploration to exploitation areamong the major advantages of the HHO algorithmAccording to these behaviors the HHO has been applied toseveral global optimization and real-world engineeringproblems including image segmentation [18 19] featureselection [20] spatial assessment of landslide susceptibility[21] parameter estimation of photovoltaic cells [22] imagedenoising [23] and others [24ndash29] However the HHOsuffers from some limitations that affect its performancesuch that its exploration ability is weaker than its exploi-tation ability and this leads to degradation of the perfor-mance of convergence and the quality of the solution Inaddition there is plenty of room to investigate the potentialimprovements in terms of speed of convergence and qualityof solutions generated by the HHO

A promising research direction which hybridizes one ormore heuristicsmetaheuristics to leverage the strengths ofthese algorithms while reducing their impediments hasattracted tremendous attention from researchers in variousresearch domains In this study an integrated version of theHHO algorithm with simulated annealing (HHOSA) wasproposed as an attempt to improve the rate of convergenceand local search of HHO To the best of our knowledge noresearch study found in the literature tries to investigate theabove-mentioned improvements with the performance ofHHO while tackling the job scheduling problem Hence themain motivation of our study is to propose the hybridHHOSA approach for optimization of job scheduling incloud computing

0e major contributions of this paper can be summa-rized as follows

(1) Design and implementation of a hybrid version ofHHO and SA for optimum job scheduling in cloudcomputing

(2) Empirical analysis of the convergence trend for 15different job scheduling instances using HHOSA andother evaluated algorithms

(3) Performance comparison of HHOSA against theoriginal HHO and other popular metaheuristics in

2 Computational Intelligence and Neuroscience

terms of makespan and performance improvementrate ()

0e remainder of this paper is structured as followsSection 2 presents a review of related works on existing jobscheduling algorithms Section 3 formulates the jobscheduling problem and presents the original HHO and SAalgorithms Design of the proposed HHOSA algorithm andits description are introduced in Section 4 Performanceevaluation and discussion of the achieved results are pro-vided in Section 5 Finally conclusions and outlines forpotential future works are given in Section 6

2 Related Works

Recently there has been a significant amount of interest inusing metaheuristics (MHs) for solving different problemsin several domains0eMHmethods have many advantagessuch as flexibility and simplicity 0erefore they can used tosolve a different number of optimization problems thatcannot be solved by traditional methods In addition theyare easy to implement According to these advantagesseveral studies established that the MH methods providegood results for the task scheduling problems in cloudcomputing than other traditional methods [16 30] 0eauthors in [31 32] provided a comprehensive review ofvarious metaheuristics that have been developed for solvingthe task scheduling problem in cloud computing

Guo et al [33] presented a task scheduling approachdepending on a modified PSO algorithm which aims tominimize the processing cost of user tasks through em-bedding crossover and mutation operators within the PSOprocedure 0e results showed that the modified PSOprovides a good performance especially with a large-scaledataset Similarly Khalili and Babamir [34] developed amodified version of PSO by using different techniques toupdate its inertia weight 0en this version was applied in acloud environment to reduce the makespan of the workloadscheduling Alla et al [35] provided two hybrid PSO versionswhich depend on dynamic dispatch queues (TSDQ) for taskscheduling0e first approach combined the fuzzy logic withPSO (TSDQ-FLPSO) while the second approach combinedsimulated annealing with PSO (TSDQ-SAPSO) 0e resultsof TSDQ-FLPSO outperform those of the other methodsincluding the TSDQ-SAPSO Other works related to theapplication of PSO to task scheduling in cloud computinghave been reported in the literature [36ndash38]

Genetic algorithm (GA) has also been applied to solvethe task scheduling problem For example Rekha andDakshayini [39] introduced the GA to find a suitable so-lution for the task allocation which seeks to reduce taskcompletion time 0e results of the GA are assessed bycomparing it with the simple allocation methods in terms ofthroughput and makespan 0e results illustrated that theGA outperforms other compared algorithms 0e authors in[40] presented a modified version of the GA using a heu-ristic-based HEFT to find a suitable solution for the statictask scheduling in the cloud Akbari et al [41] developed newoperators to enhance the quality of the GA and used this

model to enhance the results of task scheduling In [42] theauthors provided a modified GA called MGGS which is acombination of the GA and greedy strategy 0e MGGS iscompared with other approaches and the experimentalresults established its ability to find a suitable solution for thetask scheduling problem Besides a modified version of theGA is proposed in [43] which combines the GA with PSO0e developed method called GA-PSO is provided to solvethe task scheduling so as tominimize themakespan and costAdditionally a hybrid genetic-particle swarm optimization(HGPSO) method [44] is proposed to solve the taskscheduling issue In the HGPSO the user tasks are for-warded to a queue manager and then the priority iscomputed and proper resources are allocated0is algorithmfocuses on optimizing parameters of QoS Moreover thereare several hybrid techniques in which the PSO and GA arecombined and utilized to handle the task scheduling in cloudcomputing [45ndash47] Other works combining the GA andfuzzy theory have been proposed in [48] 0e proposedapproach called FUGE aims to perform proper cloud taskscheduling considering the execution cost and time 0eperformance of FUGE is compared with that of other taskscheduling approaches and the results illustrate its efficiencyusing different measures such as execution time the averagedegree of imbalance and execution cost

Moreover the ant colony optimization (ACO) has be-come one of the most popular task scheduling methods[49ndash53] Keshk et al [54] proposed a task scheduling al-gorithm based on the ACO technique in the cloud com-puting environment 0e modified version calledMACOLB aims at minimizing the makespan time whilebalancing the system load Also the firefly algorithm (FA)has been applied to enhance the results of the job schedulingsuch as in [55] 0e FA is proposed as a local search methodto improve the imperialist competitive algorithm (ICA) andthis leads to enhancing the makespan Esa and Yousif [56]proposed the FA to minimize the execution time of jobscompared the results with those of the first-come first-served(FCFS) algorithm and found the FA outperforms the FCFSalgorithm For more details about using the FA refer[57ndash59] In addition the salp swarm algorithmwas proposedto improve the placement of the virtual machine in cloudcomputing as in [60] Braun et al [61] introduced a com-parison between eleven algorithms for mappingassigningscheduling independent tasks onto heterogeneous distrib-uted computing systems 0ese methods include opportu-nistic load balancing (OLB) minimum execution time(MET) minimum completion time (MCT) min-min max-min duplex SA GA tabu and Alowast heuristic In additionthe operators of SA are combined with the operators of theGA and this version is called genetic simulated annealing(GSA) In this algorithm (ie GSA) the mutation andcrossover are similar to the GA while the selection process isperformed by using the cooling and temperature of SA

Furthermore the symbiotic organisms search (SOS) hasattracted much attention recently as an alternative approachto solve task scheduling In [62] a discrete version of the SOS(DSOS) is proposed to find the optimal scheduling of tasks incloud computing0e comparison results illustrated that the

Computational Intelligence and Neuroscience 3

DSOS is more competitive and performs better than bothSAPSO and PSO Moreover it converges faster in the case oflarge instances 0e work in [63] presents a modified versionof the SOS based on the SA procedure to solve the taskscheduling issue in cloud computing 0e developed modelcalled SASOS is compared with the original SOS and theresults showed the high performance of the SASOS in termsof makespan convergence rate and the degree of imbalanceAbdullahi et al [6] proposed amultiobjective large-scale taskscheduling technique based on improving the SOS usingchaotic maps and chaotic local search (CLS) strategy 0eaim of using the chaotic map is to construct the initialsolutions and replace the random sequence to improve thediversity In contrast the CLS strategy is used to update thePareto fronts 0e proposed CMOS algorithm producedsignificant results when compared with other methodsincluding ECMSMOO [64] EMS-C [65] and BOGA [66]0ese algorithms aim to achieve balancing between themakespan and the cost without any computational over-head0e experimental results demonstrate that the CMSOShas potentials to enhance the QoS delivery

To sum up according to the previous studies the above-mentioned MH methods provide high ability to find asuitable solution for job scheduling in cloud computingHowever this performance still needs much improvementwith a focus on finding suitable operators to balance betweenthe exploration and the exploitation

3 Background

31ModelandProblemFormulation 0e IaaS cloud is a verycommon model from the perspective of resource manage-ment thus scheduling in such systems has gained greatattention especially from the research community [67] 0eIaaS cloud model provides computing resources as virtualresources that are made accessible to consumers through theInternet [68 69] Indeed virtualization is one of the primaryenablers for cloud computing With virtualization tech-nology all physical resources in the cloud environment arerepresented as virtual machines (VMs) [70] Hence cloudproviders must supply their customers with infinite vir-tualized resources in accordance with the service levelagreement (SLA) [71] and must decide the best resourceconfiguration to be utilized according to their profitabilityprinciples

In our problem description there is a general frameworkthat focuses on the interaction between the cloud infor-mation service (CIS) the cloud broker and the VMs [72]When user requests are submitted to the cloud these re-quests are forwarded to the cloud broker who maintains itscharacteristics and resource requirements 0e cloud brokerwill then consult the CIS to determine the services requiredto process the received requests from the consumer and thenmap the job requests on the detected services For the sake ofclarity suppose there is a set of independent jobsJ J1 J2 Jn1113864 1113865 that are submitted by the cloud con-sumers to be processed0e processing requirements of a job

are referred to as job length and are measured in millioninstructions (MI) 0e cloud broker is then responsible forassigning those jobs onto the set of VMs available within thecloud data center to meet the usersrsquo demands Let VM

VM1VM2 VMm1113864 1113865 denote the set of VMs Each VMj is aset of computing entities with limited capabilities (eg CPUpower memory space storage capacity and network band-width) [73] It is assumed that VMs are heterogeneous andtheir CPU capabilities (measured in MIPS (millions of in-structions per second)) are used to estimate the executiontime of user requests 0is indicates that a job executed ondifferent VMs will encounter different execution cost Ouraim is to schedule a set of submitted jobs on available VMs toachieve higher utilization of resources with minimal make-span We formulate our scheduling problem based on theldquoexpected time to computerdquo (ETC) model [74] 0e ETC isdefined as the expected execution time of all jobs to computeon each VM obtained by using the ETCmatrix as in equation(1) 0is means that based on the specifications of the VMsand submitted jobs the cloud broker computes an n times m ETCmatrix where n is the total number of user jobs and m is thetotal number of available VMs0e element ETCij representsthe expected time for VMj to process the job Ji

ETCij

ETC11 ETC12 ETC1m

ETC21 ETC22 ETC2m

ETCn1 ETCn2 ETCnm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

ETCij JobLengthi

VMPowerj

(2)

where ETCij refers to the expected execution time of the ith

job on the jth VM JobLengthi is the length of the job i interms of MI and VMPowerj is the computing capacity ofVMj in terms of MIPS

0e main purpose of job scheduling is to find an optimalmapping of jobs to resources that optimize one or moreobjectives In addition the most common objective noticedin the reviewed literature is the minimization of job com-pletion times also known as makespan [75]0us the aim ofthis study is to reduce the makespan of job scheduling byfinding the best allocation of virtual resources to jobs on theIaaS cloud

For any schedule X the makespan (MKS) is the maxi-mum completion time and is calculated as follows

MKS(X) maxjisin12m

1113944

n

i1ETCij (3)

where m and n are the number of machines and jobs re-spectively ETCij is defined in equation (2) 0en thescheduling problem is formulated mathematically as

Obj f(X) minMKS(X) min maxjisin12m

1113944

n

i1ETCij (4)


32 Simulated Annealing Algorithm 0e simulatedannealing (SA) algorithm is considered one of the mostpopular single-solution-based optimization algorithms thatemulate the process of annealing in metallurgy [76 77] 0eSA begins by setting an initial value for a random solution Xand determining another solution Y from its neighborhood0e next step in SA is to compute the fitness value for X andY and set X Y if F(Y)leF(X)

However SA has the ability to replace the solution X byY even when the fitness of Y is not better than the fitness ofX 0is depends on the probability (Prob) that is defined inthe following equation

Prob eminusΔEkT

ΔE F(X) minus F(Y)(5)

where k and T are the Boltzmann constant and the value forthe temperature respectively If Probgt rand then X Yotherwise X will not change 0e next step is to update thevalue of the temperature T as defined in the followingequation

T β times T (6)

where β isin [0 1] represents a random value0e final steps ofthe SA algorithm are given in Algorithm 1

33 Harris Hawks Optimizer 0e Harris hawks optimizer(HHO) is a new metaheuristic algorithm developed to solveglobal optimization problems [17] In general the HHOsimulates the behaviors of the hawks in nature during theprocess of searching and catching their prey Similar to otherMH methods the HHO performs the search process duringtwo stages (ie exploration and exploitation) based ondifferent strategies as given in Figure 1 0ese stages will beexplained in more detail in the following sections

331 Exploration Phase At this stage the HHO has theability to update the position of the current hawk(Xi i 1 2 N) (where N indicates the total number ofhawks) depending on either a random position of anotherhawk (Xr) or the average of the positions (XAvg) for allhawks 0e selection process has the same probability toswitch between the two processes and this is formulated asin the following equation

Xi(t + 1) Xr(t) minus r1 Xr(t) minus 2r2X(t)

11138681113868111386811138681113868111386811138681113868 qge 05

Xb(t) minus XAvg(t)1113872 1113873 minus ω qlt 05

⎧⎪⎨

⎪⎩

(7)

where ω r3(LB + r4(UB minus LB)) and XAvg is formulated as

XAvg(t) 1N

1113944

N

i1Xi(t) (8)

In general the main goal of this stage is to broadlydistribute the hawks across the search space In the followingsection we will discuss how hawks change their status fromexploration to exploitation

332 Changing from Exploration to Exploitation In thisstage the hawks transfer to exploitation based on theirenergies E which are formulated as

E 2E0 1 minust

tmax1113888 1113889 (9)

where E0 isin [minus1 1] represents a random value and tmax and trepresent the total number of iterations and the currentiteration

333 Exploitation Phase 0e exploitation stage of the HHOis formulated using several strategies and a few randomparameters used to switch between these strategies [17]0ese strategies are formularized as follows (1) soft besiege(2) hard besiege (3) soft besiege with progressive rapiddives and (4) hard besiege with progressive rapid dives

(i) Soft besiege in this phase the hawks move aroundthe best one and this is formulated by using thefollowing equations

X(t + 1) ΔX(t) minus E J times Xb(t) minus X(t)1113868111386811138681113868

1113868111386811138681113868

J 2 1 minus r5( 1113857(10)

ΔX(t) Xb(t) minus X(t) (11)

(ii) Hard besiege in this phase the hawks update theirposition based on the distance between them and thebest hawk as given in the following equation

X(t + 1) Xb(t) minus E times|ΔX(t)| (12)

(iii) Soft besiege with progressive rapid dives at thisstage it is supposed that the hawks have the abilityto choose the following actions 0is can be cap-tured from the following equation

Y Xb(t) minus E J times Xb(t) minus X(t)1113868111386811138681113868

1113868111386811138681113868 (13)

0e Levy flight (LF) operator is used to calculate therapid dives during this stage and this is formulated as

Z Y + S times LF(D) (14)

where S represents a random vector with size 1 times D andD is the dimension of the given problem In additionthe LF operator is defined as

LF(x) 001 timesu times σv|1β

1113868111386811138681113868

σ Γ(1 + β) times sin(πβ2)

Γ((1 + β)2) times β times 2((βminus1)2)1113888 1113889

1β

(15)

where u and v represent random parameters of the LFoperator and β 15


0e HHO aims to select the best from Y and Z asdefined in equations (13) and (14) and this is for-mulated as

X(t + 1) Y if F(Y)ltF(X(t))

Z if F(Z)ltF(X(t))1113896 (16)

(iv) Hard besiege with progressive rapid dives in thisstage the hawks finish the exploitation phase with a

hard besiege and this is performed using the fol-lowing equation

X(t + 1) Yprime if F Yprime( 1113857ltF(X(t))

Zprime if F Zprime( 1113857ltF(X(t))

⎧⎨

⎩ (17)

where Zprime and Yprime are computed as in the followingequations

Yprime Xb(t) minus E J times Xb(t) minus XAvg(t)11138681113868111386811138681113868

11138681113868111386811138681113868

Zprime Yprime + S times LF(D)(18)

For clarity the previous strategies are performeddepending on the energy of the hawks E and a randomnumber r For example considering |E| 15 means that theoperators of the exploration phase are used to update theposition of the hawk When E 07 and r 06 the softbesiege strategy will be used In case of E 03 and r 06the hawksrsquo position will be updated using the operators ofthe hard besiege strategy In contrast when E 07 andr 03 the hawksrsquo position will be updated using the softbesiege with progressive rapid dives strategy Otherwise thehard besiege with progressive rapid dives strategy will beused to update the current hawk

0e final steps of the HHO algorithm are illustrated inAlgorithm 2

4 Proposed Algorithm

In this section an alternative approach for job scheduling incloud computing is developed which depends on themodified HHO using the operators of SA 0e main ob-jective of using SA is to employ its operators as local op-erators to improve the performance of the HHO0e steps ofthe developed method are given in Algorithm 3

Input value of the initial temperature (T0) dimension of the solution n and total number of iterations tmaxGenerate the initial solution xAssess the quality x by calculating its fitness value F(x)

Set the best solution xb x and F(xb) F(x)

Set t 1 and T T0while tlt tmax doFind the neighbor solution Y for the solution XCalculate the fitness value F(Y) for Yif F(Y)ltF(Xi) then

Xi Y

elseCompute the difference between the fitness value of X and Y as δ F(Xi) minus F(Y)

if (Proble r5) thenxi Y

Update the value of temperature T using equation (6)if F(Xb)gtF(X) thenXb X

Set t t + 1Output the best solution xb

ALGORITHM 1 SA method

Exploration

Perching based on

random locations

Hard besiege with

progressive rapid dives

So besiege with


r lt 05

q ge 05

|E| ge

1

|E| ge

05

|E| lt

05

|E| = 1

q lt 05

E

Perching based on the

positions of other hawks

Exploitation

Hard besiege

So besieger ge 05

Figure 1 Stages of the HHO [17]


In general the developed HHOSA method starts bydetermining its parameters in terms of the number of indi-viduals N in the population X the number of jobs n thenumber of virtual machines m and the total number of it-erations tmax 0e next step is to generate random solutions Xwith the dimension N times n Each solution xi isin X has n valuesbelonging to the interval [1 m]0ereafter the quality of each

solution is assessed by computing the fitness value (F) that isdefined in equation (4) 0en xb is determined Finally theindividualsrsquo setXwill be updated according to the operators ofthe HHOSA method 0e process of updating X is iterateduntil the terminal criteria are reached A description withmore details for each step of the proposed approach will beillustrated in the following sections

Input size of the population N and maximum number of iterations tmaxGenerate initial population xi(i 1 2 N)

while (terminal condition is not met) doCompute fitness valuesFind the best solution Xb

for i 1 N doUse equation (9) to update Eif (|E|ge 1) thenCompute new position for Xi using equation (7)

if (|E|lt 1) thenif (rlt 05 and |E|ge 05) thenCompute new value for xi using equation (16)

else if (rlt 05 and |E|lt 05) thenCompute new value for xi using equation (17)

else if (rge 05 and |E|lt 05) thenCompute new value for xi using equation (12)

else if (rge 05 and |E|ge 05) thenCompute new value for xi using equation (10)

Return Xb

ALGORITHM 2 Steps of the HHO algorithm [17]

(1) Input number of solutions N number of jobs n maximum number of iterations tmax and number of machines m(2) Set the initial value for the parameters of the HHO(3) Construct a random integer solution X with size N times n (as described in the initial stage)(4) t 1(5) repeat(6) Compute the quality (Fi) of each solution xi i 1 N

(7) Determine the best solution xb which has the best fitness function Fb

(8) for i 1 N do(9) Compute the probability Pri using equation (20) and rpr using equation (21)(10) if Pri le rpr then(11) Find the neighbor solution Y for the solution xi

(12) Calculate the fitness value F(Y) for Y(13) if F(Y)ltF(xi) then(14) xi Y

(15) else(16) Compute the difference between the fitness value of xi and Y as δ F(xi) minus F(Y)

(17) if (Proble r5) then(18) xi Y

(19) Update the value of temperature T using equation (6)(20) else(21) Compute the energy E using equation (9)(22) Update xi using operators of the HHO as in Algorithm 2(23) t t + 1(24) Until tgt tmax(25) Return the best solution xb

ALGORITHM 3 HHOSA scheduler for job scheduling in cloud computing


41 Initial Stage At this stage a set of random integersolutions is generated which represents a solution for the jobscheduling 0is process focuses on identifying the di-mension of the solutions that is given by the number of jobsn as well as the lower lb and upper ub boundaries of thesearch space which are determined in our job schedulingmodel by 1 and m respectively 0erefore the process ofgenerating xi isin X(i 1 2 N) is given by the followingequation

xij Rod lbij + rnd times ubij minus lbij1113872 11138731113872 1113873 j 1 2 n

(19)

where each value of xi belongs to an integer value in theinterval [1 m] (ie xij isin [1 m]) Meanwhile the Rodfunction is applied to round the value to the nearest wholenumber rnd represents a random number belonging to [01]

For more clarity consider there are eight jobs and fourmachines and the generated values for the current solutionare given in xi as xi 4 1 4 4 2 3 1 31113858 1113859 In this rep-resentation the first value in xi is 4 and this indicates thatthe first job will be allocated on the fourth machine 0us itcan be said that the first third and fourth jobs are allocatedon the fourth machine while the second and seventh jobswill be allocated on the first machine Meanwhile the sixthand eighth jobs will be allocated on the third machinewhereas the second machine will only execute the fifth job

42 Updating Stage 0is stage begins by computing thefitness value for each solution and determining xb which hasthe best fitness value Fb until the current iteration t 0enthe operators of either SA or HHOwill be used to update thecurrent solution and this depends on the probability (Pri) ofthe current solution xi that is computed as

Pri Fi

1113936Ni1 Fi

(20)

0e operators of the HHOwill be used when the value ofPri gt rpr otherwise the operators of SA will be used Sincethe value of rpr has a larger effect on the updating process wemade it automatically adjusted as in the following equation

rpr LPri+ rand times UPri

minus LPri1113872 1113873 (21)

where LPriand UPri

are the minimum and maximumprobability values for the i-th solution respectively Whenthe HHO is used the energy of escaping E will be updatedusing equation (9) According to the value of E the HHOwill go through the exploration phase (when |E|gt 1) orexploitation phase (when |E|lt 1) 0e value of xi will beupdated using equation (7) in the case of the explorationphase Otherwise xi will be updated using one strategy fromthose applied in the exploitation phase which are repre-sented by equations (10)ndash(17)0e selection strategy is basedon the value of the random number r and the value of |E|

(which assumes its value may be in the interval [05 1] or lessthan 05) Meanwhile if the current solution is updatedusing the SA (ie Pri le rpr) then a new neighboring solution

Y to xi will be generated and its fitness value FY will becomputed In the case of FY ltFxi

then xi Y otherwise thedifference between Fxi

and FY is computed (ieδ F(xi) minus F(Y)) and the value of Prob will be checked (asdefined in equation (5)) If its value is less than r5 isin [0 1]then xi Y otherwise the value of the current solution willnot change

0e next step after updating all the solutions using eitherHHO or SA is to check the termination conditions if theyare reached then running the HHOSA is stopped and thebest solution is returned otherwise the updating stage isrepeated again

5 Experimental Results and Analysis

In this section we present and discuss various experimentaltests in order to assess the performance of our developedmethod In Section 51 we introduce a detailed descriptionof the simulation environment and datasets employed in ourexperiments Section 52 explains the metrics used forevaluating the performance of our HHOSA algorithm andother scheduling algorithms in the experiments FinallySection 53 summarizes the results achieved and providessome concluding remarks

51 Experimental Environment and Datasets 0is sectiondescribes the experimental environment datasets and ex-perimental parameters To evaluate the effectiveness of thedeveloped HHOSA approach the performance evaluationsand comparison with other scheduling algorithms wereperformed on the CloudSim simulator 0e CloudSimtoolkit [78] is a high-performance open-source frameworkfor modeling and simulation of the CC environment Itprovides support for modeling of cloud system componentssuch as data centers hosts virtual machines (VMs) cloudservice brokers and resource provisioning strategies 0eexperiments were conducted on a desktop computer withIntel Core i5-2430M CPU 240GHz with 4GB RAMrunning Ubuntu 1404 and using CloudSim toolkit 303Table 1 presents the configuration details for the employedsimulation environment All the experiments are performedby using 25 VMs hosted on 2 host machines within a datacenter 0e processing capacity of VMs is considered interms of MIPS

For experiments both synthetic workload and standardworkload traces are utilized for evaluating the effectivenessof the proposed HHO technique 0e synthetic workload isgenerated using a uniform distribution which exhibits anequal amount of small- medium- and large-sized jobs Wehave considered that each job submitted to the cloud systemmay need different processing time and its processing re-quirement is also measured in MI Table 2 summarizes thesynthetic workload used

Besides the synthetic workload the standard parallelworkloads that consist of NASA Ames iPSC860 andHPC2N (High-Performance Computing Center North) areused for performance evaluation NASAAmes iPSC860 andHPC2N set log are among the most well-known and widely


used benchmarks for performance evaluation in distributedsystems Jobs are supposed to be independent and they arenot preemptive More information about the logs used in ourexperiments is shown in Table 3

For the purpose of comparison each experiment wasperformed 30 times 0e specific parameter settings of theselected metaheuristic (MH) methods are presented inTable 4

52 EvaluationMetrics 0e following metrics are employedto evaluate the performance of the HHOSA method de-veloped in this paper against other job scheduling techniquesin the literature

521 Makespan It is one of the most commonly usedcriteria for measuring scheduling efficiency in cloud com-puting It can be defined as the finishing time of the latestcompleted job Smaller makespan values demonstrate thatthe cloud broker is mapping jobs to the appropriate VMsMakespan can be defined according to equation (3)

522 Performance Improvement Rate (PIR) It is utilized tomeasure the percentage of the improvement in the per-formance of each method with regard to other comparedmethods as presented in equation (22) 0is provides aninsight into the performance of the presented HHOSAagainst the state-of-the-art approaches in the literature 0ePIR is defined as follows

PIR() S minus Sprime( 1113857

Sprimelowast 100 (22)

where Sprime and S are the fitness values obtained by the pro-posed algorithm and the compared one from the relatedliterature respectively

53 Result Analysis and Discussion 0is section introducesthe result analysis and discussion of experimentation of theproposed HHOSA job scheduling strategy To objectivelyevaluate the performance of the HHOSA strategy we havevalidated it over five well-known metaheuristic algorithmsnamely particle swarm optimization (PSO) [79] salp swarmalgorithm (SSA) [80] moth-flame optimization (MFO) [81]firefly algorithm (FA) [82] and Harris hawks optimizer(HHO) [17]

To display the performance of HHOSA against SSAMFO PSO FA and HHO we plotted graphs of solutionrsquosquality (ie makespan) versus the number of iterations forthe three datasets as shown in Figures 2ndash16 From theconvergence curves of the synthetic workload shown inFigures 2ndash6 HHOSA converges faster than other algorithmsfor 200 400 600 800 and 1000 cloudlets Besides for NASAAmes iPSC860 HHOSA converges at a faster rate thanPSO SSA MFO FA and HHO for 500 1000 1500 2000and 2500 cloudlets as depicted in Figures 7ndash11 Moreoverfor the HPC2N real workload HHOSA converges fasterthan other algorithms when the jobs vary from 500 to 2500as shown in Figures 12ndash16 0is indicates that the presentedHHOSA generates better quality solutions and converges at

Table 1 Experimental parameter settings

Cloud entity Parameters Values

Data center No of data centers 1No of hosts 2

Host

Storage 1 TBRAM 16GB

Bandwidth 10GbsPolicy type Time shared

VM

No of VMs 25MIPS 100 to 5000RAM 05GB

Bandwidth 1GbsSize 10GBVMM Xen

No of CPUs 1Policy type Time shared

Table 2 Synthetic workload settings

Parameters ValuesNo of cloudlets (jobs) 200 to 1000Length 1000 to 20000 MIFile size 300 to 600MB

Table 3 Description of the real parallel workloads used in per-formance evaluations

Log Duration CPUs Jobs Users File

NASAiPSC

Oct1993ndashDec

1993128 18239 69

NASA-iPSC-1993-31-clnswf

HPC2N Jul 2002ndashJan2006 240 202871 257 HPC2N-2002-

22-clnswf

Table 4 Parameter settings of each MH method evaluated

Algorithm Parameter Value

PSOSwarm size 100

Cognitive coefficient c1 149Social coefficient c2 149

FA

Swarm size 100α 05β 02c 1

SSA Swarm size 100c1 c2 and c3 [0 1]

MFOSwarm size 100

b 1a minus1⟶ 0ndash2

HHO Swarm size 100E0 [minus1 1]

HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA

400 600 800 1000200No of iterations

Figure 2 Convergence trend for synthetic workload (200 jobs)

No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA

Figure 7 Convergence trend for real workload NASA iPSC (500jobs)


200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA

Figure 12 Convergence trend for real workload HPC2N (500jobs)

200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



a faster rate than other compared algorithms across all theworkload instances

To evaluate the algorithms the performances of eachalgorithm were compared in terms of makespan 0e valuesobtained for this performance metric are as reported inTables 5ndash70e results given in Tables 5ndash7 state that HHOSAusually can find better average makespan than other eval-uated scheduling algorithms namely PSO SSA MFO FAand HHO 0is means that the HHOSA takes less time toexecute the submitted jobs and outperforms all the otherscheduling algorithms in all the test cases More specificallythe results demonstrate that the HHO is the second best Wealso find that MFO performs a little better than SSA in mostof the cases both of them fall behind the HHO algorithmMoreover in almost all the test cases FA is ranked far belowSSA and PSO falls behind FA 0is reveals that the averagevalues of makespan using HHOSA are more competitivewith those of the other evaluated scheduling methods

0e PIR() based on makespan of the HHOSA ap-proach as it relates to the PSO SSA MFO FA and HHOalgorithms is presented in Tables 8ndash10 For the syntheticworkload the results in Table 8 show that the HHOSAalgorithm produces 9251ndash9675 7476ndash85156610ndash8208 6187ndash7681 and 1889ndash2387makespan time improvements over the PSO FA SSA MFOand HHO algorithms respectively For the execution ofNASA iPSC real workload (shown in Table 9) HHOSAshows 8536ndash9324 6699ndash7701 6693ndash74696531ndash7431 and 1505ndash2470 makespan time im-provements over the PSO FA SSA MFO and HHO al-gorithms respectively In addition the HHOSA algorithmgives 8830ndash9409 7983ndash8247 7636ndash80837544ndash7775 and 1355ndash2085 makespan time im-provements over the PSO FA SSA MFO and HHO ap-proaches for the HPC2N real workload shown in Table 100at is to say the performance of HHOSA is much betterthan that of the other methods

54 Influence of the HHOSA Parameters In this section theperformance of HHOSA is evaluated through changing thevalues of its parameters where the value of population size isset to 50 and 150 while fixing the value of β 085 On thecontrary β is set to 035 050 and 095 while fixing thepopulation size to 100 0e influence of changing the pa-rameters of HHOSA using three instances (one from eachdataset) is given in Table 11 From these results we cannotice the following (1) By analyzing the influence ofchanging the value of swarm size Pop it is seen the per-formance of HHOSA is improved when Pop is increasedfrom 100 to 150 and this can be observed from the bestaverage and worst values of makespan In contrastmakespan for the swarm size equal to 50 becomes worse thanthat of swarm size equal to 100 (2) It can be found that whenβ 035 the performance of HHOSA is better than thatwhen β 085 as shown from the best makespan value atHPC2N as well as the best and worst makespan values atNASA iPSC Also in the case of β 05 and 095 theHHOSA provides better makespan values in four cases

200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



compared with the β 085 case as given in the table Fromthese results it can be concluded that the performance of theproposed HHOSA at β 085 and Pop 100 is better thanthat at other values

To summarize the results herein obtained reveal that thedeveloped HHOSA method can achieve near-optimal per-formance and outperforms the other scheduling algorithmsMore precisely it performs better in terms of minimizing the

Table 5 Best values of makespan for the HHOSA algorithm and compared algorithms

Instances PSO FA SSA MFO HHO HHOSA

Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949

Table 6 Average values of makespan for the HHOSA algorithm and compared algorithms


Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006

Table 7 Worst values of makespan for the HHOSA algorithm and compared algorithms


Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171


makespan while maximizing the utilization of resources0is allows us to infer that the hybrid HHOSA approach isan effective and efficient strategy for scheduling of jobs onIaaS cloud computing

6 Conclusions

0is paper proposes an alternative method for job sched-uling in cloud computing 0e proposed approach dependson improving the performance of the Harris hawks opti-mizer (HHO) using the simulated annealing algorithm 0eproposed HHOSA algorithm has established its perfor-mance since it utilizes several operators which have highability during the searching process to balance between theexploitation and the exploration0is leads to enhancing the

convergence rate towards the optimal solution as well as thequality of the final output Motivated from these im-provements this study proposes the HHOSA approach foraddressing the problem of cloud job scheduling To assessthe performance of our method a set of experimental seriesare performed using a wide range of instances ranging from200 to 1000 cloudlets for synthetic workload and up to 2500cloudlets in case of standard workload traces Besides it isvalidated over five well-known metaheuristics includingMFO SSA FA PSO and the traditional HHO 0e simu-lation results provide evidence about the high quality of thedeveloped approach over all the other methods Accordingto the high performance obtained by the developed HHOSAalgorithm it can be extended in the future to handle otheroptimization issues in the cloud computing paradigm such

Table 8 PIR() on makespan for synthetic workload

200 400 600 800 1000PIR () over PSO 9255 9675 9462 9251 9384PIR () over FA 7476 8003 8131 8269 8515PIR () over SSA 6610 7871 7527 7888 8208PIR () over MFO 6187 7019 7438 7470 7681PIR () over HHO 2362 2387 2001 1940 1889

Table 9 PIR() on makespan for real workload NASA iPSC


Table 10 PIR() on makespan real workload HPC2N


Table 11 Influence of the variant value of the parameters

Instance Makespan β 085Pop 100

Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608

NASA iPSC (1000 jobs)Best 9108 9116535 9084299 9040409 9064667 9079272

Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617

Synthetic (1000 jobs)Best 16167 1629857 1587836 1626296 1597758 1612992

Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314


as workflow scheduling and energy consumption In addi-tion it is expected that HHOSA will be applied to otheroptimization problems in various research directions such asfog computing Internet of things (IoT) feature selectionand image segmentation

Data Availability

0e data used to support the findings of this study areavailable from the authors upon request

Conflicts of Interest

0e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

0is work was in part supported by the National Key Re-search and Development Program of China (Grant no2017YFB1402203) the Defense Industrial Technology De-velopment Program (Grant no 201910GC01) and the HubeiProvincial Key SampT Innovation Program (Grant no2019AAA024)

References

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[2] P Mell and T Grance ldquo0e NIST definition of cloud com-putingrdquo Technical report National Institute of Standards andTechnology Gaithersburg MD USA 2011

[3] L Heilig E Lalla-Ruiz S Voszlig and R Buyya ldquoMetaheuristicsin cloud computingrdquo Software Practice and Experiencevol 48 no 10 pp 1729ndash1733 2018

[4] D-K Kang S-H Kim C-H Youn and M Chen ldquoCostadaptive workflow scheduling in cloud computingrdquo in Pro-ceedings of the 8th International Conference on UbiquitousInformation Management and CommunicationmdashICUIMCrsquo14pp 1ndash8 ACM Press New York NY USA January 2014

[5] Q Zhang L Cheng and R Boutaba ldquoCloud computingstate-of-the-art and research challengesrdquo Journal of InternetServices and Applications vol 1 no 1 pp 7ndash18 2010

[6] M Abdullahi M A Ngadi S I Dishing S MuhammadAbdulhamid and B Ismarsquoeel Ahmad ldquoAn efficient symbioticorganisms search algorithm with chaotic optimizationstrategy for multi-objective task scheduling problems in cloudcomputing environmentrdquo Journal of Network and ComputerApplications vol 133 pp 60ndash74 2019

[7] J Yu R Buyya and K Ramamohanarao ldquoWorkflowscheduling algorithms for grid computingrdquo in Metaheuristicsfor Scheduling in Distributed Computing EnvironmentsF Xhafa and A Abraham Eds pp 173ndash214 Springer BerlinHeidelberg Berlin Heidelberg 2008

[8] C Zhao S Zhang Q Liu J Xie and J Hu ldquoIndependenttasks scheduling based on genetic algorithm in cloud com-putingrdquo in Proceedings of the 2009 5th International Con-ference on Wireless Communications Networking and MobileComputing pp 1ndash4 Beijing China September 2009

[9] S Pandey LWu SM Guru and R Buyya ldquoA particle swarmoptimization-based heuristic for scheduling workflow appli-cations in cloud computing environmentsrdquo in Proceedings ofthe 2010 24th IEEE International Conference on AdvancedInformation Networking and Applications pp 400ndash407 PerthAustralia April 2010

[10] Z Jia J Yan J Y T Leung K Li and H Chen ldquoAnt colonyoptimization algorithm for scheduling jobs with fuzzy pro-cessing time on parallel batch machines with different ca-pacitiesrdquo Applied Soft Computing vol 75 pp 548ndash561 2019

[11] F Xhafa J Carretero E Alba and B Dorronsoro ldquoDesignand evaluation of tabu search method for job scheduling indistributed environmentsrdquo in Proceedings of the 2008 IEEEInternational Symposium on Parallel and Distributed Pro-cessing pp 1ndash8 Sydney Australia December 2008

[12] S Sagnika S Bilgaiyan and B S P Mishra ldquoWorkflowscheduling in cloud computing environment using bat al-gorithmrdquo in Proceedings of First International Conference onSmart System Innovations and Computing A K SomaniS Srivastava A Mundra and S Rawat Eds pp 149ndash163Springer Singapore Singapore 2018

[13] R Nallakuma D N Sengottaiyan and K S Sruthi Priya ldquoAsurvey on scheduling and the attributes of task scheduling inthe cloudrdquo IJARCCE vol 3 pp 8167ndash8171 2014

[14] R Rajathy B Taraswinee and S Suganya ldquoA novel method ofusing symbiotic organism search algorithm in solving secu-rity-constrained ecotnomic dispatchrdquo in Proceedings of the2015 International Conference on Circuits Power and Com-puting Technologies [ICCPCT-2015] pp 1ndash8 Nagercoil IndiaMarch 2015

[15] S Burnwal and S Deb ldquoScheduling optimization of flexiblemanufacturing system using cuckoo search-based approachrdquoJe International Journal of Advanced Manufacturing Tech-nology vol 64 no 5ndash8 pp 951ndash959 2013

[16] C-W Tsai and J J P C Rodrigues ldquoMetaheuristic schedulingfor cloud a surveyrdquo IEEE Systems Journal vol 8 no 1pp 279ndash291 2014

[17] A A Heidari S Mirjalili H Faris I Aljarah M Mafarja andH Chen ldquoHarris hawks optimization algorithm and appli-cationsrdquo Future Generation Computer Systems vol 97pp 849ndash872 2019

[18] X Bao H Jia and C Lang ldquoA novel hybrid harris hawksoptimization for color image multilevel thresholding seg-mentationrdquo IEEE Access vol 7 pp 76529ndash76546 2019

[19] H Jia C Lang D Oliva W Song and X Peng ldquoDynamicharris hawks optimization with mutation mechanism forsatellite image segmentationrdquo Remote Sensing vol 11 no 12p 1421 2019

[20] J Too A R Abdullah and N Mohd Saad ldquoA new quadraticbinary harris hawk optimization for feature selectionrdquo Elec-tronics vol 8 no 10 p 1130 2019

[21] D T Bui H Moayedi B Kalantar et al ldquoA novel swarmintelligencemdashharris hawks optimization for spatial assess-ment of landslide susceptibilityrdquo Sensors vol 19 no 16p 3590 2019

[22] H Chen S Jiao M Wang A A Heidari and X ZhaoldquoParameters identification of photovoltaic cells and modulesusing diversification-enriched harris hawks optimization withchaotic driftsrdquo Journal of Cleaner Production vol 244 ArticleID 118778 2020

[23] N A Golilarz H Gao and H Demirel ldquoSatellite image de-noising with harris hawks meta heuristic optimization algo-rithm and improved adaptive generalized gaussian


distribution threshold functionrdquo IEEE Access vol 7pp 57459ndash57468 2019

[24] S H A Aleem A F Zobaa M E Balci and S M IsmaelldquoHarmonic overloading minimization of frequency-dependentcomponents in harmonics polluted distribution systems usingharris hawks optimization algorithmrdquo IEEE Access vol 7pp 100824ndash100837 2019

[25] H A Babikir M A Elaziz A H Elsheikh et al ldquoNoiseprediction of axial piston pump based on different valvematerials using a modified artificial neural network modelrdquoAlexandria Engineering Journal vol 58 no 3 pp 1077ndash10872019

[26] M R Elkadeem M A Elaziz Z Ullah S Wang andS W Sharshir ldquoOptimal planning of renewable energy-in-tegrated distribution system considering uncertaintiesrdquo IEEEAccess vol 7 pp 164887ndash164907 2019

[27] A A Ewees and M A Elaziz ldquoPerformance analysis ofchaotic multi-verse harris hawks optimization a case study onsolving engineering problemsrdquo Engineering Applications ofArtificial Intelligence vol 88 Article ID 103370 2020

[28] A Taher A H Shehabeldeena M Abd Elaziz and J ZhouldquoModeling of friction stir welding process using adaptiveneuro-fuzzy inference system integrated with harris hawksoptimizerrdquo Journal of Materials Research and Technologyvol 8 no 6 pp 5882ndash5892 2019

[29] A R Yıldız B S Yıldız S M Sait S Bureerat andN Pholdee ldquoA new hybrid harris hawks-Nelder-Mead op-timization algorithm for solving design and manufacturingproblemsrdquo Materials Testing vol 61 pp 735ndash743 2019

[30] F Ramezani J Lu J Taheri and F K Hussain ldquoEvolutionaryalgorithm-based multi-objective task scheduling optimizationmodel in cloud environmentsrdquo World Wide Web vol 18no 6 pp 1737ndash1757 2015

[31] A Arunarani D Manjula and V Sugumaran ldquoTaskscheduling techniques in cloud computing a literature sur-veyrdquo Future Generation Computer Systems vol 91 pp 407ndash415 2019

[32] M Kumar S C Sharma A Goel and S P Singh ldquoAcomprehensive survey for scheduling techniques in cloudcomputingrdquo Journal of Network and Computer Applicationsvol 143 pp 1ndash33 2019

[33] L Guo S Zhao S Shen and C Jiang ldquoTask schedulingoptimization in cloud computing based on heuristic algo-rithmrdquo Journal of Networks vol 7 no 3 pp 547ndash553 2012

[34] A Khalili and S M Babamir ldquoMakespan improvement ofpso-based dynamic scheduling in cloud environmentrdquo inProceedings of the 2015 23rd Iranian Conference on ElectricalEngineering pp 613ndash618 IEEE Tehran Iran May 2015

[35] H B Alla S B Alla A Touhafi and A Ezzati ldquoA novel taskscheduling approach based on dynamic queues and hybridmeta-heuristic algorithms for cloud computing environ-mentrdquo Cluster Computing vol 21 no 4 pp 1797ndash1820 2018

[36] A Al-Maamari and F A Omara ldquoTask scheduling using psoalgorithm in cloud computing environmentsrdquo InternationalJournal of Grid and Distributed Computing vol 8 no 5pp 245ndash256 2015

[37] H S Al-Olimat M Alam R Green and J K Lee ldquoCloudletscheduling with particle swarm optimizationrdquo in Proceedingsof the 2015 Fifth International Conference on CommunicationSystems and Network Technologies pp 991ndash995 IEEEGwalior India April 2015

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systemsrdquo Evolutionary Intelligence vol 12 no 2 pp 227ndash2392019

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[40] B Keshanchi A Souri and N J Navimipour ldquoAn improvedgenetic algorithm for task scheduling in the cloud environ-ments using the priority queues formal verification simu-lation and statistical testingrdquo Journal of Systems and Softwarevol 124 pp 1ndash21 2017

[41] M Akbari H Rashidi and S H Alizadeh ldquoAn enhancedgenetic algorithm with new operators for task scheduling inheterogeneous computing systemsrdquo Engineering Applicationsof Artificial Intelligence vol 61 pp 35ndash46 2017

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[43] A M Manasrah and H Ba Ali ldquoWorkflow scheduling usinghybrid ga-pso algorithm in cloud computingrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID1934784 16 pages 2018

[44] A S Kumar and M Venkatesan ldquoTask scheduling in a cloudcomputing environment using hgpso algorithmrdquo ClusterComputing vol 22 no S1 pp 2179ndash2185 2019

[45] V A Chalack S N Razavi and S J Gudakahriz ldquoResourceallocation in cloud environment using approaches basedparticle swarm optimizationrdquo International Journal ofComputer Applications Technology and Research vol 6 no 2pp 87ndash90 2017

[46] S Singh and I Chana ldquoQ-aware quality of service basedcloud resource provisioningrdquo Computers amp Electrical Engi-neering vol 47 pp 138ndash160 2015

[47] V Sontakke P Patil S Waghamare et al ldquoDynamic resourceallocation strategy for cloud computing using virtual machineenvironmentrdquo International Journal of Engineering Sciencevol 6 no 5 pp 4804ndash4806 2016

[48] M Shojafar S Javanmardi S Abolfazli and N CordeschildquoFuge a joint meta-heuristic approach to cloud job schedulingalgorithm using fuzzy theory and a genetic methodrdquo ClusterComputing vol 18 no 2 pp 829ndash844 2015

[49] A A A Ari I Damakoa C Titouna N Labraoui andA Gueroui ldquoEfficient and scalable aco-based task schedulingfor green cloud computing environmentrdquo in Proceedings ofthe IEEE International Conference on Smart Cloud pp 66ndash71New York NY USA November 2017

[50] Y Dai Y Lou and X Lu ldquoA task scheduling algorithm basedon genetic algorithm and ant colony optimization algorithmwith multi-qos constraints in cloud computingrdquo in Pro-ceedings of the 2015 7th International Conference on IntelligentHuman-Machine Systems and Cybernetics vol 2 pp 428ndash431IEEE Hangzhou China August 2015

[51] L Ding P Fan and B Wen ldquoA task scheduling algorithm forheterogeneous systems using acordquo in Proceedings of the In-ternational Symposium on Instrumentation andMeasurementSensor Network and Automation pp 749ndash751 TorontoCanada December 2013

[52] M Kaur andM Agnihotri ldquoPerformance evaluation of hybridgaaco for task scheduling in cloud computingrdquo in Proceedingsof the International Conference on Contemporary Computingand Informatics pp 168ndash172 Greater Noida India June 2017


[53] P C Pendharkar ldquoAn ant colony optimization heuristic forconstrained task allocation problemrdquo Journal of Computa-tional Science vol 7 pp 37ndash47 2015

[54] A E Keshk A B El-Sisi and M A Tawfeek ldquoCloud taskscheduling for load balancing based on intelligent strategyrdquoInternational Journal of Intelligent Systems and Applicationsvol 6 no 5 pp 25ndash36 2014

[55] S M G Kashikolaei A A R Hosseinabadi B SaemiM B Shareh A K Sangaiah and G-B Bian ldquoAn en-hancement of task scheduling in cloud computing based onimperialist competitive algorithm and firefly algorithmrdquo JeJournal of Supercomputing pp 1ndash28 2019

[56] D I Esa and A Yousif ldquoScheduling jobs on cloud computingusing firefly algorithmrdquo International Journal of Grid andDistributed Computing vol 9 no 7 pp 149ndash158 2016

[57] R Eswari and S Nickolas ldquoEffective task scheduling forheterogeneous distributed systems using firefly algorithmrdquoInternational Journal of Computational Science and Engi-neering vol 11 no 2 pp 132ndash142 2015

[58] F Fanian V K Bardsiri and M Shokouhifar ldquoA new taskscheduling algorithm using firefly and simulated annealingalgorithms in cloud computingrdquo International Journal ofAdvanced Computer Science and Applications vol 9 no 22018

[59] T Mandal and S Acharyya ldquoOptimal task scheduling in cloudcomputing environment meta heuristic approachesrdquo inProceedings of the 2015 2nd International Conference onElectrical Information and Communication Technologies(EICT) pp 24ndash28 IEEE Khulna Bangladesh December2015

[60] S S Alresheedi S Lu M A Elaziz and A A Ewees ldquoIm-proved multiobjective salp swarm optimization for virtualmachine placement in cloud computingrdquo Human-centricComputing and Information Sciences vol 9 no 1 p 15 2019

[61] T D Braun H J Siegel N Beck et al ldquoA comparison ofeleven static heuristics for mapping a class of independenttasks onto heterogeneous distributed computing systemsrdquoJournal of Parallel and Distributed Computing vol 61 no 6pp 810ndash837 2001

[62] M Abdullahi M A Ngadi and S Muhammad AbdulhamildquoSymbiotic organism search optimization based task sched-uling in cloud computing environmentrdquo Future GenerationComputer Systems vol 56 pp 640ndash650 2016

[63] M Abdullahi and M A Ngadi ldquoHybrid symbiotic organismssearch optimization algorithm for scheduling of tasks oncloud computing environmentrdquo PLoS One vol 11 no 6Article ID e0158229 2016

[64] G Yao Y Ding Y Jin and K Hao ldquoEndocrine-based co-evolutionary multi-swarm for multi-objective workflowscheduling in a cloud systemrdquo Soft Computing vol 21 no 15pp 4309ndash4322 2017

[65] Z Zhu G Zhang M Li and X Liu ldquoEvolutionary multi-objective workflow scheduling in cloudrdquo IEEE Transactionson Parallel and Distributed Systems vol 27 no 5pp 1344ndash1357 2016

[66] L Zhang K Li C Li and K Li ldquoBi-objective workflowscheduling of the energy consumption and reliability inheterogeneous computing systemsrdquo Information Sciencesvol 379 pp 241ndash256 2017

[67] L F Bittencourt A Goldman E R M Madeira N L S daFonseca and R Sakellariou ldquoScheduling in distributed sys-tems a cloud computing perspectiverdquo Computer ScienceReview vol 30 pp 31ndash54 2018

[68] S K Panda and P K Jana ldquoUncertainty-based QoS min-minalgorithm for heterogeneous multi-cloud environmentrdquoArabian Journal for Science and Engineering vol 41 no 8pp 3003ndash3025 2016

[69] S K Panda and P K Jana ldquoNormalization-based taskscheduling algorithms for heterogeneous multi-cloud envi-ronmentrdquo Information Systems Frontiers vol 20 no 2pp 373ndash399 2018

[70] S K Panda and P K Jana ldquoEfficient task scheduling algo-rithms for heterogeneous multi-cloud environmentrdquo JeJournal of Supercomputing vol 71 no 4 pp 1505ndash1533 2015

[71] S K Panda and P K Jana ldquoSla-based task scheduling al-gorithms for heterogeneous multi-cloud environmentrdquo JeJournal of Supercomputing vol 73 no 6 pp 2730ndash2762 2017

[72] D Gabi A S Ismail A Zainal Z Zakaria and A Al-Kha-sawneh ldquoCloud scalable multi-objective task scheduling al-gorithm for cloud computing using cat swarm optimizationand simulated annealingrdquo in Proceedings of the 2017 8thInternational Conference on Information Technology (ICIT)pp 1007ndash1012 Amman Jordan May 2017

[73] I Attiya and X Zhang ldquoD-choices scheduling a randomizedload balancing algorithm for scheduling in the cloudrdquo Journalof Computational and Jeoretical Nanoscience vol 14 no 9pp 4183ndash4190 2017

[74] J Jin Xu A Y S Lam and V O K Li ldquoChemical reactionoptimization for task scheduling in grid computingrdquo IEEETransactions on Parallel and Distributed Systems vol 22no 10 pp 1624ndash1631 2011

[75] S-S Kim J-H Byeon H Yu and H Liu ldquoBiogeography-based optimization for optimal job scheduling in cloudcomputingrdquo Applied Mathematics and Computation vol 247pp 266ndash280 2014

[76] D Bertsimas and J Tsitsiklis ldquoSimulated annealingrdquo Statis-tical Science vol 8 no 1 pp 10ndash15 1993

[77] S Kirkpatrick C D Gelatt and M P Vecchi ldquoOptimizationby simulated annealingrdquo Science vol 220 no 4598pp 671ndash680 1983

[78] R N Calheiros R Ranjan A Beloglazov C A F De Roseand R Buyya ldquoCloudsim a toolkit for modeling and simu-lation of cloud computing environments and evaluation ofresource provisioning algorithmsrdquo Software Practice andExperience vol 41 no 1 pp 23ndash50 2011

[79] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquo inProceedings of the ICNNrsquo95mdashInternational Conference onNeural Networks vol 4 pp 1942ndash1948 Perth AustraliaNovember 1995

[80] S Mirjalili A H Gandomi S Z Mirjalili S Saremi H Farisand S M Mirjalili ldquoSalp swarm algorithm a bio-inspiredoptimizer for engineering design problemsrdquo Advances inEngineering Software vol 114 pp 163ndash191 2017

[81] S Mirjalili ldquoMoth-flame optimization algorithm a novelnature-inspired heuristic paradigmrdquo Knowledge-Based Sys-tems vol 89 pp 228ndash249 2015

[82] X-S Yang ldquoFirefly algorithms for multimodal optimizationrdquoin Stochastic Algorithms Foundations and ApplicationsO Watanabe and T Zeugmann Eds pp 169ndash178 SpringerBerlin Heidelberg Berlin Heidelberg 2009


computing such as CPU storage memory and bandwidthare offered0e next layer in the stack is PaaS PaaS provides ahigh-level integrated environment to build test deploy andhost developer-created or -acquired applications 0e SaaS isallocated at the top of the stack and it is a software deliverymodel in which applications or services are provided over theInternet so that end users can access them through a webbrowser 0is model allows users to utilize online softwareinstead of the locally installed one SaaS has now become apopular delivery model for service apps such as web mailGoogle Docs and social networking applications

0ere is a consensus in the researcher community and ITindustries that the growth in cloud computing will far exceedthat of other computing paradigms [3] 0is is due to thefollowing reasons First the cloud offers a practical solutionto solve the issue of resource lack and greatly reduces theexpenses of purchasing and maintaining the physical re-sources [4 5] Second it provides virtually infinite resourcesat different prices to properly serve different applicationrequirements in a dynamic and elastic way As a result theemphasis of computing has recently been pushed onto cloudplatforms On the contrary with the growing adoption ofcloud services (especially the IaaS model) by several insti-tutions there has been a huge amount of computing tasksthat are implemented in the cloud computing (CC) envi-ronment Since the computing resources are heterogeneousand geographically distributed there are compromises interms of communication cost system integration andsystem performance 0us in order to efficiently execute thecloud user requests and utilize the distributed resources inan appropriate way a scheduling policy needs to be in place

Indeed many algorithms have been introduced to tacklethe job scheduling problem in a CC environment In theearly stage various heuristics were developed to address jobscheduling problems which produce optimal schedule so-lutions for small-sized problems [6] However the quality ofsolutions generated by these heuristic strategies deterioratesseverely as the problem scale and the number of objectives tobe optimized increase In addition the solutions producedby these heuristic techniques depend largely on certainunderlining rules and they are generated at high operatingcost [7] In contrast metaheuristic techniques have provento be effective robust and efficient in solving a wide varietyof real-world complex optimization problems 0is can beattributed to their ability to employ a set of candidate so-lutions for the purpose of traversing the solution spacerather than using a single candidate solution as with heu-ristic techniques 0is feature of metaheuristic algorithmsmakes them outperform other optimization methods Someof the most popular metaheuristic techniques that have beenintroduced to solve the cloud job scheduling problem in-clude genetic algorithm (GA) [8] particle swarm optimi-zation (PSO) [9] ant colony optimization (ACO) [10] tabusearch [11] BAT algorithm [12] simulated annealing (SA)algorithm [13] symbiotic organisms search (SOS) [14] andcuckoo search (CS) algorithm [15] Although some of thesealgorithms have shown promising improvements in findingthe global optimal solution for the job scheduling problem inthe cloud they are all suffering from premature convergence

and difficulty to overcome local minima especially whenfaced with a large solution space [16]0ese limitations oftenlead to suboptimal job scheduling solutions which affect thesystem performance and also violate quality of service (QoS)guarantees 0is indicates that there is an urgent need fornew adaptive and efficient algorithms to find the globaloptimal solution for the cloud job scheduling problem

Recently Heidari et al [17] proposed a population-based nature-inspired optimization technique called theHarris hawks optimizer (HHO) which mimics the socialbehavior of Harrisrsquo hawks in nature It is mainly inspired bythe cooperative behavior and chasing strategy of Harrishawks 0e exploration and exploitation phases of the HHOare modeled by exploring a prey performing a surprisepounce and then attacking the intended prey 0e Harrishawks optimizer can demonstrate a variety of attackingstrategies according to the dynamic nature of circumstancesand escaping behaviors of the prey Local optima avoidanceand smooth transition from exploration to exploitation areamong the major advantages of the HHO algorithmAccording to these behaviors the HHO has been applied toseveral global optimization and real-world engineeringproblems including image segmentation [18 19] featureselection [20] spatial assessment of landslide susceptibility[21] parameter estimation of photovoltaic cells [22] imagedenoising [23] and others [24ndash29] However the HHOsuffers from some limitations that affect its performancesuch that its exploration ability is weaker than its exploi-tation ability and this leads to degradation of the perfor-mance of convergence and the quality of the solution Inaddition there is plenty of room to investigate the potentialimprovements in terms of speed of convergence and qualityof solutions generated by the HHO

A promising research direction which hybridizes one ormore heuristicsmetaheuristics to leverage the strengths ofthese algorithms while reducing their impediments hasattracted tremendous attention from researchers in variousresearch domains In this study an integrated version of theHHO algorithm with simulated annealing (HHOSA) wasproposed as an attempt to improve the rate of convergenceand local search of HHO To the best of our knowledge noresearch study found in the literature tries to investigate theabove-mentioned improvements with the performance ofHHO while tackling the job scheduling problem Hence themain motivation of our study is to propose the hybridHHOSA approach for optimization of job scheduling incloud computing

0e major contributions of this paper can be summa-rized as follows

(1) Design and implementation of a hybrid version ofHHO and SA for optimum job scheduling in cloudcomputing

(2) Empirical analysis of the convergence trend for 15different job scheduling instances using HHOSA andother evaluated algorithms

(3) Performance comparison of HHOSA against theoriginal HHO and other popular metaheuristics in




2 Related Works










3 Background





ETCij

ETC11 ETC12 ETC1m

ETC21 ETC22 ETC2m

ETCn1 ETCn2 ETCnm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

ETCij JobLengthi

VMPowerj

(2)





MKS(X) maxjisin12m

1113944

n

i1ETCij (3)



1113944

n

i1ETCij (4)




Prob eminusΔEkT



T β times T (6)





11138681113868111386811138681113868111386811138681113868 qge 05


⎧⎪⎨

⎪⎩

(7)


XAvg(t) 1N

1113944

N

i1Xi(t) (8)



E 2E0 1 minust

tmax1113888 1113889 (9)





1113868111386811138681113868

J 2 1 minus r5( 1113857(10)






1113868111386811138681113868 (13)





1113868111386811138681113868



1β

(15)





Z if F(Z)ltF(X(t))1113896 (16)





⎧⎨

⎩ (17)



11138681113868111386811138681113868









Xi Y






Exploration

Perching based on

random locations

Hard besiege with


So besiege with


r lt 05

q ge 05

|E| ge

1

|E| ge

05

|E| lt

05

|E| = 1

q lt 05

E



Exploitation

Hard besiege

So besieger ge 05












Return Xb













(19)




Pri Fi

1113936Ni1 Fi

(20)



minus LPri1113872 1113873 (21)

where LPriand UPri


























Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References


























































































2 Related Works










3 Background





ETCij

ETC11 ETC12 ETC1m

ETC21 ETC22 ETC2m

ETCn1 ETCn2 ETCnm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

ETCij JobLengthi

VMPowerj

(2)





MKS(X) maxjisin12m

1113944

n

i1ETCij (3)



1113944

n

i1ETCij (4)




Prob eminusΔEkT



T β times T (6)





11138681113868111386811138681113868111386811138681113868 qge 05


⎧⎪⎨

⎪⎩

(7)


XAvg(t) 1N

1113944

N

i1Xi(t) (8)



E 2E0 1 minust

tmax1113888 1113889 (9)





1113868111386811138681113868

J 2 1 minus r5( 1113857(10)






1113868111386811138681113868 (13)





1113868111386811138681113868



1β

(15)





Z if F(Z)ltF(X(t))1113896 (16)





⎧⎨

⎩ (17)



11138681113868111386811138681113868









Xi Y






Exploration

Perching based on

random locations

Hard besiege with


So besiege with


r lt 05

q ge 05

|E| ge

1

|E| ge

05

|E| lt

05

|E| = 1

q lt 05

E



Exploitation

Hard besiege

So besieger ge 05












Return Xb













(19)




Pri Fi

1113936Ni1 Fi

(20)



minus LPri1113872 1113873 (21)

where LPriand UPri


























Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References


























































































3 Background





ETCij

ETC11 ETC12 ETC1m

ETC21 ETC22 ETC2m

ETCn1 ETCn2 ETCnm

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

ETCij JobLengthi

VMPowerj

(2)





MKS(X) maxjisin12m

1113944

n

i1ETCij (3)



1113944

n

i1ETCij (4)




Prob eminusΔEkT



T β times T (6)





11138681113868111386811138681113868111386811138681113868 qge 05


⎧⎪⎨

⎪⎩

(7)


XAvg(t) 1N

1113944

N

i1Xi(t) (8)



E 2E0 1 minust

tmax1113888 1113889 (9)





1113868111386811138681113868

J 2 1 minus r5( 1113857(10)






1113868111386811138681113868 (13)





1113868111386811138681113868



1β

(15)





Z if F(Z)ltF(X(t))1113896 (16)





⎧⎨

⎩ (17)



11138681113868111386811138681113868









Xi Y






Exploration

Perching based on

random locations

Hard besiege with


So besiege with


r lt 05

q ge 05

|E| ge

1

|E| ge

05

|E| lt

05

|E| = 1

q lt 05

E



Exploitation

Hard besiege

So besieger ge 05












Return Xb













(19)




Pri Fi

1113936Ni1 Fi

(20)



minus LPri1113872 1113873 (21)

where LPriand UPri


























Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References


























































































Prob eminusΔEkT



T β times T (6)





11138681113868111386811138681113868111386811138681113868 qge 05


⎧⎪⎨

⎪⎩

(7)


XAvg(t) 1N

1113944

N

i1Xi(t) (8)



E 2E0 1 minust

tmax1113888 1113889 (9)





1113868111386811138681113868

J 2 1 minus r5( 1113857(10)






1113868111386811138681113868 (13)





1113868111386811138681113868



1β

(15)





Z if F(Z)ltF(X(t))1113896 (16)





⎧⎨

⎩ (17)



11138681113868111386811138681113868









Xi Y






Exploration

Perching based on

random locations

Hard besiege with


So besiege with


r lt 05

q ge 05

|E| ge

1

|E| ge

05

|E| lt

05

|E| = 1

q lt 05

E



Exploitation

Hard besiege

So besieger ge 05












Return Xb













(19)




Pri Fi

1113936Ni1 Fi

(20)



minus LPri1113872 1113873 (21)

where LPriand UPri


























Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References


























































































Z if F(Z)ltF(X(t))1113896 (16)





⎧⎨

⎩ (17)



11138681113868111386811138681113868









Xi Y






Exploration

Perching based on

random locations

Hard besiege with


So besiege with


r lt 05

q ge 05

|E| ge

1

|E| ge

05

|E| lt

05

|E| = 1

q lt 05

E



Exploitation

Hard besiege

So besieger ge 05












Return Xb













(19)




Pri Fi

1113936Ni1 Fi

(20)



minus LPri1113872 1113873 (21)

where LPriand UPri


























Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References

































































































Return Xb













(19)




Pri Fi

1113936Ni1 Fi

(20)



minus LPri1113872 1113873 (21)

where LPriand UPri


























Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References


























































































(19)




Pri Fi

1113936Ni1 Fi

(20)



minus LPri1113872 1113873 (21)

where LPriand UPri


























Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References





































































































Host



VM








NASAiPSC

Oct1993ndashDec

1993128 18239 69



22-clnswf



PSOSwarm size 100


FA



MFOSwarm size 100



HHOSASwarm size 100

E0 [minus1 1]β 085


50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References
























































































50

100

150

200

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



No of iterations

102

Ave

rage

of m

akes

pan

200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


103

Ave

rage

of m

akes

pan

No of iterations200 400 600 800 1000

PSOFASSA

MFOHHOHHOSA


No of iterations200 400 600 800 1000

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

50

100

150

200250300350

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA



200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References
























































































200 400 600 800 1000No of iterations

102

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

103

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

104

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References




























































































200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA


105

Ave

rage

of m

akes

pan

200 400 600 800 1000No of iterations

PSOFASSA

MFOHHOHHOSA


200 400 600 800 1000No of iterations

105

Ave

rage

of m

akes

pan

PSOFASSA

MFOHHOHHOSA







Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References




























































































Synthetic

200 5964 5649 4786 4839 3810 3312400 12552 11226 10840 9934 7925 6540600 19063 17691 16281 15801 11351 9774800 23809 23449 22658 21699 14530 128241000 30577 29540 27670 27349 18261 16167

NASA iPSC

500 8256 7494 6767 6684 5464 44941000 17104 15675 14640 14084 10712 91081500 25861 24137 23442 23050 15769 139142000 34912 33803 32288 30789 20181 188142500 45138 43200 41674 40070 26121 23847

HPC2N

500 894652 876062 800193 805329 557243 4890721000 2079374 1968211 1849602 1809598 1225381 10648831500 3336163 3172751 2982493 2929583 1973212 17206452000 4813505 4574989 4380880 4263218 2807655 25031562500 6271388 6002449 5884585 5810448 3622846 3276949



Synthetic

200 6562 5956 5661 5517 4213 3408400 13378 12241 12151 11572 8422 6799600 20039 18668 18046 17955 12357 10296800 26108 24777 24260 23693 16193 135621000 32596 31134 30618 29732 19992 16816

NASA iPSC

500 9068 7836 7833 7757 5851 46931000 18161 16528 16353 16390 11704 95041500 27567 25790 25343 25396 17710 145702000 36950 35245 34674 34204 23468 199352500 47077 44678 44203 43385 29110 25303

HPC2N

500 985644 924751 895587 890951 611611 5078281000 2175553 2048989 1996524 1980062 1359103 11245991500 3469798 3288246 3258668 3177413 2138315 18020642000 4970600 4749934 4680383 4691956 3055234 26397052500 6599923 6286726 6243716 6162858 3969823 3496006



Synthetic

200 7001 6516 6763 6235 4785 3684400 13931 13125 13174 13768 9124 7456600 20836 19944 19570 20054 13798 11143800 27097 25875 26155 26178 17648 147321000 34391 32015 33200 33482 22845 17786

NASA iPSC

500 9688 8783 8968 8757 6494 49091000 19488 17543 17862 18798 13702 103911500 29092 27493 26668 29062 19925 161692000 38926 36576 37027 37262 27677 209732500 49798 46999 47552 47000 33707 27055

HPC2N

500 1043789 972910 997812 1001548 693565 5338961000 2261470 2118787 2116400 2135251 1482445 12335511500 3569154 3388020 3463310 3505564 2341163 19072552000 5116914 4915643 4992790 5037681 3535693 28300922500 6880423 6603635 6541207 6842254 4446631 3769171



6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References

























































































6 Conclusions











Pop β50 150 035 055 095

HPC2N (500 jobs)Best 489072 4945263 4866144 4881952 4912909 4946269

Average 507828 5200724 5063752 5094164 5130123 5162682Worst 533896 5579552 531788 5377362 5350381 5832608


Average 9504 9702455 9496202 9601011 9603121 9543977Worst 10391 1041675 1014676 1018874 1017581 101617


Average 16816 1729459 1649955 1694086 167829 168612Worst 17786 1855133 173191 1842198 1806842 1776314



Data Availability




Acknowledgments


References

























































































Data Availability




Acknowledgments


References






















































































































































































Documents

Job Scheduling in Cloud Computing Using a Modified Harris …downloads.hindawi.com/journals/cin/2020/3504642.pdf · Job Scheduling in Cloud Computing Using a Modified Harris Hawks