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Scientific workflow scheduling in multi-cloud computing using a hybrid multi-objective optimization algorithm

September 2021
Journal of Ambient Intelligence and Humanized Computing 14(4)

September 2021
14(4)

DOI:10.1007/s12652-021-03482-5

Authors:

Ali Mohammadzadeh

Islamic Azad University

Mohammad Masdari

Islamic Azad University of Urmia

Multi-cloud is the use of multiple cloud computing in a single heterogeneous architecture. Workflow scheduling in multi-cloud computing is an NP-Hard problem for which many heuristics and meta-heuristics are introduced. This paper first presents a hybrid multi-objective optimization algorithm denoted as HGSOA-GOA, which combines the Seagull Optimization Algorithm (SOA) and Grasshopper Optimization Algorithm (GOA). The HGSOA-GOA applies chaotic maps for producing random numbers and achieves a good trade-off between exploitation and exploration, leading to an improvement in the convergence rate. Then, HGSOA-GOA is applied for scientific workflow scheduling problems in multi-cloud computing environments by considering factors such as makespan, cost, energy, and throughput. In this algorithm, a solution from the Pareto front is selected using a knee-point method and then is applied for assigning the scientific workflows’ tasks in a multi-cloud environment. Extensive comparisons are conducted using the CloudSim and WorkflowSim tools and the results are compared to the SPEA2 algorithm. The achieved results exhibited that the HGSOA-GOA can outperform other algorithms in terms of metrics such as IGD, coverage ratio, and so on.

Workflow execution in the multi-cloud

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The GOA's flowchart

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The flowchart of the HGSOA-GOA algorithm

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Archive updating algorithm

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Determining the knee point in the inline method

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Journal of Ambient Intelligence and Humanized Computing

https://doi.org/10.1007/s12652-021-03482-5

ORIGINAL RESEARCH

Scientiﬁc workﬂow scheduling inmulti‑cloud computing using

ahybrid multi‑objective optimization algorithm

AliMohammadzadeh1· MohammadMasdari2

Received: 5 December 2020 / Accepted: 2 September 2021

Abstract

Multi-cloudis the use of multiplecloud computing in a single heterogeneous architecture. Workﬂow scheduling in multi-

cloud computing is an NP-Hard problem for which many heuristics and meta-heuristics are introduced. This paper ﬁrst pre-

sents a hybrid multi-objective optimization algorithm denoted as HGSOA-GOA, which combines the Seagull Optimization

Algorithm (SOA) and Grasshopper Optimization Algorithm (GOA). The HGSOA-GOA applies chaotic maps for producing

random numbers and achieves a good trade-oﬀ between exploitation and exploration, leading to an improvement in the

convergence rate. Then, HGSOA-GOA is applied for scientiﬁc workﬂow scheduling problems in multi-cloud computing

environments by considering factors such as makespan, cost, energy, and throughput. In this algorithm, a solution from the

Pareto front is selected using a knee-point method and then is applied for assigning the scientiﬁc workﬂows’ tasks in a multi-

cloud environment. Extensive comparisons are conducted using the CloudSim and WorkﬂowSim tools and the results are

compared to the SPEA2 algorithm. The achieved results exhibited that the HGSOA-GOA can outperformother algorithms

in terms of metrics such as IGD, coverage ratio, and so on.

Keywords Workﬂow· Scheduling· SOA· GOA· Multi-cloud· Pareto front

1 Introduction

Cloud computing is a growing ﬁeld of distributed computing

that provides dynamically scalable services over the inter-

net via virtual servers. It is focused on a market-oriented

business strategy in which consumers can purchase services

based on Service Level Agreements (SLA) and be paid

on a pay-as-you-go model, similar to traditional services

(Mateescu etal. 2011). The key beneﬁts of cloud comput-

ing are its ﬂexibility and scalability, which allows users to

reserve and unlock, services and resources as required.

The services and applications that include horizontal scal-

ing can be spread across several diﬀerent cloud computing

environments with diﬀerent pricing models. Scheduling

single-cloud environments attempt to assign tasks submit-

ted by users through various heterogeneous virtual resources

while inter-cloud environments try to target tasks submitted

by users through various heterogeneous virtual resources

dispersed across various cloud service providers. With the

popularity of inter-cloud environments, workﬂow schedul-

ing solutions for inter-cloud applications are now available,

allowing users to get the most out of the computing and

storage infrastructure that they have(Masdari and Zanga-

kani 2020). Generally, scheduling schemes in the inter-cloud

environments are divided into three categories, cloud federa-

tion, multi-cloud, and hybrid cloud. In this paper, our focus

is on multi-cloud.

When designing a process scheduling strategy, several

works consider task execution locations. For example, in

Fig.1 the eﬀect of task order on the makespan metric is

shown. Assume there are two diﬀerent cloud platforms,

cloud 1 and 2. The scheduling location for aworkﬂow appli-

cation is as follows: tasks T0, T1, T2, and T3 are scheduled to

cloud 1, and tasks T4, T5, T6, and T7 are mapped to cloud 2.

In this ﬁgure, makespan is the time it takes for a workﬂow

to complete. Tasks T1, T2, and T3 can be run concurrently

after task T0 is completed. Then, task T4 receives task T1's

* Ali Mohammadzadeh

A.Mohammadzadeh@iaurmia.ac.ir

Mohammad Masdari

M.Masdari@iaurmia.ac.ir

1 Department ofComputer Engineering, Shahindezh Branch,

Islamic Azad University, Shahindezh, Iran

2 Department ofComputer Engineering, Urmia Branch,

Islamic Azad University, Urmia, Iran

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A.Mohammadzadeh, M.Masdari

1 3

output data and begins to run. After that, task T5receives

output data of task T2, task T6 receives task T3's output and

begins execution. Tasks T4, T5, and T6 are the predecessors

of task T7. Workﬂows have been commonly used to model

large-scale research and engineering applications in a vari-

ety of ﬁelds, including Physics, Bioinformatics, Astronomy,

and Earth Science (Möller etal. 2008). Scientists required a

high-performance computing environment, such as cluster

computing, grid computing, or cloud computing, to operate

these workﬂows of varying sizes.

While multi-cloud computing has several advantages, it

still has some drawbacks that must be addressed. First, due

to virtual machines (VMs) (Masdari and Zangakani 2019)

output variations, a scientiﬁc workﬂow's total deadline can

be missed or its budget may be increased. As a result, perfor-

mance diﬀerences have a major eﬀect on workﬂow schedul-

ing in a multi-cloud computing environment. Second, when

a VM is reserved, it takes time to properly initialize it, and

when computing resources are released, it takes time to shut

down. As a result, the longer the resource acquisition time,

the longer the total execution time, and the longer the shut-

down time, the higher the average cost of the workﬂow. As a

result, the overall eﬃciency and cost of scientiﬁc workﬂows

would be impacted by these delays (Meena etal. 2016).

However, in multi-cloud environments, a variety of VMs

Fig. 1 Workﬂow execution in the multi-cloud

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Scientiﬁc workﬂow scheduling inmulti‑cloud computing using ahybrid multi‑objective…

1 3

with a variety of conﬁgurations and prices are available for

running diﬀerent workﬂows.

The multi-cloud has an unlimited number of resources,

allowing users to expand or shrink leased resources accord-

ing to application requirements; however, determining how

many virtual machines are needed is still an open issue.

Multi-cloud providers' main aim is to make money because

customers must pay for rented virtual machines on a pay-

per-use basis. As a result, workﬂow scheduling in multi-

cloud computing is a multi-objective optimization problem

in which not only the time to completion but also the cost

of execution must be considered. Multi-objective optimi-

zation is one of the most popular methods for minimizing

somemetrics at the same time (Han etal. 2021; Tirkolaee

etal. 2020).

Most researchers have developedmulti-objective meta-

heuristic algorithms like Genetic Algorithm (GA) (Falzon

and Li 2012; Ma etal. 2019), Bat Optimization Algorithm

(Mahajan etal. 2017), and Particle Swarm Optimization

(PSO) (Masdari etal. 2017) to solve workﬂow scheduling

problems and get good answers. Regardless of the amount of

energy consumed, minimizing makespan and operating costs

are commonly seen as two opposing targets. This research

aims to show how a multi-objective optimization algorithm

can be used to generate Pareto optimal solutions in multi-

cloud workﬂow applications. This paper tries to reduce

energy consumption by achieving a form of cloud comput-

ing known as green computing (Jiang etal. 2017; Singh etal.

2019; Thaman and Singh 2017). For this purpose, it presents

HGSOA-GOA, by combining the SOA and GOA algorithms

based on chaos theory. Then, this algorithm is applied for

multi-objective workﬂow scheduling regarding factors such

as: makespan, energy, throughput, and cost. According to the

simulation results, the proposed HGSOA-GOA algorithm

provides greater convergence and a more uniform distance

between solutions. The contributions of this paper can be

listed as follows:

• A hybrid binary and chaotic multi-objective optimiza-

tion algorithm denoted as HGSOA-GOA is presented by

combining the SOA and GOA algorithms.

• A workﬂow scheduling framework for handling scien-

tiﬁc workﬂows in multi-cloud environments is provided,

using the HGSOA-GOA algorithm.

• Evaluating the proposed workﬂow scheduling method for

multi-cloud environments.

• Highlighting possible future works in the multi-cloud

workﬂow scheduling context.

The rest of the paper is structured as follows: a litera-

ture review of the multi-objective workflow-scheduling

schemes is presented in Sect.2. Section3 discusses the

problem deﬁnition, while Sect.4 covers the basic SOA and

GOA algorithms. The suggested HGSOA-GOA algorithm

is presented in Sect.5. Section6 demonstrates the workﬂow

scheduling architecture and the simulation results are pre-

sented in Sect.7. Finally, Sect.8 provides the conclusion and

future research remarks.

2 Literature review

Workﬂow schedulingis an NP-hard optimization issue with

a lot of research in the last ten years. Many evolutionary

algorithms to ﬁx this issue on various cloud environments

have been introduced in previous works; we classiﬁed the

related works into four categories: workﬂow scheduling in

single-cloud, Workﬂow scheduling in multi-cloud, workﬂow

scheduling in cloud federation, and Workﬂow scheduling in

hybrid cloud.

For various computing platforms, such as grid, cluster,

and distributed processing, several task scheduling algo-

rithms have been developed. Some of these algorithms have

been adapted for use in the cloud. For incompatible paral-

lelscheduling with random precedence constraints, Liu and

Yang (2011) proposed a priority rule-based heuristic serial

schedule algorithm. To schedule the prior job-machine pair,

the priority rule can be chosen from the arithmetic mean and

variance of the processing times. Choudhary etal. (2018)

used a hybrid solution of the Gravitational Search Algorithm

(GSA) and HEFT to control cost and makespan similarly.

Many common methods for simultaneously considering

cost and makespan are to model the problem as a constrained

optimization problem, in which one goal is limited while the

other is attempted to be optimized. Many previous studies

(Chen etal. 2018; Jiang etal. 2020) looked at deadline-

constrained workﬂow scheduling issues.

Bansal etal. (2020) used dynamic voltage scale and

adaptive power control to optimize energy eﬃciency while

meeting time limits, while Wu etal. (2018) proposed a three-

phase approach for creating energy-eﬃcient schedules for

cloud workﬂows under reliability and deadlineconstraints.

The NSGA-III algorithm, in Sharma and Shukla (2019) sug-

gested an eﬀective environmental choice and simpliﬁcation

method. The environmental selection operator was created

to select solutions associated with various lines drawn from

the source and reference points in an equal manner. A sim-

pliﬁcationscheme was also proposed, in which the extreme

point is used and the designed rules are revised. The authors

in Mohammadzadeh etal. (2020a, 2021) suggest hybrid

meta-heuristic techniques to schedule scientiﬁc workﬂows

in green cloud computing and compared the results with

the SPEA2 algorithm. An upgraded Grey Wolf optimiza-

tion algorithm was introduced in Mohammadzadeh etal.

(2020b) through optimizing the exploration ability inpur-

suing competing objectives such as energy, cost, makespan,

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A.Mohammadzadeh, M.Masdari

1 3

and throughput. To enhance the GWO algorithm, used a

hill-climbing problem concept and chaotic random numbers

so instead of constant random variables.

In Camelo etal. (2010), the authorsused Division and

Bound's stochastic method to make real Pareto front solu-

tions, and they used a multi-objective heuristic algorithm in

the grid system to solve the scheduling issue.To solve the

workﬂow scheduling problem, suggested the multi-objective

evolutionary algorithm (MOEA) to minimize runtime and

cost (Yu etal. 2007).NSGA-II and SPEA2 (Deb etal. 2002;

Zitzler etal. 2001) are population-based algorithms, and

PAES and MOEA are local search algorithms (Knowles and

Corne 1999) that were used to overcome workﬂow schedul-

ing problems with opposing goals and diﬀerent constraints.

The authors of Hu etal. (2018) proposed a PSO-based

multi-objective method in multi-cloud systems, intending to

reduce time and cost while enhancing reliability. The authors

used a Poisson distribution to determine the probability of

failure and an exponential distribution to calculate the prob-

ability of task completion. They found a task queue for each

cloud service provider and believed that cloud service pro-

vider users would have access to an inﬁnite number of VMs.

The authors used Python and scientiﬁc workﬂows to perform

their assessments. They say that their algorithm outperforms

the CMOHEFT algorithm.

The authors of Maheshwari etal. (2016) propose a multi-

site method for workﬂow scheduling problems that uses per-

formance models to predict the duration of the execution

and adaptive investigates detect network throughput between

diﬀerent sites. Their claim that the method can improve

resource eﬃciency while also reducing execution time.

The authors of Gupta etal. (2016a) proposed a two-

phase priority-based workflow scheduling method for

diverse multi-cloud environments that can handle massive

workﬂows. This method takes into account metrics as an

example computing costs for priority, after that, the tasks

are mapped to the appropriate virtual machines based on

priority. They claimed that their method outperforms other

speed-up algorithms.

In Gupta etal. (2016b), the authors suggested a work-

ﬂow scheduling method for multi-clouds that takes time to

transfer. It calculates the task's B-level prioritization and

performs virtual machine selection based on the calcu-

lated task's B-level priority. In a multi-cloud environment,

however, it does not support preemptive scheduling. Their

research increases makespanand resource usage.

MOHEFT is a list-based multi-objective workflow

scheduling method for scientiﬁc workﬂows (Durillo etal.

2015). It improves the HEFT approach by using the conges-

tion distance to achieve near-optimal Pareto front, reduc-

ing makespan andcost. It was compared to the HEFT and

SPEA2. MOHEFT, according to the writers, has a better cost

andmakespan. To be more precise, MOHEFT and SPEA2

outperform HEFT in workﬂows with a few parallel tasks,

while MOHEFT outperforms SPEA2 in balanced huge

workﬂows.

Coutinho etal. (2015) proposed GraspCC-fed, a method

for determining the optimal number of virtual machines

available for each workﬂow in a single cloud service pro-

vider and federated cloud computing. The Greedy Rand-

omized Adaptive Search Procedure, which forecasts costs

based on cost and execution time, is used in GraspCC-fed.

GraspCC-fed deﬁnes the workﬂow execution setups as well

as the number of virtual machines per cloud service provider

that should be reserved for workﬂow execution based on

user constraints.

3 Problem statement

This sectiondescribes the theories and models that are used

in the rest of this paper. Table1 describes the notations used

in this section. We presume that a variety of data centers

collaborate to provide on-demand services and processing

online equipment. Virtual machines are used to represent all

computing resources in data centers, and virtual machines

from various clouds have various kinds and features. They

might, for example, have varying numbers of CPUs with

varying process time, memory capacities, and network

bandwidth utilization. We assume BE mode for allocating

resources. In thistype, requests are queued and services are

available as quickly as possible.

In this scheme, a set of m clouds is denoted by C = {C1,

C2, C3,…, Cm} and a set of n VMs is denoted by VM = {VM1,

VM2, VM3,…, VMn}. G(T, E) denotes a task graph, in which

T denotes a collection of tasks, and E denotes a collection

ofedges between tasks. Ei jk = (Ti j → Tik) is an edge. The

task Ti j and task Tik are dependent on each other, which is

represented by Ei. It's important to note that the total number

of tasks in one virtual machine |VMi| does not have to be the

same as the total number of tasks in another virtual machine

|VMj|. However, all of the virtual machines are distinct and

heterogeneous. Each task has a unique arrival time and can

be applied to a cloud service provider using BE mode. A

task should not begin until all preceding tasks have been

completed. On diﬀerent clouds, each task takes a diﬀerent

amount of time to complete. The execution time of task j on

the ith VM located on the kth cloud is denoted by ETCi j,k.

Equation(1) indicates the ETC matrix. Since in this scheme

a heterogeneous multi-cloudsystem is considered, the task

execution time is diﬀerent in eachcloud environment (Panda

and Jana 2015).

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1 3

The problem of workflow scheduling, given an ETC

matrix, is to assign all of the tasks to the clouds regarding

their order in workﬂow, aiming to minimize the makespan

of the workﬂow. ET(i, p) is execution times of ith task (ti)

on pth resource (rp). In Eq.(2), Ti is the size of the task, and

pprp is the processing power of the rp resource. EC(i, p) in

Eq.(3) is execution cost. Also, Μp denotes the cost per unit

of pth resources usage for each time interval.

The ﬁrst execution start time and the ﬁrst completion time

of the ith task (ti) on the pth resource (rp) are EST(ti,rp)

and EFT(ti,rp), respectively. We will use for the beginning

task Eq.(4), and for other tasks Eqs. (5) and (6) were used

(Verma and Kaushal 2017). Parent(ti) is a set of parent tasks

for ith task (ti), and avail(rp) is the time that pth resources

(1)

ETC

VMType1

⎧

⎪

⎨

⎪

⎩

T11

⋮

T1p1

⋮

VMTypen

⎧

⎪

⎨

⎪

⎩

Tn1

⋮

Tnpn

⎧

⎪

⎨

⎪

⎩

ETC11,1 …ETC11,m

⋮⋮⋮

ETC1p1,1 …ETC1p1,m

⋮⋮⋮

ETCn1,1 …ETCn1,m

⋮⋮⋮

ETCnpn,1 …ETCnpn,m

⎫

⎪

⎬

⎪

⎭

C1…Cm

(2)

ET(i,p)=T

∕PP

(3)

EC(i,p)=Mp×ET(i,p)

execute the task. The AFT is the actual ﬁnish time for each

jth task (tj). In Eq.(7), on the pth resource, the Actual start

time (AST) is determined for each ith task (Xu etal. 2014).

According to Eq.(8), the makespan is the maximum

actual ﬁnish time of the last workﬂow task (Schwiegelshohn

2010). The energy equation is based on the capacitance of

CMOS logic circuits, according to Eq.(9). The symbol A

represents the number of switches per clock cycle, C repre-

sents total capacitance, V represents the voltage of supply,

and f represents frequency. This equation depicts voltage's

inﬂuence on decreasing energy consumption. Equation(10)

can be used to evaluate the energy usage of the execution of

tasks (Mezmaz etal. 2011).

(4)

EST(

entry

=avail(r

(5)

EST

ti,rp



=max



avail(rp)

maxt

∈parent(t

)



AFT





+ct



(6)

EFT(

=ET(i,p)+EST

(

(7)

AST(

=max(EST

(

,Avail(r

p))

(8)

makespan

=max

{

AFT(t

exit

)

}

(9)

Pc=ACV 2f

Table 1 Notations Symbol Semantics

ET(i,p)

Task ti execution times on the rp resource

The size of the task ith

The rp resources' processing power

EC(i,p)

Task ti execution cost on rp resource

𝜇p

For each period, the cost per unit of rp resource usage

EST(

The task ti’s ﬁrst execution start time on the pth resource

avail(rp)

The amount of time it takes for rp resources to approve a task execution request

AFT

(

The actual ﬁnish time for each ith task on the pth resource

The time it takes for data to be transferred between two interconnected tasks

ET(i,p)

The makespan of ith task on pth resource

EFT(

Time for the ﬁrst completion of the ith task on the pth resource

AST

(

Actual start time for ith task on the pth resource

makespan

The total amount of time it takes to complete all tasks

CMOS capacitance

The number of switches per iteration

Capacity

Voltage

Frequency

EConsumption of energy

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A.Mohammadzadeh, M.Masdari

1 3

4 Applied meta‑heuristic algorithms

This section discusses the Seagull and Grasshopper Optimi-

zation Algorithms that are used in this scheme to provide a

hybrid multi-swarm optimization algorithm. The integration

of these algorithms provides the optimal balance between

exploitation andexploration. Table2 describes the semantic

of notations used in this section.

4.1 Seagull Optimization Algorithm

The SOA algorithm is inspired by the seagull’s hunt. In

the exploration phase, a seagull must meet three condi-

tions: collision avoidance, movement in the direction of the

best neighbor, keep in touch with the best search agent. To

(10)

∑

i=1

ACV 2f.ET (i,p

)

prevent collisions between neighbors, a new search agent

location is determined using an additional variable A.

In this equation, Xs measures the search agent's position

that isn't in competition with any other search agent, Ps is

the current location of the agent, A indicates the movement

behavior of the search agent, and x is the current iteration.

Following the avoidance of collisions between neighbors,

the agents switch in the direction of the best neighbor. In

Eq.(12), the symbol B is a random number between 0 and 1,

and Ms shows the distance between the current search agent

(Ps) and the best seagull position (Pbs). Finally, the search

agent will change its positionin terms of the best search

agent. Seagulls can change the angle and speed continuously

during the attack. The spiral movement activity happens in

the air when attacking the prey.

Equations(13), (14), and (15) deﬁne this behavior in the

x, y, and z planes.

In which, k is a random number between 0 and 2π. r is

the radius of each turn of the spiral. Finally, Ps(x) saves the

best solution and modiﬁes the location of other agents. The

distance between the search agent and the best-ﬁt agent is

represented by Ds.

4.2 GOA algorithm

The Grasshopper Optimization Algorithm is a new optimi-

zation algorithm base on grasshopper swarms (Saremi etal.

2017). The grasshoppers provide Exploration and exploita-

tion stages in the hunt for food. The particles travel locally

in the exploitation stage, while these agents are permitted

to make abrupt movements in the exploration stage. The

movement of the grasshopper is typically divided into three

models, the wind advection operator (Ai), the social interac-

tion (Si), and the gravity force (Gi) shown in Eq.(17). In this

equation Xi denotes the ith grasshopper’s position.

(11)

��⃗

Xs=A×

��⃗

Ps(x)

(12)

��⃗

s=B×

(

��⃗

Pbs(x)

)

−

��⃗

Ps(x

))

(13)

x�=r×

cos

(k)

(14)

y�=r×sin(k)

(15)

z�=r×k

(16)

��⃗

s(x)=

(

��⃗

Ds×x�×y�×z�

)

��⃗

Pbs(x

)

(17)

Xi=Gi+Si+Ai

Table 2 Notations

Symbol Semantics

The search agent's movement patterns

� � �⃗

Ps(x)

The search agent's current location in the xth iteration

��⃗

The distance between the currentand the best agent

Between 0 and 1 is a random number

��⃗

Pbs

)

The best location for seagull

x′

y′

z′

New values x, y, z

rThe spiral's radius at each turn

kA random number between 0 and 2π

� � �⃗

The distance between the currentand the best agent

The gravity force

The wind advection operator's social interactions

The Wind advection

Constant of Gravitation

̂eg

Unity vector towards the earth's core

The social forces' power

dij

The distance between the ith and the jth agent

Constant drift

̂ew

Unity vector towards the wind

The attraction intensity

the real value

The attractive length scale

The ith particle location in the dth dimension

A factor that reduces the attraction zone's size

lbd,ubd

The lower and upper bounds in the dth dimension

The dth dimension’s target value

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1 3

where g represents the gravitational constant,

̂eg

represents

unity vector towards the earth's core in Eqs.(18). In Eq.(19),

N represents the number of agents, and dij indicates the dis-

sociation between the ith and the jth agent. In Eq.(20), u

describes a constant drift, and

̂ew

represents a unity vector

towards the wind. Equation(21) shows the modiﬁed version

of the proposed equation to solve the problems.

The lower and upper limits are denoted by lbd and ubd.

Also, T is the perfect solution that has been discovered in the

dth dimension, which is the target value. C is a decreasing

factor that causes the gravitation, expulsion, and comfort

zones to shrink. The GOA ﬂowchart is presented in Fig.2.

5 The proposed HGSOA‑GOA algorithm

Like some metaheuristic algorithms, the SOA algorithm

suffers from the local optimum problem (Dhiman and

Kumar 2019; Jia etal. 2019b). Also, the GOA algorithm

has a good ability to escape local optima, but this algorithm

does not have a good convergence rate (Jia etal. 2019a;

Luo etal. 2018). Hence, a new hybrid algorithm, denoted

as HGSOA-GOA, is proposed based on the SOA and GOA

which use GOA's ability to escape local optima and SOA's

ability to increase the search convergence speed to boost

(18)

=−g×

(19)

∑

j=1,j≠i

Xj−Xi

)Xj−Xi

dij

(20)

Ai=ûew

(21)

i=C

N



j≠i

Cubd−lbd



j−Xd



Xj−Xi

dij



both exploitation and exploration. To combine the two algo-

rithms, we used multi-swarm mode. These two algorithms

are suitable for hybridization because of their strengths, the

global search ability of SOA, and GOA's high eﬃciency and

accuracy in determining the global optimal, and the ability

to escape local optima. The proposed hybrid algorithm inte-

grates algorithms to reach a good trade-oﬀ between exploita-

tion and exploration and provides considerably better results

in terms of accuracy and convergence rate than the tradi-

tional SOA and GOA algorithms. The meaning of notations

used in the rest of this study is described in Table3. Greedy

algorithms are commonly describedas simple, and their exe-

cution time is short (Cerrone etal. 2017). As a consequence,

the proposed hybrid algorithm has been easily adapted to

the greedymode. In most cases, a greedy approach yields

an optimal local solution in a fair amount of time, as well

as an approximately optimal ultimate answer. The greedy

algorithm discovers a global solution focused on the best

local selection at every step.

In this paper, a random number is generated for each ele-

ment. Moreover, a threshold is created based on the number

of iterations in the range of 0.6–0.8. In each step, if the ran-

dom number of the particle is greater than the threshold, it

acts greedily; otherwise, it will shift non-greedily regardless

of the degree of ﬁtness. The threshold value is decreasing

with an increase in the number of steps from 0.8 to 0.6.

Equation(22) shows this. At ﬁrst, the initial population

after create randomly is divided into two subpopulations

per algorithm. The operation of each algorithm is applied

separately to subpopulations. Since the initial population is

random, it does not matter how the population is assigned

to the algorithms.

Fig. 2 The GOA's ﬂowchart

Table 3 Notations

Symbol Semantic

T(x) A transfer function

XPosition of the particle

IThe total number of particles

DDimension

TThe number of iteration

NtThe real Pareto front’s number

The Euclidean distance between the ith true Pareto

frontand the ideal Pareto front solution obtained as

near as possible

P, QIn the search space,two separate sets of Pareto optimal

solutions

SThe set of optimal Pareto front

MThe number of metrics

The value of the mth objective in ith solution

The mean of di

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A.Mohammadzadeh, M.Masdari

1 3

Also, in the proposed hybrid algorithm, we store n best

solutions of both algorithms in shared memory and the

size of n should not exceed 30% of the original popula-

tion according to the experimental results. We can use the

mutation on 25% of the population to increase discovery

and establish a balance between exploration and exploita-

tion. Finally, the best solutions are chosen from the shared

memory using the objective function.

5.1 Chaotic random numbers

Chaos theory deals with deterministic processes whose

action can be predicted in theory. One of the famous appli-

cations is the introduction of chaos theory into optimiza-

tion. The results show that usingchaos functions can pre-

vent trapping into the local optimum and may speed up the

convergence rate. To improve the performance of the pre-

sented hybrid algorithm, ﬁve chaotic functions are used in

this scheme (Mukherjee and Mukherjee 2016). In each step,

one function of such options is chosen at random. As seen

in Table4, the initial value of 0.7 is considered for all func-

tions (Saremi etal. 2014). Chaos functions create numbers

between 0 and 1. These numbers are predictable for a short

period and are then random for an extended period.

5.2 Hybrid binary algorithm

Using the proposed algorithm, we try to ﬁnd a solution to the

workﬂow scheduling problem which is a discrete problem.

To enable handling discrete problems, some transfer func-

tions are used to produce binary solutions. These functions

are simple to implement are fast and low-cost (Gharehpasha

and Masdari 2020; Mirjalili and Lewis 2013). Four S-shaped

(S1–S4) and V-shaped (V1–V4) transfer functions are used

to transform the continuous proposed algorithm to binary

in this article. The proposed algorithm, like the non-binary

algorithm, updates the particle's position in the ﬁrst step.

Thenew position is in the continuous space. In the second

step, these functions are used to convert the location to a

(22)

Threshold =1−(iteration∕max_iteration)

new value in discrete space according to Eqs.(23) and (24)

(Table5).

The proposed algorithm changes the particle position

according to Eq.(23) using a set of S-shaped functions.

In Eq.(23), X

in dth dimension is the ith particle’s posi-

tion, T(x) is the S-shaped function, and the current iteration

number is t. The search agent is not limited to the interval

[0, 1] by the V-shaped function. Equation(24) shows how

V-shaped transfer functions can be used to update the par-

ticle's position. In Eq.(24),

¬X

is supplement X. Figure3

shows the ﬂowchart of the algorithm.

The proposed algorithm stores the various non-dominated

solutions in an archive. However, the archive is only used

to save non-dominated solutions in this case. As a result,

it is regarded as an inputparameter in the proposed algo-

rithm.The archive is modiﬁed in two steps: ﬁrst, after the

algorithm's initial population, which only happens once, and

second, during the algorithm's primary iterative process.

This code is generated using the NSGAII non-dominated

sorting with the operator of diversity preserving (Kishor

etal. 2016). The archived solutions and the current swarm

are combined into one population, and each solution is given

a rank. Rank 1 and 2 are for the best solutions, and the sec-

ond-best solutions, and so on.

As a result, diﬀerent fronts of solutions are created, and

all solutions in one front are non-dominated by the other but

are dominated by solutions of a lower rank. Solutions are

archived in order of rank. If there is no space in the archive

for all of the solutions of a rank, the rank's crowding distance

is calculated to force the necessary number of solutions into

the archive. The archive update algorithm indicates in Fig.4.

(23)

i(t+1)=

{

1if rand(0,1)<T(ΔX

i(t+1)

)

0otherwise

(24)

i(t+1)=

{

¬X

i(t)if rand(0,1)<T(ΔX

i(t+1)

)

(t)otherwise

Table 4 Chaotic maps

No. Name Function

1 Iterative

Vb+1

=sin

(

𝜋

∕V

b),

C = 0.7

2 Logistic

Vb+1=CVb(1−Vb)

, C = 4

3 Sine

Vb+1

=(C∕4)sin

(

𝜋V

,C=

4 Singer

1=𝜇(7.86Vb−23.31V

+28.75V

−13.3V

𝜇

= 1.07

5 Sinusoidal

Vb+1

=CV

sin(𝜋V

Table 5 V-shaped and S-shaped transfer functions

S-shaped

family

Transfer function V-shaped

family

Transfer function

T(x)=1∕(1+e−2x)

(x)=



erf



(



𝜋∕2)x





T(x)=1∕(1+e−x)

T(x)=|tanh(x)|

T(x)=

∕(

+e(

−x

))

(x)=

�

x∕

√

1+x2

�

T(x)=

∕(

+e(

−x

))

(x)=

𝜋

arctan

(

𝜋

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1 3

Fig. 3 The ﬂowchart of the

HGSOA-GOA algorithm

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A.Mohammadzadeh, M.Masdari

1 3

5.3 Selecting fromPareto front

This section aims to introduce a method for locating a knee

point in the Pareto front (Liang etal. 2018). In this method,

the core idea is to determine a knee point of the distances of

all solutions in the non-dominated front to the extreme line.

In Fig.5, an example is given to demonstrate this method.

The extreme line will be determined by two extreme points

according to Eq.(25) (point 1 and point 6, which point 1

have the largest value in the ﬁrst objective and point 6 having

the largest value in the second objective function).

In the knee point method, only solutions in the convex

knee regions are of importance for minimization problems.

As a result, the distance measurecan be demonstratedas fol-

lows in Eq.(26). This distance can easily be applied to opti-

mization problems with more than two targets, in which case

the extreme line becomes a hyperplane (Zhang etal. 2014).

6 Workow scheduling architecture

This section presents the architecture of the scheduling

scheme. Figure6 indicates the abstracted model of our

scheduling approach. In this scheme, the ﬁrst step is for the

cloud user to create a workﬂow framework. In the second

step, the multi-objective scheduling approach is designed

with four metrics. Finally, workﬂow tasks will be assigned

to the correct cloud platforms and VM types. Every cloud

provider has a task queue, and the workﬂow architecture

determines how these tasks are processed. For example,

since cloud users have access to an inﬁnite number of VM

resources, parallel tasks in the queue will often be completed

at the same time, while sequence tasks are always operated

according to sequences. In this multi-cloud scheme, it is

assumed that there are several cloud providers, each with

its set of VMs.

(25)

Ax +By +C=0

(26)

distance



Ax +By +C



∕



A2+B2ifAx +By +C<

−



Ax +By +C



∕



A2+B2

Merge the current swarm and the archive into one population

Sort the population by non-dominated sorting techniques

If ( |Pareto front| > |archive| )

Compute crowding distance for every solution of Pareto front

Select a solution with a lower crowding distancefirst

End If

Fig. 4 Archive updating algorithm

Fig. 5 Determining the knee point in the inline method

Fig. 6 Proposed workﬂow scheduling architecture for multi-cloud environments

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7 Simulation andresults

This section describes the workﬂows, simulation environ-

ment, and performance criteria applied in the simulation

process. We have evaluated the results of the HGSOA-

GOA and the SPEA2 algorithm on a variety of scientiﬁc

workﬂows. The SPEA2 algorithm is chosen because it is

more eﬃcient than other multi-objective algorithms, such

as PEAS and NSGAII (Khalili and Babamir 2017; Zhou

etal. 2019). This scheme applies the Workﬂowsim and the

Cloudsim simulators (Chen and Deelman 2012) conducting

the required experiments.

7.1 Workﬂows

In this paper, we have used LIGO, Cybershake, Montage,

and Epigenomics scientiﬁc workﬂows for evaluation. These

workﬂows are achieved from the Pegasus website along with

information such as the volume of transmitted data, task exe-

cution time, task dependencies (Adhikari etal. 2020; Deel-

man etal. 2015; Liu etal. 2015; Pasdar etal. 2020; Saeedi

etal. 2020). To analyze the eﬀect of workﬂow size on the

eﬃciency of the algorithm, three diﬀerent workﬂow sizes are

chosen: small 50 tasks, medium 100 tasks, and large 1000

tasks. Figure7 depicts a graph of these workﬂows (Mas-

dari etal. 2016). There are two diﬀerent types of workﬂow

scheduling: balanced and unbalanced (Fard etal. 2012; Yu

etal. 2007). Cybershake and Montage are unbalanced, LIGO

and Epigenomics are balanced. The unbalanced workﬂow

is more diﬃcult to manage, with several parallel activities

involving numerous resources, but a balanced workﬂow has

several pipelines.

7.2 Simulation environment

To introduce algorithms and model workﬂow, the Work-

ﬂowsim simulator was used. It's used to simulate a com-

puter with a Core i7 CPU and a 2.4GHz processing speed,

and 8GB RAM. A data center simulation environment with

the information shown in Table6 is given. Figure8 depicts

data center components such as the infrastructure, etc. Green

computing is a type of cloud environment that is discussed in

this article. Table7 displays the SPEA2 and proposed algo-

rithm parameters (Yu etal. 2007). The jMetal package was

used in the Cloudsim environment to implement the SPEA2

algorithm (Durillo and Nebro 2011). The SPEA2 algorithm

Fig. 7 Scientiﬁc workﬂows in a non-cyclic graph

Table 6 Parameters of the

virtual machine Virtual machine

number

Million instruction

per second

Number of

CPU

Ram (GB) Storage (GB) Band-

width

(GB/s)

1–250 1500 2 1 15 2

251–500 1500 2 1 15 2

501–750 2000 2 2 25 2

751–1000 2500 4 2 25 1

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A.Mohammadzadeh, M.Masdari

1 3

is a new version of the SPEA. This algorithm has been

reported to perform well in searching and contains important

advantages such as density estimation, ﬁne-grained ﬁtness

assignment strategy, archiving of individuals with good ﬁt-

ness. This paper compared some metrics of output obtained

by the presented algorithm and the SPEA2. To assess the

quality of Pareto fronts constructed by multi-objective algo-

rithms, we used a variety of eﬃciency evaluation criteria.

Most of the results were in favor of the presented algorithm.

7.3 Eﬃciency metrics

The various eﬃciency performance metrics are presented in

this section to determine the validity of Pareto fronts gener-

ated by multi-objective algorithms. A Pareto front should be

precise and well-distributed in ideal situations (Okabe etal.

2003). Someperformance metrics were used to measure the

Pareto fronts generated by the algorithms. In the following,

we will examine these performance criteria.

7.3.1 Inverted generational distance

Inverted generational distance is a performance criterion that

showsan algorithm's convergence andaccuracy. In Eq.(27),

nt is the number of real Pareto front solutions, and

is the

Euclidean distance between the ith true Pareto front solution

and the nearest perfect ideal Pareto front solution. This met-

ric's low values indicate that the algorithm is more consistent

and convergent.

7.3.2 Coverage ratio

The coverage ratio is used to analyze a list of solutions of

the optimizer algorithm. In Eq.(28), dominate(P, Q) is

the total number of P answers which can dominate set Q's

answers if P and Q are diﬀerent sets of the Pareto optimal

(27)

IGD

�∑

i=1(di)2

in the problem space. The fact that this equation is equal to

1 implies that all P solutions take precedence over Q solu-

tions. This criterion's proximity to 0 or 1 denotes low or

high quality.

7.3.3 Maximum spread

The eﬃciency of the distance between boundary solutions is

indicated by the maximum distribution. S is the collection of

Pareto optimal solutions, f

is the value of the ith solution's

objective function on mth objective function, and M is the

objective function's maximum number in Eq.29. At bound-

ary points, high values have a lot of coverage.

7.3.4 Spacing

The level of deviation in the Pareto optimal collection is

indicated by the spacing. di is the real diversity between the

ith solution of the ideal set of S and other answers,

is di's

mean, M is the targets number, and fm(si) is the value of the

ith solution's in mth objective function. The lower value of

this metric, the more eﬃcient it will be.

7.4 Evaluation results

The HGSOA-GOA algorithm and the SPEA2 have been

implemented on several scientiﬁc workﬂows to improve four

diﬀerent metrics: makespan, energy, throughput, and cost.

These experiments are conducted on the small, medium, and

large-sized workﬂows and the algorithms are executed 10,

50, and 100 times. The results of performance criteria on

various workﬂows were indicated in Table8.

Table3 shows that the proposed algorithm outperforms

the other algorithm in all iterations. The results of IGD

indicate that superior convergence exists and the proposed

algorithm outperforms the SPEA2 algorithm. The number of

solutions of the presented algorithm's set that can resolve the

solutions of set SPEA2 is more than the SPEA2 algorithm,

according to the results of the coverage ratio. According

to the results of the maximum spread criterion, one may

(28)

Dominate(P,Q)=|qj∈Q;∃pi∈P∶pi>qj|∕|Q|

(29)





M



m=1

(max

i=1toSfi

m−min

i=1toSfi

∈S and s

≠s

(30)









−1

S



i=1

(di−d)2,di=minM

m=1







−fm







∈S ands

≠s

Fig. 8 Data and host center setup

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conclude that the presented algorithm contains a greater

number of boundary points. In spacing metric lower values

indicate dominance. These metric values, which display the

variety of solutions, show that the proposed algorithm is

superior in diﬀerent sizes and iterations in Table8.

The comparison results of the algorithms on various cri-

teria are shown in Figs.9, 10, 11 and 12. The criteria for this

comparison are cost, makespan, throughput, and energy. The

presented algorithm and the SPEA2 are compared in this

section. The results are obtained on four workﬂows of dif-

ferent sizes. According to the experiments, we conclude that

the results of the presented algorithm on unbalanced work-

ﬂows are better than the results of the SPEA2 algorithm.

On Montage and Cybershake workﬂows in diﬀerent sizes

and number of repetitions, the results of makespan, cost,

5000

5500

6000

6500

Proposed SPEA2

Makespan

Montage 1000

1000

2000

3000

4000

ProposedSPEA2

Makespan

Montage 100

1000

2000

3000

4000

5000

6000

ProposedSPEA2

Makespan

Montage 50

1000

2000

3000

4000

5000

Proposed SPEA2

Cost

Montage 1000

100

200

300

400

ProposedSPEA2

Cost

Montage 100

100

150

200

ProposedSPEA2

Cost

Montage 50

1000

2000

3000

Proposed SPEA2

Energy

Montage 1000

500

1000

1500

ProposedSPEA2

Energy

Montage 100

200

400

600

800

1000

ProposedSPEA2

Energy

Montage 50

200

400

600

800

Proposed SPEA2

Throughput

Montage 1000

ProposedSPEA2

Throughput

Montage 100

ProposedSPEA2

Throughput

Montage 50

Runs :10 Runs :50Runs :100 Runs :10 Runs :50 Runs :100Runs :10Runs :50Runs :100

Fig. 9 Results of Montage workﬂow

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A.Mohammadzadeh, M.Masdari

1 3

5000

10000

15000

ProposedSPEA2

Makespan

Cybershake 1000

1000

2000

3000

4000

5000

6000

ProposedSPEA2

Makespan

Cybershake 100

200

400

600

800

ProposedSPEA2

Makespan

Cybershake 50

2000

4000

6000

8000

ProposedSPEA2

Cost

Cybershake 1000

200

400

600

800

ProposedSPEA2

Cost

Cybershake 100

100

200

300

400

ProposedSPEA2

Cost

Cybershake 50

26000

28000

30000

32000

34000

36000

ProposedSPEA2

Energy

Cybershake 1000

1000

2000

3000

4000

5000

ProposedSPEA2

Energy

Cybershake 100

2000

4000

6000

8000

10000

12000

ProposedSPEA2

Energy

Cybershake 50

360

380

400

420

440

460

ProposedSPEA2

Throughput

Cybershake 1000

ProposedSPEA2

Throughput

Cybershake 100

ProposedSPEA2

Throughput

Cybershake 50

Runs :10 Runs :50Runs :100 Runs :10 Runs :50 Runs :100Runs :10Runs :50 Runs :100

Fig. 10 Results of Cybershake workﬂow

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Scientiﬁc workﬂow scheduling inmulti‑cloud computing using ahybrid multi‑objective…

1 3

50000

100000

150000

200000

ProposedSPEA2

Makespan

LIGO 1000

5000

10000

15000

20000

ProposedSPEA2

Makespan

LIGO 100

14500

15000

15500

16000

Proposed SPEA2

Makespan

LIGO 50

28000

30000

32000

34000

36000

38000

ProposedSPEA2

Cost

LIGO 1000

2600

2800

3000

3200

3400

3600

ProposedSPEA2

Cost

LIGO 100

1560

1570

1580

1590

1600

1610

1620

Proposed SPEA2

Cost

LIGO 50

50000

100000

150000

200000

250000

300000

ProposedSPEA2

Energy

LIGO 1000

11500

12000

12500

13000

13500

ProposedSPEA2

Energy

LIGO 100

9000

9500

10000

10500

11000

11500

12000

Proposed SPEA2

Energy

LIGO 50

580

600

620

640

660

680

Proposed SPEA2

Throughput

LIGO 1000

ProposedSPEA2

Throughput

LIGO 100

Proposed SPEA2

Throughput

LIGO 50

Runs :10Runs :50Runs :100 Runs :10Runs :50Runs :100 Runs :10Runs :50Runs :100

Runs :10Runs :50Runs :100 Runs :10Runs :50Runs :100 Runs :1 0Runs :50Runs :100

Fig. 11 Results of LIGO workﬂow

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A.Mohammadzadeh, M.Masdari

1 3

1000000

2000000

3000000

4000000

5000000

Proposed SPEA2

Makespan

Epigenomics 997

100000

200000

300000

400000

ProposedSPEA2

Makespan

Epigenomics 100

5000

10000

15000

20000

25000

Proposed SPEA2

Makespan

Epigenomics 47

Runs :10 Runs :50Runs :100 Runs :10 Runs :50 Runs :100Runs :10Runs :50 Runs :100

1100000

1150000

1200000

1250000

1300000

1350000

1400000

Proposed SPEA2

Cost

Epigenomics 997

50000

100000

150000

200000

ProposedSPEA2

Cost

Epigenomics 100

1000

2000

3000

4000

5000

6000

Proposed SPEA2

Cost

Epigenomics 47

1000000

2000000

3000000

4000000

5000000

6000000

Proposed SPEA2

Energy

Epigenomics 997

180000

200000

220000

240000

260000

ProposedSPEA2

Energy

Epigenomics 100

10000

20000

30000

40000

50000

Proposed SPEA2

Energy

Epigenomics 47

560

570

580

590

600

610

620

630

Proposed SPEA2

Throughput

Epigenomics 997

ProposedSPEA2

Throughput

Epigenomics 100

Proposed SPEA2

Throughput

Epigenomics 47

Fig. 12 Results of Epigenomics workﬂow

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energy, and throughput criteria are in favor of the presented

algorithm. These results can be seen in Figs.9 and 10.

The outcomes of the algorithms on balanced workﬂows

are close to each other. On these workﬂows, as shown in

Figs.11 and 12, we have similar results for both algorithms.

According to the experimental results, we conclude that the

improved hybrid algorithm performs better than the SPEA2

on more complex problems. The paper attempted to improve

the scheduling problem with an improved algorithm since

most of the scheduling provided does not get the absolute

best results in all scenarios.

7.5 Runtime comparison

This sectionentails the proposed and SPEA2 algorithms in

terms of execution time. Table9 shows the average execu-

tion time of the algorithms over ten iterations. The proposed

algorithm has a small increase in runtime, according to the

ﬁndings. The increase in execution time is due to the code

complexity, which was anticipated. The time complexity

was not determined in this experiment because minimizing

complexity is not one of the measurement objectives (Anwar

and Deng 2018; Gupta etal. 2020; Mirjalili 2015; Mirjalili

etal. 2017).

8 Conclusions andfuture work

This paper proposes a workﬂow scheduling algorithm for

heterogeneous multi-cloud computing environments. For

this purpose, a hybrid optimization algorithm, denoted as

HGSOA-GOA, is presented by combining the SOA and

GOA algorithms. Afterward, the HGSOA-GOA is applied

to schedule scientiﬁc workﬂows on the VMs of several avail-

able cloud computing data centers. To indicate the eﬃciency

of the proposed scheduling method several experiments have

been conducted on the scientiﬁc workﬂows with diﬀerent

sizes on the Workﬂowsim and Cloudsim simulators. The

achieved results are compared with the results of the SPEA2

algorithm and it is shown that the presented algorithm out-

performs SPEA2 in terms of various metrics.

Table 7 Parameters of the algorithm

Parameter HGSOA-GOA SPEA2

Population size 40 40

Archive size 10 10

Max. iteration 10 –

Max. generation – 100

Mutation probability – 0.5

Crossover probability – 0.9

Table 8 Results of performance criterions

Workﬂow size IGD Coverage ratio Maximum spread Spacing

Workﬂow: Montage, VMs: 1000, Runs: 10

Small HGSOA-GOA: 0.3670 C (HGSOA-GOA, SPEA2): 0.30 PROPOSED: 0.2091 PROPOSED: 0.0001

SPEA2: 0.4256 C (SPEA2, HGSOA-GOA): 0.20 SPEA2: 0.0482 SPEA2: 0.0023

Medium HGSOA-GOA: 0.3092 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 0.3127 HGSOA-GOA: 0.0012

SPEA2: 0.4190 C (SPEA2, HGSOA-GOA): 0.30 SPEA2: 0.3029 SPEA2: 0.0032

Large HGSOA-GOA: 0.2011 C (HGSOA-GOA, SPEA2): 0.20 HGSOA-GOA: 0.6746 HGSOA-GOA: 0.0041

SPEA2: 0.2187 C (SPEA2, HGSOA-GOA): 0.10 SPEA2: 0.4352 SPEA2: 0.0063

Workﬂow: Montage, VMs: 1000, Runs: 50

Small HGSOA-GOA: 0.6710 C (HGSOA-GOA, SPEA2): 0.42 HGSOA-GOA: 0.1081 HGSOA-GOA: 0.0001

SPEA2: 3.0143 C (SPEA2, HGSOA-GOA): 0.31 SPEA2: 0.0439 SPEA2: 0.0054

Medium HGSOA-GOA: 0.0098 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 0.1982 HGSOA-GOA: 0.0021

SPEA2: 2.7610 C (SPEA2, HGSOA-GOA): 0.20 SPEA2: 0.0187 SPEA2: 0.0034

Large HGSOA-GOA: 1.1459 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 0.9556 HGSOA-GOA: 0.0010

SPEA2: 2.3109 C (SPEA2, HGSOA-GOA): 0.12 SPEA2: 0.0919 SPEA2: 0.0031

Workﬂow: Montage, VMs: 1000, Runs: 100

Small HGSOA-GOA: 0.0100 C (HGSOA-GOA, SPEA2): 0.42 HGSOA-GOA: 0.2182 HGSOA-GOA: 0.0056

SPEA2: 0.1321 C (SPEA2, HGSOA-GOA): 0.34 SPEA2: 0.1864 SPEA2: 0.0081

Medium HGSOA-GOA: 0.0192 C (HGSOA-GOA, SPEA2): 0.32 HGSOA-GOA: 0.3780 HGSOA-GOA: 0.0033

SPEA2: 0.1340 C (SPEA2, HGSOA-GOA): 0.21 SPEA2: 0.3460 SPEA2: 0.0062

Large HGSOA-GOA: 0.1029 C (HGSOA-GOA, SPEA2): 0.48 HGSOA-GOA: 0.3892 HGSOA-GOA: 0.0023

SPEA2: 0.1102 C (SPEA2, HGSOA-GOA): 0.13 SPEA2: 0.1381 SPEA2: 0.0055

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A.Mohammadzadeh, M.Masdari

1 3

Table 8 (continued)

Workﬂow size IGD Coverage ratio Maximum spread Spacing

Workﬂow: Cybershake, VMs: 1000, Runs: 10

Small HGSOA-GOA: 0.3201 C (HGSOA-GOA, SPEA2): 0.32 HGSOA-GOA: 1.5041 HGSOA-GOA: 0.0021

SPEA2: 0.8192 C (SPEA2, HGSOA-GOA): 0.11 SPEA2: 1.4872 SPEA2: 0.0083

Medium HGSOA-GOA: 0.3992 C (HGSOA-GOA, SPEA2): 0.22 HGSOA-GOA: 2.2011 HGSOA-GOA: 0.0011

SPEA2: 0.8672 C (SPEA2, HGSOA-GOA): 0.01 SPEA2: 2.1872 SPEA2: 0.0016

Large HGSOA-GOA: 0.4092 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 4.1120 HGSOA-GOA: 0.0017

SPEA2: 0.7521 C (SPEA2, HGSOA-GOA): 0.24 SPEA2: 3.1083 SPEA2: 0.0059

Workﬂow: Cybershake, VMs: 1000, Runs: 50

Small HGSOA-GOA: 0.1881 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 3.1101 HGSOA-GOA: 0.0024

SPEA2: 0.1902 C (SPEA2, HGSOA-GOA): 0.20 SPEA2: 2.9843 SPEA2: 0.0219

Medium HGSOA-GOA: 0.1178 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 3.8104 HGSOA-GOA: 0.0088

SPEA2: 0.1845 C (SPEA2, HGSOA-GOA): 0.20 SPEA2: 2.7648 SPEA2: 0.0986

Large HGSOA-GOA: 0.1901 C (HGSOA-GOA, SPEA2): 0.31 HGSOA-GOA: 4.3123 HGSOA-GOA: 0.0107

SPEA2: 0.1985 C (SPEA2, HGSOA-GOA): 0.24 SPEA2: 3.0364 SPEA2: 0.0562

Workﬂow: Cybershake, VMs: 1000, Runs: 100

Small HGSOA-GOA: 0.1109 C (HGSOA-GOA, SPEA2): 0.24 HGSOA-GOA: 2.9096 HGSOA-GOA: 0.0100

SPEA2: 0.1983 C (SPEA2, HGSOA-GOA): 0.02 SPEA2: 2.5627 SPEA2: 0.0513

Medium HGSOA-GOA: 0.1100 C (HGSOA-GOA, SPEA2): 0.39 HGSOA-GOA: 3.6890 HGSOA-GOA: 0.0143

SPEA2: 0.1392 C (SPEA2, HGSOA-GOA): 0.01 SPEA2: 2.5425 SPEA2: 0.0564

Large HGSOA-GOA: 0.1347 C (HGSOA-GOA, SPEA2): 0.20 HGSOA-GOA: 5.1240 HGSOA-GOA: 0.0272

SPEA2: 0.1736 C (SPEA2, HGSOA-GOA): 0.05 SPEA2: 4.1093 SPEA2: 0.0782

Workﬂow: LIGO, VMs: 1000, Runs: 10

Small HGSOA-GOA: 2.1902 C (HGSOA-GOA, SPEA2): 0.41 HGSOA-GOA: 5.6734 HGSOA-GOA: 0.0267

SPEA2: 3.9027 C (SPEA2, HGSOA-GOA): 0.11 SPEA2: 4.1783 SPEA2: 1.1298

Medium HGSOA-GOA: 2.3084 C (HGSOA-GOA, SPEA2): 0.50 HGSOA-GOA: 6.9327 HGSOA-GOA: 0.0938

SPEA2: 5.9283 C (SPEA2, HGSOA-GOA): 0.30 SPEA2: 4.9896 SPEA2: 1.2546

Large HGSOA-GOA: 2.8930 C (HGSOA-GOA, SPEA2): 0.81 HGSOA-GOA: 12.9879 HGSOA-GOA: 0. 7989

SPEA2: 3.0947 C (SPEA2, HGSOA-GOA): 0.60 SPEA2: 8.8474 SPEA2: 1.2395

Workﬂow: LIGO, VMs: 1000, Runs: 50

Small HGSOA-GOA::2.0911 C (HGSOA-GOA, SPEA2): 0.40 HGSOA-GOA: 8.0409 HGSOA-GOA: 0.2341

SPEA2: 2.9745 C (SPEA2, HGSOA-GOA): 0.11 SPEA2: 7.8346 SPEA2: 1.1093

Medium HGSOA-GOA: 2.0649 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 9.1432 HGSOA-GOA: 0.3240

SPEA2: 2.0835 C (SPEA2, HGSOA-GOA): 0.27 SPEA2: 7.6470 SPEA2: 1.9874

Large HGSOA-GOA: 2.8796 C (HGSOA-GOA, SPEA2): 0.33 HGSOA-GOA:8.2310 HGSOA-GOA: 0.1092

SPEA2: 5.1298 C (SPEA2, HGSOA-GOA): 0.38 SPEA2: 7.6375 SPEA2: 1.1124

Workﬂow: LIGO, VMs: 1000, Runs: 100

Small HGSOA-GOA: 2.0981 C (HGSOA-GOA, SPEA2): 0.20 HGSOA-GOA: 8.9097 HGSOA-GOA: 0.5209

SPEA2: 5.7383 C (SPEA2, HGSOA-GOA): 0.12 SPEA2: 3.9839 SPEA2: 0.6787

Medium HGSOA-GOA: 3.7676 C (HGSOA-GOA, SPEA2): 0.12 HGSOA-GOA: 7.9872 HGSOA-GOA: 0.4254

SPEA2: 4.8928 C (SPEA2, HGSOA-GOA): 0.04 SPEA2: 2.2562 SPEA2: 0.5637

Large HGSOA-GOA: 2.5630 C (HGSOA-GOA, SPEA2): 0.10 HGSOA-GOA: 9.0317 HGSOA-GOA: 0.7340

SPEA2: 3.7836 C (SPEA2, HGSOA-GOA): 0.04 SPEA2: 1.5161 SPEA2: 1.8653

Workﬂow: Epigenomics, VMs: 1000, Runs: 10

Small HGSOA-GOA: 0.8603 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 8.0892 HGSOA-GOA: 0.0763

SPEA2: 1.7862 C (SPEA2, HGSOA-GOA): 0.20 SPEA2: 7.8927 SPEA2: 1.8347

Medium HGSOA-GOA: 0.7656 C (HGSOA-GOA, SPEA2): 0.20 HGSOA-GOA: 11.0982 HGSOA-GOA: 0.7654

SPEA2: 1.8270 C (SPEA2, HGSOA-GOA): 0.07 SPEA2: 9.7367 SPEA2: 1.6736

Large HGSOA-GOA: 0.0429 C (HGSOA-GOA, SPEA2): 0.32 HGSOA-GOA: 12.0976 HGSOA-GOA:0.1423

SPEA2: 0.2110 C (SPEA2, HGSOA-GOA): 0.02 SPEA2: 8.5360 SPEA2: 2.6748

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Scientiﬁc workﬂow scheduling inmulti‑cloud computing using ahybrid multi‑objective…

1 3

Table 9 Results of statistical of the average execution time

Workﬂow HGSOA-GOA SPEA2

Montage, size: Large, VMs: 1000 7.1092 2.2309

Cybershake, size: Large, VMs: 1000 6.2067 3.9575

LIGO, size: Large, VMs: 1000 6.0012 3.9104

Epigenomics, size: Large, VMs: 1000 4.6092 2.8760

Workﬂow size IGD Coverage ratio Maximum spread Spacing

Workﬂow: Epigenomics, VMs: 1000, Runs: 50

Small HGSOA-GOA: 0.0013 C (HGSOA-GOA, SPEA2): 0.45 HGSOA-GOA: 10.0984 HGSOA-GOA: 0.0876

SPEA2: 0.0091 C (SPEA2, HGSOA-GOA): 0.30 SPEA2: 9.4320 SPEA2: 1.7831

Medium HGSOA-GOA: 0.0567 C (HGSOA-GOA, SPEA2): 0.31 HGSOA-GOA: 11.0878 HGSOA-GOA: 2.0236

SPEA2: 0.2908 C (SPEA2, HGSOA-GOA): 0.21 SPEA2: 9.6541 SPEA2: 2.6725

Large HGSOA-GOA: 0.1768 C (HGSOA-GOA, SPEA2): 0.23 HGSOA-GOA: 11.2323 HGSOA-GOA: 2.3327

SPEA2: 0.2781 C (SPEA2, HGSOA-GOA): 0.01 SPEA2: 10.6754 SPEA2: 2.9830

Workﬂow: Epigenomics, VMs: 1000, Runs: 100

Small HGSOA-GOA: 0.1098 C (HGSOA-GOA, SPEA2): 0.30 HGSOA-GOA: 9.2205 HGSOA-GOA: 0.5234

SPEA2: 0.2893 C (SPEA2, HGSOA-GOA): 0.20 SPEA2: 3.3414 SPEA2: 0.7351

Medium HGSOA-GOA: 0.1440 C (HGSOA-GOA, SPEA2): 0.31 HGSOA-GOA: 9.3087 HGSOA-GOA: 0.4346

SPEA2: 0.2409 C (SPEA2, HGSOA-GOA): 0.03 SPEA2: 8.9038 SPEA2: 0.8801

Large HGSOA-GOA: 0.0873 C (HGSOA-GOA, SPEA2): 0.29 HGSOA-GOA: 9.8134 HGSOA-GOA: 0.1680

SPEA2: 0.1728 C (SPEA2, HGSOA-GOA): 0.10 SPEA2: 9.1290 SPEA2: 0.4352

Table 8 (continued)

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Eel and grouper optimizer: a nature-inspired optimization algorithm

Article

Full-text available

Jun 2024
CLUSTER COMPUT

This paper proposes a meta-heuristic called Eel and Grouper Optimizer (EGO). The EGO algorithm is inspired by the symbiotic interaction and foraging strategy of eels and groupers in marine ecosystems. The algorithm’s efficacy is demonstrated through rigorous evaluation using nineteen benchmark functions, showcasing its superior performance compared to established meta-heuristic algorithms. The findings and results on the benchmark functions demonstrate that the EGO algorithm outperforms well-known meta-heuristics. This work also considers solving a wide range of real-world practical engineering case studies including tension/compression spring, pressure vessel, piston lever, and car side impact, and the CEC 2020 Real-World Benchmark using EGO to illustrate the practicality of the proposed algorithm when dealing with the challenges of real search spaces with unknown global optima. The results show that the proposed EGO algorithm is a reliable soft computing technique for real-world optimization problems and can efficiently outperform the existing algorithms in the literature.

MCPF: Fault-Tolerant Scheduling of Scientific Workflow on Cloud Computing

Preprint

Full-text available

Mar 2024

Scientific workflow applications entail extensive amounts of tasks and data-sets necessitating systematic processing. Cloud platform is utilized for executing these applications which provide access to extensive amounts of scalable and on demand resources. Running scientific workflow applications on cloud computing experiences a huge amount of failure, i.e., hardware failures, software failures, network failures, etc., due to the large scale heterogeneity and distributed nature. That affects overall workflow execution time, monitory cost, and resource utilization. Numerous fault-tolerance methods are used to resolve and handle failures in cloud computing environment. In this paper, we used the MCPF (Multiple Critical Partitions with Failure) technique. The proposed technique has two phases. In the first phase, the rank of all tasks is calculated by summing the ranks, i.e., downward and upward rank. And then, in the second phase tasks are scheduled based on their ranking on the VMs, which has a lower failure rate. We evaluated the performance of our proposed technique under different conditions using parameters, i.e., makespan and cost. We have compared the results of MCPF with well-known existing HEFT, and RDEARP algorithms. Simulation results obtained through experiments and their comparison with existing techniques lead us to the conclusion that our proposed technique yields better results than existing algorithms.

Security Driven Cost-Effective Deadline Aware Workflow Allocation Strategy in Cloud Computing Environment

Conference Paper

Nov 2023

In cloud computing, a pay-per-use framework enables dynamic scalability in response to the demands of workflow applications. Workflow allocation is an essential issue due to the trade-off between obtaining high computing performance and offering the appropriate level of security protection. This paper integrates security services into the workflow allocation to enhance the security measures in the cloud system. Therefore, we propose a multi-constraints workflow allocation strategy for heterogeneous tasks in cloud computing. Our proposed strategy is to minimize the risk probability and the execution cost while meeting the budget, and deadline constraints. The findings show that our approach consistently outperforms the existing algorithms in the proposed system, which uses multi-constraints.

Multi-strategy Improved Seagull Optimization Algorithm

Article

Full-text available

Sep 2023
INT J COMPUT INT SYS

Aiming at the shortcomings of seagull optimization algorithm in the process of searching for optimization, such as slow convergence speed, low precision, easy falling into local optimal, and performance dependent on the selection of parameters, this paper proposes an improved gull optimization algorithm based on multi-strategy fusion based on the analysis of gull population characteristics. Firstly, L–C cascade chaotic mapping is used to initialize the population so that seagulls are more evenly distributed in the initial solution space. Secondly, to improve the algorithm’s global exploration ability in the early stage, the nonlinear convergence factor is incorporated to adjust the position of seagulls in the migration stage. At the same time, the group learning strategy was introduced after the population position update to improve the population quality and optimization accuracy further. Finally, in the late stage of the algorithm, the golden sine strategy of the Levy flight guidance mechanism is used to update the population position to improve the population’s diversity and enhance the local development ability of the algorithm in the late stage. To verify the optimization performance of the improved algorithm, CEC2017 and CEC2022 test suites are selected for simulation experiments, and box graphs are drawn. The test results show that the proposed algorithm has apparent convergence speed, accuracy, and stability advantages. The engineering case results demonstrate the proposed algorithm’s advantages in solving complex problems with unknown search spaces.

Energy-aware workflow scheduling in fog computing using a hybrid chaotic algorithm

Article

Full-text available

May 2023
J SUPERCOMPUT

Fog computing paradigm attempts to provide diverse processing at the edge of IoT networks. Energy usage being one of the important elements that may have a direct influence on the performance of fog environment. Effective scheduling systems, in which activities are mapped on the greatest feasible resources to meet various competing priorities, can reduce energy use. Consequently, a hybrid discrete optimization method called HDSOS-GOA, which uses the Dynamic voltage and frequency scaling (DVFS) approach, is proposed to handle scientific workflow scheduling challenges in the fog computing environment. HDSOS-GOA combines the search qualities of Symbiotic Organisms Search (SOS) and the Grasshopper Optimization Algorithm (GOA) algorithms and the selection of these algorithms for performing workflow scheduling is based on the probability calculated by the learning automata. The HEFT method is used to determine the task sequence. Our solution focuses on reducing the energy consumption of the scheduling process by reducing the number of Virtual Machines required for workflow execution in addition to optimizing the makespan. Comprehensive experiments are carried out on four different scientific workflows with different sizes with and without deadline constraints to evaluate the performance of the suggested scheduling strategy. The results of the experiments show that scheduling with the suggested approach outperforms other well-known metaheuristic algorithms.

Enhancement of Cloud Performance using the Clustering Method of Scientific Workflow Task

Conference Paper

Oct 2023

AI-based & heuristic workflow scheduling in cloud and fog computing: a systematic review

Article

Full-text available

May 2024
CLUSTER COMPUT

Fog and cloud computing are emerging paradigms that enable distributed and scalable data processing and analysis. However, these paradigms also pose significant challenges for workflow scheduling and assigning related tasks or jobs to available resources. Resources in fog and cloud environments are heterogeneous, dynamic, and uncertain, requiring efficient scheduling algorithms to optimize costs and latency and to handle faults for better performance. This paper aims to comprehensively survey existing workflow scheduling techniques for fog and cloud environments and their essential challenges. We analyzed 82 related papers published recently in reputable journals. We propose a subjective taxonomy that categorizes the critical difficulties in existing work to achieve this goal. Then, we present a systematic overview of existing workflow scheduling techniques for fog and cloud environments, along with their benefits and drawbacks. We also analyze different workflow scheduling techniques for various criteria, such as performance, costs, reliability, scalability, and security. The outcomes reveal that 25% of the scheduling algorithms use heuristic-based mechanisms, and 75% use different Artificial Intelligence (AI) based and parametric modelling methods. Makespan is the most significant parameter addressed in most articles. This survey article highlights potentials and limitations that can pave the way for further processing or enhancing existing techniques for interested researchers.

Use of whale optimization algorithm and its variants for cloud task scheduling a review

Chapter

Full-text available

Nov 2023

Scheduling is an important issue in distributed computing platforms which decides the allocation of resources to the user-submitted tasks to optimize certain scheduling objectives. Due to the dynamic nature of cloud resources and the growing size of tasks and requests, there are serious problems with resource usage, system performance, task allocation, load balancing, and other factors. To find near-optimal solutions to task scheduling issues, considerable researchers have used various kinds of scheduling strategies. But compared to traditional heuristics and exact scheduling approaches, meta-heuristic scheduling algorithms produce the most successful results. The whale Optimization Algorithm (WOA) is a well-known meta-heuristic method, which has been revealed useful for resolving a wide variety of optimization problems. WOA is suitable for load balancing, workflow scheduling, and dynamic task scheduling. This study presents a detailed analysis of various types of WOA-based scheduling strategies published during the years 2015-2022 using comprehensive evaluation measures in the fog and cloud computing environment.

Optimizing Network-on-Chip using metaheuristic algorithms: A comprehensive survey

Article

Nov 2023
MICROPROCESS MICROSY

Chaotic hybrid multi-objective optimization algorithm for scientific workflow scheduling in multisite clouds

Article

Full-text available

Apr 2023
J OPER RES SOC

A cloud is made up of many data centers, with their own set of data and resources. The reasons for employing several cloud sites to operate a workflow are that the data is already dispersed, and the required resources surpass the constraints of a single site. This paper presents a hybrid multi-objective optimization algorithm denoted as HSOS-SOA, achieved by combining the Symbiotic Organisms Search and Seagull Optimization Algorithm. The HSOS-SOA uses chaotic maps to generate random numbers and performs a good trade-off between exploration and exploitation, resulting in a higher convergence rate. HSOS-SOA is used to solve scientific workflow scheduling problems in multisite cloud computing by taking into consideration elements such as makespan, cost, and reliability. A solution is chosen from the Pareto front using the knee-point approach in this approach. Extensive analyses are performed out in Microsoft Azure multisite cloud and the results exhibited that the HSOS-SOA can outperform other algorithms in terms of metrics such as IGD, Coverage Ratio, and so on. Experimental results of experiments reveal that the results in makespan improvement in the range of 5.72-28.61%, the cost in the range of 5.16-45.16%, and reliability in the range of 3.11-25% over well-known metaheuristic algorithms.

Energy and Cost-Aware Workflow Scheduling in Cloud Computing Data Centers Using a Multi-objective Optimization Algorithm

Article

Full-text available

Jul 2021
J NETW SYST MANAG

A multi-objective optimization approach is suggested here for scientific workflow task-scheduling problems in cloud computing. More frequently, scientific workflow involves a large number of tasks. It requires more resources to perform all these tasks. Such a large amount of computing power can be supported only by cloud infrastructure. To implement complex science applications, more computing energy is expended, so the use of cloud virtual machines in an energy-saving way is essential. However, even today, it is a difficult challenge to conduct a scientific workflow in an energy-aware cloud platform. The hardness of this problem increases even more with several contradictory goals. Most of the existing research does not consider the essential characteristic of cloud and significant issues, such as energy variation and throughput besides makespan and cost. Therefore, a hybridization of the Antlion Optimization (ALO) algorithm with the Grasshopper Optimization Algorithm (GOA) was proposed and used multi-objectively to solve the scheduling problems. The novelty of the proposed algorithm was enhancing the search performance by making algorithms greedy and using random numbers according to Chaos Theory on the green cloud environment. The purpose was to minimize the makespan, cost of performing tasks, energy consumption, and increase throughput. WorkflowSim simulator was used for implementation, and the results were compared with the SPEA2 algorithm. Experimental results indicate that based on these metrics, a proposed multi-objective optimization algorithm is better than other similar methods.

A hybrid multi-objective metaheuristic optimization algorithm for scientific workflow scheduling

Article

Full-text available

Jun 2021
CLUSTER COMPUT

Workflow is composed of some interdependent tasks and workflow scheduling in the cloud environment that refers to sorting the workflow tasks on virtual machines on the cloud platform. We will encounter many sorting modes with an increase in virtual machines and the variety in task size. Reaching an order with the least makespan is an NP-hard problem. The hardness of this problem increases even more with several contradictory goals. Hence, a meta-heuristic algorithm is what required in reaching the optimal response. Thus, the algorithm is a hybridization of the ant lion optimizer (ALO) algorithm with a Sine Cosine Algorithm (SCA) algorithm and used it multi-objectively to solve the problem of scheduling scientific workflows. The novelty of the proposed algorithm was to enhance search performance by making algorithms greedy and using random numbers according to Chaos Theory on the green cloud computing environment. The purpose was to minimize the makespan and cost of performing tasks, to reduce energy consumption to have a green cloud environment, and to increase throughput. WorkflowSim simulator was used for implementation, and the results were compared with the SPEA2 workflow scheduling algorithm. The results show a decrease in the energy consumed and makespan.

A discrete chaotic multi-objective SCA-ALO optimization algorithm for an optimal virtual machine placement in cloud data center

Article

Full-text available

Oct 2021

Cloud computing, with its immense potentials in low cost and on-demand services, is a promising computing platform for both commercial and non-commercial computation applications. It focuses on the sharing of information and computation in a large network that are quite likely to be owned by geographically disbursed different venders. Power efficiency in cloud data centers (DCs) has become an important topic in recent years as more and larger DCs have been established and the electricity cost has become a major expense for operating them. Server consolidation using virtualization technology has become an important technology to improve the energy efficiency of DCs. Virtual machine (VM) assignment is the key in server consolidation. In the past few years, many methods to VM assignment have been proposed, but existing VM assignment approaches to the VM assignment problem consider the energy consumption by physical machines (PM). In current paper a new approach is proposed that using a combination of the sine cosine algorithm (SCA) and ant lion optimizer (ALO) as discrete multi-objective and chaotic functions for optimal VM assignment. First objective of our proposed model is minimizing the power consumption in cloud DCs by balancing the number of active PMs. Second objective is reducing the resources wastage by using optimal VM assignment on PMs in cloud DCs. Reducing SLA levels was another purpose of this research. By using the method, the number of increase of migration of VMs to PMs is prevented. In this paper, several performance metrics such as resource wastage, power consumption, overall memory utilization, overall CPU utilization, overall storage space, and overall bandwidth, a number of active PMs, a number of shutdowns, a number of migrations, and SLA are used. Ultimately, the results obtained from the proposed algorithm were compared with those of the algorithms used in this regard, including First Fit (FF), VMPACS and MGGA.

Improved chaotic binary grey wolf optimization algorithm for workflow scheduling in green cloud computing

Article

Full-text available

Dec 2021

The workflow scheduling in the cloud computing environment is a well-known NP-complete problem, and metaheuristic algorithms are successfully adapted to solve this problem more efficiently. Grey wolf optimization (GWO) is a recently proposed interesting metaheuristic algorithm to deal with continuous optimization problems. In this paper, we proposed IGWO, an improved version of the GWO algorithm which uses the hill-climbing method and chaos theory to achieve better results. The proposed algorithm can increase the convergence speed of the GWO and prevents falling into the local optimum. Afterward, a binary version of the proposed IGWO algorithm, using various S functions and V functions, is introduced to deal with the workflow scheduling problem in cloud computing data centers, aiming to minimize their executions’ cost, makespan, and the power consumption. The proposed workflow scheduling scheme is simulated using the CloudSim simulator and the results show that our scheme can outperform other scheduling approaches in terms of metrics such as power consumption, cost, and makespan.

A Modified Sine Cosine Algorithm with Novel Transition Parameter and Mutation Operator for Global Optimization

Article

Full-text available

Mar 2020
EXPERT SYST APPL

Inspired by the mathematical characteristics of sine and cosine trigonometric functions, the Sine Cosine Algorithm (SCA) has shown competitive performance among other meta-heuristic algorithms. However, despite its sufficient global search ability, its low exploitation ability and immature balance between exploitation and exploration remain weaknesses. In order to improve Sine Cosine Algorithm (SCA), this paper presents a modified version of the SCA called MSCA. Firstly, a non-linear transition rule is introduced instead of a linear transition to provide comparatively better transition from the exploration to exploitation. Secondly, the classical search equation of the SCA is modified by introducing the leading guidance based on the elite candidate solution. When the above proposed modified search mechanism fails to provide a better solution, in addition, a mutation operator is used to generate a new position to avoid the situation of getting trapped in locally optimal solutions during the search. Thus, the MSCA effectively maximizes the advantages of proposed strategies in maintaining a comparatively better balance of exploration and exploitation as compared to the classical SCA. The validity of the MSCA is tested on a set of 33 benchmark optimization problems and employed for training multilayer perceptrons. The numerical results and comparisons among several algorithms show the enhanced search efficiency of the MSCA.

Hybrid scheduling for scientific workflows on hybrid clouds

Article

Aug 2020
COMPUT NETW

Scientific workflows consist of many interdependent tasks dictated by their data dependencies. As these workflows are becoming resource-intensive in both data and computing, private clouds struggle to cope with their resource requirements. Private cloud’s limitations are claimed to be addressed by public clouds, however, the complete offloading of workflow execution to public clouds causes excessive data transfer. In this paper, we address the problem of scheduling scientific workflows on hybrid clouds aiming at cost reduction while improving execution time, with the consideration of public cloud costs, by minimizing data movements between private cloud and public cloud. To this end, we develop Hybrid Scheduling for Hybrid Clouds (HSHC) as a novel data-locality aware scheduling algorithm. HSHC adopts a hybrid approach consisting of static phase and dynamic phase. The former solves the problem of workflow scheduling, using an extended genetic algorithm, with static information of workflows and resources. The latter dynamically adapts the static schedule in response to changing execution conditions, such as locality of intermediate output data and performance degradation of tasks and resources. We evaluate HSHC with both random workflows and real-world scientific applications in execution time and cost. Experimental results compared with seven state-of-the-art algorithms demonstrate HSHC significantly reduces the cost by up to 40% and improves the execution time by up to 25%.

Multi-Objective Optimization for the Reliable Pollution-Routing Problem with Cross-Dock Selection using Pareto-based Algorithms

Article

Jul 2020
J CLEAN PROD

Cross-docking practice plays an important role in improving the efficiency of distribution networks, especially, for optimizing supply chain operations. Moreover, transportation route planning, controlling the Greenhouse Gas (GHG) emissions and customer satisfaction constitute the major parts of the supply chain that need to be taken into account integratedly within a common framework. For this purpose, this paper tries to introduce the reliable Pollution-Routing Problem with Cross-dock Selection (PRP-CDS) where the products are processed and transported through at least one cross-dock. To formulate the problem, a Bi-Objective Mixed-Integer Linear Programming (BOMILP) model is developed, where the first objective is to minimize total cost including pollution and routing costs and the second is to maximize supply reliability. Accordingly, sustainable development of the supply chain is addressed. Due to the high complexity of the problem, two well-known meta-heuristic algorithms including Multi-Objective Simulated-annealing Algorithm (MOSA) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) are designed to provide efficient Pareto solutions. Furthermore, the ε-constraint method is applied to the model to test its applicability in small-sized problems. The efficiency of the suggested solution techniques is evaluated using different measures and a statistical test. To validate the performance of the proposed methodology, a real case study problem is conducted using the sensitivity analysis of demand parameter. Based on the main findings of the study, it is concluded that the solution techniques can yield high-quality solutions and NSGA-II is considered as the most efficient solution tool, the optimal route planning of the case study problem in delivery and pickup phases is attained using the best-found Pareto solution and the highest change in the objective function occurs for the total cost value by applying a 20% increase in the demand parameter.

Cost and Makespan Scheduling of Workflows in Clouds Using List Multiobjective Optimization Technique

Article

Jul 2020
J SYST ARCHITECT

Highly scalable resource supply capacity of cloud computing has greatly improved the execution speed of workflow applications, however, traditional workflow scheduling algorithms which focus on the optimization of makespan (execution time) of workflows, become inappropriate for the design of large-scale workflow systems. Workflow scheduling in cloud computing is particularly a multiobjective optimization problem, in which many critical issues besides the execution time of workflows should be taken into account. Although many heuristics and meta-heuristics have been proposed to solve this problem, most of them cannot produce satisfactory cost-makespan tradeoffs and have a long time overhead. In this paper, we propose an efficient heuristic named CMSWC (Cost and Makespan Scheduling of Workflows in the Cloud) to solve the workflow scheduling problem, by simultaneously minimizing cost and makespan of workflows. CMSCW follows a two-phase list scheduling philosophy: ranking and mapping. Furthermore, CMSCW incorporates with three designs specifically for the multiobjective challenges: (i) The mapping phase is designed to avoid exploring useless resources for tasks, which significantly narrows down the search space. (ii) A new method is proposed to select non-dominated solutions, by combining the quick non-dominated sorting approach and Shift-Based Density Estimation (SDE) based crowding distance. (iii) Several elitist study strategies are designed to make solutions close to the true Pareto front as well as avoid trapping into local optimum. Extensive experiments on real-life workflows demonstrate that our approach can generate better cost-makespan tradeoff fronts than that of several state-of-the-art approaches.

Improved Many-objective Particle Swarm Optimization Algorithm for Scientific Workflow Scheduling in Cloud Computing

Article

Jul 2020
COMPUT IND ENG

Optimized scientific workflow scheduling can greatly improve the overall performance of cloud computing. As workflow scheduling belongs to NP-complete problem, so, meta-heuristic approaches are more preferred option. Most studies on workflow scheduling in cloud mostly consider at most two or three objectives and there is a lack of effective studies and approaches on problems with more than three objectives remains; because the efficiency of multi-objective evolutionary algorithms (MOEAs) will seriously degrade when the number of objectives is more than three, which are often known as many-objective optimization problems (MaOPs). In this paper, an approach to solve workflow scheduling problem using Improved Many Objective Particle Swarm Optimization algorithm named I_MaOPSO is proposed considering four conflicting objectives namely maximization of reliability and minimization of cost, makespan and energy consumption. Specifically, we use four improvements to enhance the ability of MaOPSO to converge to the non-dominated solutions that apply a proper equilibrium between exploration and exploitation in scheduling process. The experimental results show that the proposed approach can improve up to 71%, 182%, 262% the HyperVolume (HV) criterion compared with the LEAF, MaOPSO, and EMS-C algorithms respectively. I_MaOPSO opens the way to develop a scheduler to deliver results with improved convergence and uniform spacing among the answers in compared with other counterparts and presents results that are more effective closer to non-dominated solutions.

Multi-objective scheduling strategy for scientific workflows in cloud environment: A Firefly-based approach

Article

May 2020
APPL SOFT COMPUT

Cloud computing is a distributed computing paradigm, that provides infrastructure and services to the users using the pay-as-you-use billing model. With the increasing demands and diversity of the scientific workflows, the cloud providers face a fundamental issue of resource provisioning and load balancing. Although, the workflow scheduling in the cloud environment is extensively studied, however, most of the strategies ignore to consider the multiple conflicting objectives of the workflows for scheduling and resource provisioning. To address the above-mentioned issues, in the paper, we introduce a new workflow scheduling strategy using the Firefly algorithm (FA) by considering multiple conflicting objectives including workload of cloud servers, makespan, resource utilization, and reliability. The main purpose of the FA is to find a suitable cloud server for each workflow that can meet its requirements while balancing the loads and resource utilization of the cloud servers. In addition, a rule-based approach is designed to assign the tasks on the suitable VM instances for minimizing the makespan of the workflow while meeting the deadline. The proposed scheduling strategy is evaluated over Google cluster traces using various simulation runs. The control parameters of the FA are also thoroughly investigated for better performance. Through the experimental analysis, we prove that the proposed strategy performs better than the state-of-the-art-algorithms in terms of different Quality-of-Service (QoS) parameters including makespan, reliability, resource utilization and loads of the cloud servers.

Scientific workflow scheduling in multi-cloud computing using a hybrid multi-objective optimization algorithm

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