A Modified GA-based Workflow Scheduling for Cloud Computing Environment

A Modified GA-based Workflow Scheduling for
Cloud Computing Environment
Safwat A. Hamad
Department of Computer Science,
Faculty of Computers & Information, Cairo University,
Cairo, Egypt
mcssafr@gmail.com
Fatma A. Omara
Department of Computer Science,
Faculty of Computers & Information, Cairo University,
Cairo, Egypt
f.omara@fci-cu.edu.eg
Abstract— The Cloud computing becomes an important topic
in the area of high performance distributed computing. On the
other hand, task scheduling is considered one the most significant
issues in the Cloud computing where the user has to pay for the
using resource based on the time. Therefore, distributing the
cloud resource among the users' applications should maximize
resource utilization and minimize task execution Time. The goal
of task scheduling is to assign tasks to appropriate resources that
optimize one or more performance parameters (i.e., completion
time, cost, resource utilization, etc.). In addition, the scheduling
belongs to a category of a problem known as an NP-complete
problem. Therefore, the heuristic algorithm could be applied to
solve this problem. In this paper, an enhanced dependent task
scheduling algorithm based on Genetic Algorithm (DTGA) has
been introduced for mapping and executing an application’s
tasks. The aim of this proposed algorithm is to minimize the
completion time. The performance of this proposed algorithm has
been evaluated using WorkflowSim toolkit and Standard Task
Graph Set (STG) benchmark.
Keywords—Cloud Computing; Task Scheduling; Genetic
Algorithm; Directed Acyclic Graph; Optimization Algorithm
I. INTRODUCTION
The Cloud computing is emerging technology and great
popularity in recent years which grants the users with high
scalability, reliability, security, cost effective mechanism,
group collaboration and ease of access to various applications
[1]. In addition, The Cloud computing provides dynamic
services as Software as a service (SaaS), Platform as a service
(PaaS) and Infrastructure as a service (IaaS) via the internet [2].
The Cloud computing has some challenges (e.g., security,
performance, resource management, etc.). Therefore, the task
scheduling is considering one of the most challenges that
related to resource management [3]. In general, task scheduling
is a problem of assigning tasks to the machine to complete their
work. In the same context, the scheduling in the Cloud
computing environment means that large number of the tasks
are executing on the available resources in a suitable way
depending on many parameters (i.e., minimize completion
time, minimize the cost of execution tasks, maximize resource
utilization, etc.) [3]. Therefore, task scheduling in the Cloud
computing environment is considered one of the most factors
would affect reliability and performance of the Cloud services
[2].
Generally, the problem of assigning tasks to apparently
unlimited computing resources in the Cloud computing
environment is an NP-Complete problem. According to the
process of task scheduling, the user’s jobs are submitted to the
Cloud scheduler. In turn, the Cloud scheduler inquires the
Cloud information service about the statues of the available
resources, and then allocates the various tasks on different
resource (i.e., virtual machines) as per the task requirements
[2]. The good task scheduling must assign the virtual machine
in an optimal way [3].
Therefore, task scheduling problem is considering the
challenge in the Cloud computing environment. The
researchers are trying to apply heuristic methods to solve this
problem and get optimal solution [4]. Therefore, the Meta-
heuristic based techniques deal with this problem by providing
near optimal solutions. In addition, Meta-heuristic has gained
huge popularity in past years due to its efficiency and
effectiveness to solve the large and complex problem. There
are many of Meta-heuristic algorithms (e.g., Genetic Algorithm
(GA), Particle Swarm Optimization (PSO), Ant Colony
Optimization (ACO), etc.).[5].
Further, task scheduling algorithms are different based on
dependency among tasks to be scheduled. According to
dependent task scheduling, there is precedence orders exist in
tasks where any task can only be scheduled after finishing
execution all its parent tasks. Otherwise, tasks are independent
of each other, and they can be scheduled in any sequence. In
addition, the dependent task scheduling is known as workflow
scheduling and independent task scheduling is known as
independent scheduling [5].
The aim of this paper is to develop a workflow scheduling
algorithm in the Cloud computing environment based on
Genetic Algorithm for allocating and executing dependent
tasks to improve task completion time.
The rest of the paper is as follows: in Section 2, the related
works are discussed. In Section 3, a model for task scheduling
problem is described. Sections 4, the principles of the modified
GA-based dependent task scheduling are described. The
configuration of the Workflowsim simulator, implementation
of the proposed Genetic Algorithm, as well as, performance
evaluation is discussed in Section 5. Finally, conclusion and
future work are given in Section 6.
International Journal of Computer Science and Information Security (IJCSIS),
Vol. 15, No. 8, August 2017
276 https://sites.google.com/site/ijcsis/
ISSN 1947-5500

II. RELATED WORK
In recent years, the problem of task scheduling in the Cloud
computing environment has caught the attention of researchers.
One of the solutions that try to solve task scheduling is use
Meta-heuristic algorithm. On the other hand, task scheduling in
the Cloud computing environment is considered critical issue
by considering different factors like completion time, the total
cost for executing user’s tasks, utilization resource, power
consumption, fault tolerant, etc.
In this paper, a modified Genetic Algorithm has been
introduced to scheduling dependent tasks.
In many types of research, different GA based task
scheduling algorithms have been introduced; each of these
algorithms proposes some modifications to the default Genetic
Algorithm. In [6], fixed bit string representation is used, where
the solutions are encoded as a fixed length binary string. Also,
there are others approaches as Direct Representation is used
[7]. The Permutation based representation is applied using 2D
vector to represent a chromosome. One dimension represents
the resources and other shows the order of tasks on each
resource [8-10]. In addition, the Tree representation has been
used for mapping the relationship between virtual machine and
physical machine [11, 12].
On the other hand, the initial population is generated
randomly in basic Genetic Algorithm. Therefore, some
approaches have been applied to enhance optimal results and
increase the convergence of Genetic Algorithm. In [9], the
Minimum Execution Time (MET) and Min-min heuristic are
used to generate initial population. Genetic Algorithm has been
used to solve workflow scheduling problem, where the
precedence of tasks is considered through the initial population
generation
Further, one of the main steps of Genetic Algorithm is
crossover and mutation, therefore the modification on basic
crossover has applied to enhance the performance of Genetic
Algorithm. In [3], a new model of crossover has been used
differently from the used crossover in the default Genetic
Algorithm. Therefor, the two selected chromosomes for
crossover process to generate two offspring are also considered
as offsprings. After producing the offspring, the two best
offsprings are chosen. In [12], the crossover and mutation
operators have been developed to make them appropriate for a
tree representation of chromosome.
On the other side, many studies have considered Genetic
Algorithm to solve task scheduling problem to minimize
makspan, improve load balance among virtual machines,
minimizing total cost to execute tasks, maximize resource
utilization and save energy consumption. In [13], an immune
Genetic Algorithm has proposed for workflow scheduling to
minimize the makspan and cost, which considered five
objectives and solved constraint satisfaction problem associated
with task scheduling constraints. A task scheduling algorithm
based on Genetic Algorithm has been proposed with the aim of
minimizing makspan and improve load balance among virtual
machines [7]. Genetic Algorithm has been used to achieve
good load balance among virtual machines [6, 8, 14, 15].
In [16], Genetic Algorithm and Fuzzy Theory called
(FUGA) algorithm had been introduced to minimize makspan,
cost and enhancement imbalance in the Cloud computing
during scheduling task. The Fuzzy Theory is used to compute
fitness value of the solution and for crossover operation.
The energy efficient is consider one of the most parameters
of task scheduling process, so there are approaches have been
introduced using Genetic Algorithm to enhance the energy
consumption of datacenters. In [17], energy aware task
scheduling algorithm has been presented based on shadow
price guided Genetic Algorithm (SGA) where shadow price is
used into Genetic Algorithm to improve solution’s fitness
value. In addition, the gene has been modified in order to
enhance the probability of producing better solutions. In [18],
pareto-solution based Genetic Algorithm approach for
workflow scheduling has been introduced to optimize
objectives.
In addition, there are many studies have been proposed
using other Meta-heuristic approaches as Particle Swarm
Optimization (PSO), Cuckoo Search (CS), Tabu Search, etc. In
[19, 20], the authors have introduced a modified task
scheduling algorithm by merging the PSO and Cuckoo
algorithms to minimize the execution time, as well as,
maximize the resource utilization. Two hybrid task scheduling
algorithms have been introduced to enhance the default PSO
algorithm by using a Best-Fit algorithm to initialize population
instead of being initiated randomly as in the default PSO
algorithm and using Tabu Search algorithm to improve the
local search by avoiding the trap of local which could be
occurred in default PSO algorithm [21, 22].
Further, a modified PSO algorithm has been proposed to
allocate dependent tasks on available resources to minimize the
execution time, as well as, computation cost [23].
III. MODEL OF TASK SCHEDULING PROPLEM
The model for task scheduling for Cloud computing
according to this work is defined as follows:
The Cloud resources are provided to the user as a number
of Heterogeneous Virtual Machine (VM) through virtualization
technology. The user’s application submitted to the Cloud
service center and it has been split into several tasks with
known data dependence. Generally, association task scheduling
is defined as a Directed Acyclic Graph (DAG) composed of
Nodes (n1, n2, …., nN). Each node in the graph represents a
task that must be executed sequentially without preemption in
the same VM. If a node in the DAG has no parent node (input),
calls (entry node), and if the node has no any child node, calls
(exit node) [24].
In addition, the graph has directed edges E representing a
partial order among the task nodes. The partial order introduces
a precedence-constraints DAG and implies that for example if
ni nj, then nj is a child, which cannot start until its parent ni
finishes. After all task nodes have been scheduled, the schedule
length is defined as Completion Time to execute the last task.
The objective of task scheduling problem is to fined optimal
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assignment task on available VMs and minimize the
completion time with precedence-constraints are preserved.
IV. SCHEDULING ALGORITHM
Task scheduling problem is considered one of the most
issues in the Cloud computing environment, perspective the
Cloud provider and Cloud user. The Cloud provider should
guarantee optimal scheduling of the user’s task according to
SLA. At the same time, he should guarantee throughput and
good utilization of Cloud resources. Therefore, he needs a good
algorithm to schedule the tasks in Cloud. As a result, task
scheduling is classified as an optimization problem.
Therefore, heuristic algorithms such as Genetic Algorithm
(GA), Particle Swarm Optimization (PSO), Ant Colony
Optimization (ACO), etc. could be used to solve the problem.
In this work, a workflow Scheduling has been proposed
based on the default GA with some modifications. According
to these modifications, the parents will be considered in each
population beside the produced childs after the crossover
process. Also, the Tournament Selection is used to select the
better chromosomes to overcome the limitation of the
population size. Therefore, the proposed algorithm is called
Dependent Task Genetic Algorithm (DTGA).
A- Default Genetic Algorithm (DGA)
Genetic Algorithm (GA) is based on the biological concept
of generating the population. GA is considered a rapidly
growing area of Artificial Intelligence [25, 26]. The Genetic
Algorithms (GAs) was inspired from Darwin's theory of
evolution. According to Darwin's theory, term “Survival of the
fittest” is used as the method of scheduling in which the tasks
are mapped to resources according to the value of fitness
function for each parameter of the task scheduling process [27].
Generally, the default Genetic Algorithm consists of five
steps; Initial population, fitness function, selection process,
crossover, and mutation (see Figure 1) [5].
B- The Proposed Genetic Based Dependent Task
Scheduling
In this work, a Genetic Based Dependent Task scheduling
(DTGA) algorithm has been proposed for the Cloud
environment. This proposed algorithm is considered an
extension of our previous GA algorithm by concerning
scheduling of dependent tasks instead of independent ones [3].
By considering a DAG with seven tasks to be executed on 4
VMs, the steps of the proposed DTGA algorithm is illustrated
as follows (see Figure 2):
1. Representation of Chromosome
According to the proposed DTGA algorithm, the
representation of chromosome is divided into two parts;
mapping (for VMs) and schedule (for tasks Ts) as shown in
Figure 3
2. Initial Population
The population is randomly generated. The first part of the
chromosome (VMs mapping) is chosen randomly from 1 to
No_VMs where No_VMs is the number of the Virtual Machine
in the Cloud system. The second part (schedule TS) is
generated randomly such that the topological order of the DAG
graph is preserved.
3. Fitness Function Representation
In the GA, each chromosome in population has a value
called (fitness function) measured based on which fitness of
solution. Therefore, the fitness function for task scheduling
problem in the Cloud computing environment is considered the
Completion Time of all tasks on the available VMs.
In the case of dependent task scheduling, a task may have
more than one parent. Therefore, the maximum Completion
Time of a task's parent is considered the start execution time of
it.
According to Figs. 2 and 3, suppose task 2 completes its
work on VM1 at 4 unit, and task 3 completes its work at 5 unitFigure 1. Pseudo Code of Default Genetic Algorithm [5].
Procedure GA
1. Initialization: Generate initial population P consisting of
chromosomes.
2. Fitness: Calculate the fitness value of each chromosome using
fitness function.
3. Selection: Select the chromosomes for producing next
generation using selection operator.
4. Crossover: Perform the crossover operation on the pair of
chromosomes obtained in step 3.
5. Mutation: Perform the mutation operation on the chromosomes.
6. Fitness: Calculate the fitness value of these newly generated
chromosomes known as offsprings.
7. Replacement: Update the population P by replacing bad
solutions with better chromosomes from offsprings.
8. Repeat steps 3 to 7 until stopping condition is met. Stopping
condition may be the maximum number of iterations or no change
in fitness value of chromosomes for consecutive iterations.
9. Output best chromosome as the final solution.
End Procedure
1
4
3
2
5
6
7
Figure 2. DAG with seven Tasks.
VM 3 VM 1 VM 4 VM 1 VM 2 VM 3 VM 4
T 1 T 5 T 7 T 3 T 2 T 6 T 4
Figure 3. Representation of Chromosomes.
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Crossover point = 4
Offspring 1
Offspring 2
Parent 2
Parent 1
T 1 T 5 T 7 T 3 T 2 T 6 T 4
T 1 T 4 T 6 T 5 T 2 T 7 T 3
T 1 T 5 T 7 T 3 T 2 T 6 T 4
T 1 T 4 T 6 T 5 T 2 T 7 T 3
Figure 4. One point croosover operator.
on VM4, then the execution of task 6 will start from unit 5 on
VM3 if no task active at that time.
Therefore, the starting time (ST) of a task is calculated
using equation (1).
STi = max max (completion time of parent Ti) . . (1)
Where is the starting time of task Ti on VMj.
The completion time of task Ti is calculated using equation
(2).
CTij = STi + execution time of Ti on VMj … … … … … . (2)
Therefore, the completion time for all tasks on all VMs is
calculated as equation (3).
=
_
… … … … … … (3)
Where n is the number of tasks, No_VMs is the number
of VMs, and CTij is the execution time of task i on VM j
4. Reproduction
• Tournament selection; In this step, the selection
method is applying to select two chromosomes from
an available solution according to the fitness value to
generate a new population. There are different
approaches that can be applied in selection phase.
Therefore, in our proposed DTGA algorithm the
Tournament selection is used to select pairs of a
parent for crossover process.
• Crossover; After the selection process, the crossover
is implemented on two chromosomes to generate a
new solution with considering the dependency of the
tasks
In our proposed DTGA algorithm, the crossover is
implemented using two steps:
a. Apply crossover point
The single crossover point is applied to mapping (for VMs)
part according to a value generated randomly. As an example,
two parents 1, 2 are used and crossover point value is 4 (see
Figure 4).
This crossover generates new offspring and at the same
time, its preserve the dependency for the tasks.
b. Apply New Model of Crossover
In this model, the two parents who are selected to crossover
to generate two offspring will be considered as offspring too.
So, the proposed new model of crossover produces 4 children
(see Figure 5). After that, the two best children are chosen from
these [3].
• Mutation
The mutation applies according to two points generated
randomly and makes a check whether there is a dependency
between tasks at these points or not. If no dependency, swap
their position with VM number. Otherwise, generate another
mutation point which allows mutation. As an example,
Suppose the mutation point for parent 1 in Fig. 4 are (2 and 5).
Now, check whether task 2 and task 5 are dependencies or not.
Because there is no dependency between them, swap them and
generate a new solution (see Figure 6).
5. Enhancement Population
Two modifications have been introduced to enhance
population. According to the first modification, bad solutions
will be considered besides the good ones instead of replacing
them as in the default GA algorithm. These will help to
generate an optimal solution.
According to the second modification, new chromosomes
will generate randomly and involve in the population after each
iteration to enhance the diversity of the population. These
random chromosomes are considered 5% of the chromosomes
in the population. The toleration of this percentage could be
considered as a future work.
Figure 5. New Model of Crossover Process [3]
Parent 1 Child 1
Crossover
Copy
Parent 2 Child 2
Child 3
Child 4
Before mutation
After mutation
T 1 T 5 T 7 T 3 T 2 T 6 T 4
T 1 T 5 T 7 T 3 T 2 T 6 T 4
Figure 6. New chromosome after mutation.
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TABLE 2 THE COMPLETION TIME OF RRA, RA, GA, AND DTGA
ALGORITHMS USING 4 VMS
No. Task RRA RA GA DTGA No. VM
50 295.32 261.25 233.05 167.23
4100 564.59 505.3 455.6 322.29
300 1,511.02 1,369.48 1,211.29 801.93
TABLE 4 THE COMPLETION TIME OF RRA, RA, GA, AND
DTGA ALGORITHMS USING 12 VMS
50 107.22 99.82 80.51 56.07
12100 236.7 192.43 172.39 110.16
300 702.95 584.1 499.07 335.46
0
200
400
600
800
1000
1200
1400
1600
50100300
Time(second)
Number of Tasks
RRA
RA
GA
DTGA
Figure 7. the comparison completion time of four algorithms RRA, RA,
GA and DTGA.
V. PERFORMANCE EVALUATION
In this section, the experimental evaluation of the proposed
DTGA algorithm relative to the default GA, Random
Algorithm (RA) and Round-Robin algorithms is presented.
A. The Experimental Environment
Workflow scheduling can be composed of a large number
of tasks and execution of these tasks may require many
complex modules and software. Also, the evaluation of the
performance of workflow optimization techniques in real
infrastructure is complex and time consuming. As a result, the
simulation-based studies have become a widely accepted way
to evaluate workflow system.
On the other hand, WorkflowSim simulator is considered
the commonly used simulator to implement and evaluate the
performance of task scheduling algorithms in the Cloud
computing. It is considered an extension of the existing
Cloudsim simulator by providing a higher layer of workflow
management [28].
B. Experimental Results
By using WorkflowSim toolkit, the proposed DTGA algorithm
is implemented, and a comparative study has been made among
four algorithms; Round-Robin Algorithm (RRA), Random
Algorithm (RA), the default GA, and the developed DTGA
algorithms using benchmark programs [29]. The Completion
time is considered to evaluate the performance. The used
benchmark programs are listed in Table 1.
The completion time of RRA, RA, default GA and the
proposed DTGA algorithms using 4, 8 and 12 VMs and tasks
of Random graphs are represented in Tables 2, 3, 4 and
Figures. 7, 8, and 9.
Tables 5, 6 and 7 illustrate the completion time improvement
No. Task Notes
50 Random graphs
100 Random graphs
300 Random graphs
88 Robot control program
96 Sparse matrix solver
TABLE 1 SELECTED BENCHMARK PROGRAM [29].
TABLE 3 THE COMPLETION TIME OF RRA, RA, GA, AND DTGA
ALGORITHMS USING 8 VMS
50 175.71 157.91 138.47 87.4
8100 349.77 325.17 291.94 171.9
300 1,009.31 945.51 862.82 537.01
Figre 8. the comparison completion time of four algorithms RRA, RA, GA
and DTGA.
0
200
400
600
800
1000
1200
50100300
Time(second)
Number of Tasks
RRA
RA
GA
DTGA
GA and DTGA.
0
100
200
300
400
500
600
700
800
50100300
Time(second)
Number of Tasks
RRA
RA
GA
DTGA
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Task RRA RA GA DTGA No. VM
Robot 88 629.4 581.02 529.33 375.24
4
Sparse 97 734.05 679.35 588.11 401.52
GA and DTGA.
0
100
200
300
400
500
600
700
800
Robot 97 TsksSparse 88 Tasks
Time(second)
RRA
RA
GA
DTGA
Robot 88 301.12 299.5 241.76 159.2
8
Sparse 97 415.87 374.2 299.47 195.69
Robot 88 215.45 190.4 167.65 113.87
12
Sparse 97 300 271.02 199.05 134.1
GA and DTGA.
0
50
100
150
200
250
300
350
Robot 88 TasksSparse 97 Tasks
Time(second)
RRA
RA
GA
DTGA
for the proposed DTGA algorithm relative to RRA, RA, and
default GA algorithms using 4, 8 and 12 VMs.
Table 8 and Figure (10) represent the completion time of RRA,
RA, default GA and the proposed DTGA algorithms using 4
VMs with the task of Robot control program and Sparse matrix
solver.
Table 9 and Figure, (11) represent the completion time of
RRA, RA, default GA and the proposed DTGA algorithms
using 8 VMs with the task of Robot control program and
Sparse matrix solver.
Table 10 and Figure, (12) represents the completion time of
RRA, RA, default GA and the proposed DTGA algorithms
using 12 VMs with the task of Robot control program and
Sparse matrix solver.
DTGA vs.
No. Task RRA RA GA No. VM
50 43.37 35.98 28.24
4
100 42.91 36.21 29.26
300 46.92 41.44 33.79
Average 44.4 % 37.87 % 30.43 %
TABLE 5 THE IMPROVE COMPLETION TIME OF DTGA VS. RRA, RA,
AND GA ON 4 VMS.
DTGA vs.
50 50.25 44.65 36.88
8
100 50.85 47.13 41.11
300 46.79 43.2 37.76
Average 49.29 % 44.99 % 38.58 %
TABLE 6 THE IMPROVE COMPLETION TIME OF DTGA VS. RRA,
RA, AND GA ON 8 VMS.
DTGA vs.
50 47.7 43.82 30.35
12
100 53.46 42.75 36.09
300 52.27 42.56 32.78
Average 51.14 % 43.04 % 33.07 %
TABLE 7 THE IMPROVE COMPLETION TIME OF DTGA VS. RRA,
RA, AND GA ON 12 VMS.
GA and DTGA.
0
50
100
150
200
250
300
350
400
450
Robot88 TasksSparse 97 Tasks
Time(second)
RRA
RA
GA
DTGA
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DTGA vs.
Task RRA RA GA No. VM
Robot 47.13 46.84 34.14
8Sparse 52.94 47.7 34.65
Average 50.03 % 47.27 % 34.39 %
AND GA ON 8 VMS.
Tables 11, 12 and 13 illustrate the completion time
improvement of the proposed DTGA algorithm relative to
RRA, RA, and default GA algorithms using 4, 8 and 12 VMs
respectively.
According to the results in Table 5, it is found that the
completion time of the proposed DTGA algorithm is reduced
by (44.4%), (37.87%) and (30.43%) with respect to the RRA,
RA and the default GA algorithms respectively. With respect to
the results in Table 6, the completion time of the proposed
DTGA algorithm is reduced by (49.29%), (44.99%) and
(38.58%) relative to RRA, RA and the default GA algorithms
respectively. For the results in Table 7, the completion time of
the proposed DTGA algorithm is reduced by (51.14%),
(43.04%) and (33.07%) relative to RRA, RA and the default
GA algorithms respectively.
According to the results in Table 11, the completion time of
GA algorithms respectively . With respect to the results in
Table 12, the completion time of the proposed DTGA
algorithm is reduced by (50.03%), (47.27%) and (34.39%)
relative to RRA, RA and the default GA algorithms
respectively. For the results in Table 13, the completion time of
GA algorithms respectively.
VI. CONCLUSION AND FUTURE WORK
According to the work in this paper, an improved Genetic
(DTGA) algorithm for dependent task scheduling problem has
been proposed for the Cloud computing environment. The
proposed algorithm targets to minimize the completion time. A
comparative study has been contacted to evaluate the
performance of the proposed algorithm with respect to the
RRA, RA and the default GA algorithms using STC
benchmark (three random graphs, Robot graph, and Spars
graph). According to the comparative results using three
random graphs and 4, 8 and 12 VMs, the completion time of
the proposed DTGA algorithm has been reduced in average by
48.28%, 42%, and 33.98% with respect to RRA, RA and the
default GA algorithms respectively. According to the
comparative results using Robot and Sparse graphs, and 4, 8,
and 12 VMs, the completion time of the proposed DTGA
algorithm has been reduced in average by48%, 43.59%, and
32.38% with respect to RRA, RA and the default GA
algorithms respectively.
Generally, the proposed DTGA algorithm outperforms the
RRA, RA and the default GA algorithms by 48.14%, 42.8%,
and 33.18% respectively in average with respect to the
completion time.
For future work, the proposed algorithm can be extended to
consider the possibility of the dynamic characteristic of VMs.
Moreover, the users QoS requirements would be considered.
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Vol. 15, No. 8, Augus 2017
ISSN 1947-5500

A Modified GA-based Workflow Scheduling for Cloud Computing Environment

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