Institute of Advanced Engineering and Science
IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 1, No. 4, Dec 2012, pp. 171~181
ISSN: 2252-8938
171
Independent Task Scheduling in Grid Computing Based on
Queen-Bee Algorithm
Zahra Pooranian*, Mohammad Shojafar**, Bahman Javadi***
* Department of Computer Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran
** Electrical and Computer Department, Qazvin Islamic Azad University, Qazvin, Iran
*** School of Computing, Engineering and Mathematics, University of Western Sydney, Sydney, Australia
ABSTRACT
Article Info
Article history:
th
Received August 05 , 2012
Revised Oct 1st, 2012
Accepted Oct 16th, 2012
Keyword:
Grid computing
Scheduling
Queen-Bee
PSO
Genetic
SA
Grid computing is a new model that uses a network of processors connected
together to perform bulk operations allows computations. Since it is possible
to run multiple applications simultaneously may require multiple resources
but often do not have the resources; so there is a scheduling system to
allocate resources is essential. In view of the extent and distribution of
resources in the grid computing, task scheduling is one of the major
challenges in grid environment. Scheduling algorithms must be designed
according to the current challenges in grid environment and they assign tasks
to resource to decrease makespan which is generated. Because of the
complex issues of scheduling tasks on the grid is deterministic algorithms
work best for this offer. In this Paper, the Queen-bee algorithm is presented
to solve the problem and the results have been compared to several other
meta-heuristic algorithms. Also, it is shown that the proposed algorithm
decline calculation time beside decreasing makespan compared to other
algorithms.
Copyright © 2012 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Mohammad Shojafar,
Electrical and Computer Department,
Qazvin Islamic Azad University,
Barajin, Qazvin, Iran. 34197-416, Tel: +98-281-366-5275 Fax: +98-281-366-5279.
Email: Shojafar@qiau.ac.ir
1.
INTRODUCTION
The idea of task distribution has been considered from many centuries ago in order to achieve high
speed and in other words, to save the time. In fact, Grid technology makes it possible to make use of the
resources and decentralized systems and the interconnection of these systems. When the Grid technology
invented for the first time, it just aimed at cooperating the resources of the system and provide a powerful
system and generally it was at the disposal of research institutes. But today, there are higher expectations
from the Grid and much more importance had been dedicated to it, especially in the e-commerce and the
decentralized and distributed commercial systems. The modern Grids could be found in different
organizations like scientific research and medicine detection organizations and also in the analysis of
financial risks, Weather Forecast, designing, simulating, commercial intelligence and the transaction
processing environments all over the world. In fact, Grids make use of the resources of the computers
interconnected with the network and they could perform complex calculations using the resultant power of
these resources. They do this by segmenting this operation and assigning each segment to a computer in the
system.
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One of the most important parts in the Grid systems is scheduler. Due to the vastness of grid and the
assignation of each task to a specific computer and the necessity for each computer to assign a time to the
grid, there is a need to use a scheduler. Scheduling plays the most important role in the improvement of
grid’s efficiency. Weak scheduling increases the execution time and therefore reduces grid’s performance.
Grid system performs hundreds or thousands jobs simultaneously and therefore making weak about the
execution place could notoriously decrease the efficiency. But, effective scheduling or in other words, good
decision – making about the execution place in NP-complete problem that faces with different challenges.
Different scheduling algorithms have been proposed for grid systems; such as, max-min, min-min[1]
and because of the complexity of the scheduling problem, it has been shown that using heuristic algorithms is
more suitable for this purpose, different algorithms such as GA (Genetic Algorithm)[2], PSO (Particle Swarm
Optimization) [3], PSO-SA (Simulated Annealing) [4], TS (Tabu Search) [5], GA-TS [6], GA-SA [7] have
been proposed in this area.
In GGA [8], A combination of two genetic and GELS Algorithms has been proposed to solve the
problem of independent task scheduling. Since genetic algorithm works weakly in local searches, combining
it with GELS Algorithm has improved this problem. In this algorithm, two factors including time and the
number of missed tasks have been considered. On the other hand, GGA takes much time to analyze Tasks
and if the tasks are increased enormously, it is unable to perform good results in task deadlines.
MSA [9] algorithm is a mutated SA algorithm to perform scheduling in the grid. This Algorithm has
been applied to schedule the independent tasks and acts statistically. The difference between static and
dynamic scheduling is that in static scheduling, all the data necessary for the tasks, processors, execution
times and the number of processors are specified a priori. The change in this algorithm in comparison with
standard SA is that in search neighboring step per temperature range more than one neighboring solution is
provided. In other words, the mutated stimulation provides more than one solution and then selects one of
them on the basis of its fitness function. This change provides for better solutions and increases the change
for finding out the global optimization. Its weakness is searching in global problems because, it able to work
in local search for tasks and most of grid tasks are assigned globally to the resources. Global searching means
that algorithm is able to search whole space problem generally, but local searching could have one solution
that searches part of space problem.
GSA [10] is a combination of genetic algorithm and SA for solving the problem of independent task
scheduling. The main function of this algorithm is finding out a solution with the minimum execution time.
Since the genetic algorithm searches the problem space globally and acts weakly in local searches, by mixing
it with SA which is a local searching algorithm. It is tried to resolve this deficiency and this way a mixture of
the advantages of these two algorithms have been used. In a contrary, although GSA is an combined
algorithm which is formed by local and global search, It able to search problem suitable, but, its searching
duration raised dramatically, and it is less beneficial for grid scheduling which is dynamic and needs to
schedule before task deadlines.
In this Study, the Queen-bee [11] algorithm has been used for scheduling independent tasks in
computing grids. In addition to this, also, four other heuristic algorithms have been used including GA, SA,
GSA, PSO-SA and the results of the simulation of these algorithms have been shown.
The aim of this paper is to investigate a new biologic algorithm inspire of bee insects for resolving
scheduling problem with minimized mean makespan and rune-time. The remainder of this paper is organized
as follows. In Section 2, the problem studied in this research is described in detail. In Section 3, the structure
of the proposed algorithms is explained. Then numerical tests are established to solve the problems in section
4. This is followed by a demonstration of the simulation results. Finally Section 5 presents a summary of the
research with concluding remarks and recommendations for further research.
2. PROBLEM DESCRIPTION
The scheduling problem of independent tasks is a NP-hard problem that consists of N tasks and M
machines. Each task should be processed by each M machine, as the Makespan is minimized. In other word,
we have introduced a Deadline (D) for every task as each task should end its implementation before ending
D. Each task can be just implemented on a resource and it is not stopped before finalizing its execution. We
use the expected time to compute (ETC) matrix model. Since the proposed scheduling algorithm is as static,
we have supposed that expected implementation time for each task, i, on each resources j, was determined
before and was set on ETC matrix, ETC[i, j]. In this paper, we propose five meta-heuristic algorithms for the
above problem. The framework of these algorithms is described in the next section.
3. THE PROPOSED ALGORITHMS
In this section, we have offered 5 Meta-heuristic algorithms to solve the scheduling problem of the
grid.
IJ-AI Vol. 1, No. 4, Dec 2012 : 171 – 181
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3.1. Queen-Bee Algorithm
Human being is hard wired to achieve the best, so, the problem of optimization theory have been
raised since a long time ago, but since in most cases recognizing and defining all the dominant conditions is
impossible, instead of the best solution or the absolute optimal solution a satisfactory solution suffices.
Therefore, due to human disability of optimization the improvement receives a specific value. In most cases
the improvement is what is done for optimization. Optimization seeks to improve the performance in order to
reach the optimal point or points. Algorithms which have been obtained inspiring the physical and biological
rules are called heuristic algorithms. These algorithms are able to find out solution approximate with optimal
solutions for the problems that there are or are not optimal solutions for them will the sound calculation time.
Genetic algorithms are the oldest type of Evolutionary algorithms has been widely used to solve the
optimization problems. It was first proposed by John Holland in 1975[12], but Queen Bee [13] algorithm has
been proposed in 2003 for the first time. Queen bee algorithm has got common concepts with genetic
algorithms like, gens, chromosomes. Population crossover and mutation operators – This algorithm has two
major differences with genetic algorithm. First in the normal genetic algorithm, a cost function is calculated
for the initial population and the population is arranged in proportion with increase in this function.
Then some of the worst members of the population are cross out and the rest are selected which
have lower cost for generating descendants. This means that equal numbers of parents are selected and using
crossover algorithm they reproduce some offspring equal to the number of population disposed previously.
So, the new offspring are replaced for the worst population.
In Queen Bee Algorithm, the stages of selecting the initial population and classifying them are on
the basis of the cost function and disposing the worst similar genetic members. But in this algorithm just one
mother is selected which is the Queen Bee and the queen produces a number of offspring by mixing with
male counter parts using crossover operator. Therefore the number of marriages in Queen Bee is less than
this number in genetic algorithm this leads to much speed rate in this algorithm in comparison with the
genetic algorithm. But the high speed rate of convergence results in the emergence of this premature
phenomenon. In this phenomenon, Instead of finding out the optimum result, the algorithm converges to a
local minimum. One of them mutates with a normal mutation rate and the other one does so will strong
mutation by Pm probability rate which is normally higher than Pm; i.e., P’m is higher than Pm. Therefore a
variety is emerged in the offspring will be more and the premature convergence is avoided. The proportion of
these two probabilities is defined equal to the four parameters. You could see the Pseudo-code of the
algorithm in Figure 1.
// t: time //
// n: population size //
// p: populations //
// σ: normal mutation rate //
// Pm: normal mutation probability //
// P’m: strong mutation probability //
// Iq: a queen-bee //
// Im: selected bees //
01 t 0
02 initialize P (t)
03 evaluate P (t)
04 while (not termination-condition)
05 do
06 t t+1
07 select p (t) from P (t-1) (*)
08 P (t) = {Iq (t-1), Im (t-1)}
09 recombine P (t)
10 do crossover
11 do mutation (*)
12 for i = 1 to n
13 if i ≤ (σ x n)
14
do mutation with Pm
15 else
16
do mutation with P’m
17 end if
18 end for
19 evaluate P (t)
20 end
Figure 1. Queen-Bee Pseudo-code
Title of manuscript is short and clear, implies research results (First Author)
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3.2. Genetic Algorithm(GA)
After offering the genetic algorithm by Holland [12], this method was completed in 1989 by
Goldberg [14]. In order to use genetic algorithm to solve task scheduling problem, a number of parameters
must be defined. That is described in the following parts.
• Showing Chromosomes
Here, a simple method has been used to present chromosomes, so that real numbers are used to
coding the chromosomes. So that the numbers of gens are random numbers between 1 to k. k is the resources
N.O. and the length of chromosomes is considered equal to the size of the number of input tasks. Figure 2
show a sample of chromosomes arrangement which is assigned T1 to the resource 2, R2, in chromosome2, and
then the primary population of chromosomes is made randomly.
T1
R1
R2
Chromosome1
Chromosome2
•
T2
R2
R3
T3
R3
R4
T4
R4
R2
Figure 2. The sample of chromosomes illustration
Fitness function
The main purpose that is considered in all proposed algorithms in this paper for scheduling problem
is to make it possible to minimize makespan. This time is considered equal to the maximum completion time
for each task, i, per resource, j, in addition to the Time – Finish [j] that is calculated as equations (1) and (2)
as follow:
Fitness(chromosomei)=
1
makespan(chromosomei )
(1)
Makespan=Max(Time_Finish[j]+ ETC[i,j] ) 1≤i≤N , 1≤j≤M
•
(2)
Selection Operator
Before using mutation and crossover operators, it is the selection step. Here tournament operator has
been used of chromosome selection.
•
Crossover Operator
Two points crossover operator has been used in the proposed algorithm. Therefore, two random
points over two selected chromosomes have been chosen by previous level and the gen between these two
points are transferred in chromosome (Figure 3).
Parents
Children
T1
T2
T3
T4
T5
T6
T7
T8
T9
T1
T2
T3
T4
T5
T6
T7
T8
T9
R3
R3
R2
R1
R2
R3
R1
R1
R3
R3
R3
R2
R3
R1
R2
R1
R1
R3
T1
T2
T3
T4
T5
T6
T7
T8
T9
T1
T2
T3
T4
T5
T6
T7
T8
T9
R1
R3
R1
R3
R1
R2
R2
R1
R3
R1
R3
R1
R1
R2
R3
R2
R1
R3
•
Figure 3. A sample of operation for two-point crossover
Mutation Operator
In the previous level, one point is selected randomly over each chromosome and one random
number in the range of 1 to M is created. Figure 4 shows a sample of this operation.
IJ-AI Vol. 1, No. 4, Dec 2012 : 171 – 181
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T1
R3
•
ISSN: 2252-8938
T2
R3
T3
R2
T4
R3
T5
R2
T6
R3
T7
R1
T8
R1
175
T9
R2
T1
T2
T3
T4
T5
T6
T7
T8
T9
R3
R3
R2
R1
R2
R3
R1
R1
R2
Figure 4. A sample of Mutation Operating
Termination Condition
Algorithm finishes when the iteration time of the algorithm reaches its maximum. The best
chromosome is selected as a solution for scheduling issue.
3.3. Simulated Annealing (SA)
SA method is one of the possible algorithm methods that have been offered for solving optimization
problem by Kirkpatrick [15] in 1983 which has a big searching space. SA method has been originated from
cooling metals. In this method, if each searching space is supposed to be s. Each s' state from searching space
is a reply to the problem. The problem begins with a primary state and moves gradually towards the optimum
solution by transferring from one state to another in searching space. In each iteration, SA algorithm of s’
state is selected as a neighbor and moves towards the next state from the existing possibility to the existing
state or remains in the existing state. This trend continues till the relatively optimum solution is found out or
it continues ill the maximum iteration time of the algorithm is resulted. Accepting the neighboring state as a
reply to this problem is based on a probability. Accepting the neighboring state is considered as a solution for
the problem based on a probability. If the cost of neighboring state is better than that of the existing state, the
neighboring state will be accepted as a solution. The cost of this algorithm is the criteria and parameter that is
used in searching a solution for the problem. So, it could go beyond the scope of the local optimum solution.
In SA method, the temperature parameter (T) is used for achieving the acceptance probability of the
neighboring state, so that first the maximum number of neighbors is selected as a solution and this
temperature gradually reduced by increasing the number of iterations, so that before the finishing time of
maximum iterations, the algorithm execution equals to zero. Therefore, increasing the number of iterations
leads to a decrease in the possibility of accepting the neighboring state that has no better cost saving
advantage for the problem. How T parameter reduces in each step and how to reach the neighboring state in
this algorithm and also determining the primary amount for the temperature parameter (T) and the maximum
number of iterations of max algorithm is considerably important. The Pseudo-code of SA algorithm has been
shown in Figure 5. Showing the primary solution in the algorithm is similar to Figure 1. Also the cost
algorithm is like Equation 1.
t= T0
Initial Solution= S0
Best solution= S0
OF0= Object Function(S0)
OF Best Solution= OF0
For i=1 to Max do {
S1= Generate neighbor(S0)
OF1= Object Function(S1)
If OF1 ≥ OF0 then {
S0= S1
OF0 = OF1
If OF1 ≥ OF Best Solution then {
Best Solution= S1
OF Best Solution= OF1 }
}
Else {
��0 −��1
Accept= � −( � )
r= Random(0,1)
if ( r > Accept) then {
S0= S1
OF0 = OF1
}
}
T= 0.95 *t }// end For
Return (Best Solution)
Figure 5. Simulated Annealing Pseudo-code
Title of manuscript is short and clear, implies research results (First Author)
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3.4. GSA
In this part, hybrid GSA algorithm has been formed by mixing genetic and SA algorithms. Since the
genetic algorithm searches the space of the problem globally and searching local space it hasn’t any ideal
performance, mixing it with SA algorithm which is a local one, it has been tried to improve this weak point
and this way a mixture of the advantages of these two algorithms has been utilized. The illustration form of
chromosomes is like Figure 1; also, fitness function is like Equation 1. The hybrid schema has been shown in
Figure 6. As it is specified in the figure instead of assigning each number of populations to SA, after
finishing the genetic algorithm, the best solution is delivered to SA algorithm so that a solution is made for it.
This could reduce the calculation cost.
Selection
operation
Random initial
population
Best
solution
Mutation/
Crossover
Y
Terminate
condition
N
Genetic algorithm
SA
Outpu
Figure 6. Hybrid proposed for Resolving Scheduling Problem Methodology
3.5. PSO-SA
PSO method has been offered by Abrhat and kennedy [16] in 1995. This method has been inspired
by behavior of bird flocking and schooling fish. In this algorithm, we have a swarm of the particles; the
structure of this algorithm is as follow:
•
Initialize Swarm
The first issue in using PSO to solve optimization problem is to create a correspondence between the
problem and particle vector.
The dimensions of the problem are equal to the number of input tasks. So the length of each particle
and speed vector is considered equal to the number of tasks – the amounts in each particle has been
considered as an integer random number between 1 to K. You see a population of particles in Figure 7. So
that T4 is executed on resource, R4, in particle1. Then, the initial population is produced randomly and then
for each particle an initial velocity vector is produced in which the amounts in the speed vector interval have
been defined:
T1
R3
R4
R2
Particle 1
Particle 2
Particle 3
T2
R1
R1
R1
T3
R3
R1
R4
T4
R4
R2
R2
…
•
Figure 7. Particle Presentation
Fitness Function
In order to estimate each particle defined fitness function in equation 1 has been used. The fitness
amount is calculated for each particle and if the fitness amount of each particle is less than that of pbest of
each particle; new coordinate is set in pbest. It is clear that in the first moment, the coordinate of each particle
is considered as pbest. The best pbest is considered as gbest.
•
Update of the Particles Position
After producing the initial particle population as Xi, a position vector has its own velocity and
fitness amount. In each iteration, the algorithm of position ad velocity amounts changes by Equations (3) and
(4).
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Vi+1= ω Vi + C1 rand1(pbesti - Xi) + C2 rand2(gbesti - Xi)
Xi+1= Xi + Vi+1
177
(3)
(4)
In the above mentioned equation, ω is a factor of inertia weight that is obtained by Equation (5),
pbest is the optimum position of the before particle and gbest is the best position of the previous position of
all particles in all previous steps, Vi is position and the velocity of ith particle, rand1, rand2 are two random
numbers, and C1& C2 are two constant indices.
w = wmax −
wmax − wmin
.iter
itermax
(5)
Where, ω max: Initial value of weighting coefficient;
ω min: Final value of weighting coefficient;
itermax: Maximum of iteration;
iter: Current iteration;
After producing the new population, it is possible that the amounts in the position vector are decimal
position amounts which are invalid amounts for resources number. So, in the offered algorithm, the nearest
obtained decimal amount is rounded to the nearest integer number. This trend keeps on going so that the
algorithm reaches its maximum iteration number.
•
Update gbest by SA
After finishing PSO algorithm, gbest is obtained from it is considered as the best solution to this
problem. Since PSO algorithm works weakly in the local search, in order to keep away from falling into a
local optimum, achieved gbest from PSO is given to SA in order to produce a neighboring solution.
4.
EXPERIMENTAL RESULTS AND ANALYSIS
In this section, the result achieved from proposed algorithm is described and it is compared with other
algorithms. Here, performance measurement is considered makespan minimizing. All algorithms are
simulated in java environment on a PC with CPU 2.66 GHZ and RAM 4GB. Table 1 illustrates initialized
parameters in proposed algorithm. The simulated results are shown in Table 2.
Here, achieved results are surveyed for 100 and 300 iterations. Also, task numbers are changed in
iteration between 50 to 500 and resource numbers between 10 to 30 resources. As a result, Queen-bee
algorithm provides better result compared SA, GA, and GSA. Moreover, it produces less makespan
compared to combined algorithm (PSO-SA) in three parameters.
Table 1. Tuned Values of the Parameters of the Algorithms
Algorithms
Parameter
Value
Vmax
number of resources
PSO
C1,C2
1
Initial Velocity
[1, W max]
ω max
0.9
ω min
P-Crossover
0.1
0.85
P-Mutation
0.02
Pm
0.01
P’m
0.6
Genetic
Queen-Bee
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Table 2. Comparison of makespan produced by different algorithms
(task,
resource)
(50,10)
(50,20)
(50,30)
(100,10)
(100,20)
(100,30)
(300,10)
(300,20)
(300,30)
(500,10)
(500,20)
(500,30)
(50,10)
(50,20)
(50,30)
(100,10)
(100,20)
(100,30)
(300,10)
(300,20)
(300,30)
(500,10)
(500,20)
(500,30)
iteration
100
300
SA
GA
GSA
PSO-SA
Queen-bee
136.742
98.944
71.442
307.738
190.862
138.632
973.728
585.848
384.928
1837.662
833.996
721.596
131.12
74.832
62.055
233.2
173.116
120.452
911.68
523.33
408.714
1492.616
893.262
626.162
99.198
62.496
50.53
183.49
111.1742
99.25
638.082
352.698
262.166
1105.56
602.174
449.73
89.486
60.87
47.637
172.628
111.946
90.716
570.466
327.522
253.132
1071.014
602.134
430.32
95.562
60.968
49.476
190.353
111.646
89.822
597.8
337.648
256.664
1072.362
571.796
446.646
86.98
57.304
42.932
179.062
105.314
87.846
532.968
337.428
246.48
1037.942
593.116
412.7152
89.586
53.266
40.45
167.33
100.714
73.318
511.532
288.962
216.402
887.195
504.33
352.978
87.694
53.77
41.208
167.16
100.098
70.572
526.71
296.168
205.496
896.586
493.9
339.331
93.5
60.85
45.0
177.83
105.62
73.71
521.0
315.25
248.66
1018.33
556.33
419.75
84.6
52.75
45.14
167.57
94.6
79.0
541.5
343.33
246.33
959.16
557.0
400.25
In Table 3 illustrates implementation time for proposed algorithms for 100 and 300 iterations. In
fact, Queen-bee algorithm consumes less time rather than others. Hence, although it is important to run tasks
in allotted resources in least possible time and based on grid environment is dynamic, proposed algorithm is
more suitable compared to others.
Table 3 . Algorithms Compare in Terms of Runtime
iteration
100
300
(task,
resource)
(50,10)
(50,20)
(50,30)
(100,10)
(100,20)
(100,30)
(300,10)
(300,20)
(300,30)
(500,10)
(500,20)
(500,30)
(50,10)
(50,20)
(50,30)
(100,10)
(100,20)
(100,30)
(300,10)
(300,20)
(300,30)
(500,10)
(500,20)
(500,30)
SA
GA
GSA
Queen-bee
0
0
0
0.2
0.8
1.4
1
1.6
2.4
1.4
2.8
3.4
0.4
1.4
1
1
2
1.8
2
3.8
3.8
3.2
5.4
6.2
2.6
3.4
3.4
8.8
5.4
6
13.4
15.4
16
21.2
22.2
26
28.2
29.2
26.6
28.2
44.6
48.8
105.4
99
108.6
90.8
111
176.6
3
3.4
3.6
5.6
6.6
7.4
16.2
18.4
20
25.8
30
31.8
10.6
12.4
12.8
17
20
21.4
48.2
55
58.2
78.6
90.4
93.2
2
2
2
5
5
4
12
12
13
19
20
22
6
8
7
10
12
13
32
38
39
53
65
65
Figure 8 provides comparison of makespan between algorithms for 300 iterations in 50 independent
tasks with {10, 20, 30} resources.
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140
Makespan Comparison (in 300 Iterations)
120
100
(task, resource)
80
(50,10)
(50,20)
(50,30)
60
40
20
0
Figure 8: Makespan Comparison among algorithms for 300 iterations
In Figure 8, PSO-SA is the best (lowest makespan) for (50, 10) state and SA is the worst one.
Besides, while resources increase and reached to its double one, Queen-bee (proposed method) is the best
one, although SA is fallen dramatically but it still the worst one. But, while resources are reached to 30, PSOSA will be the best, because, if we have sufficient resources PSO will be free to use them and allocate tasks
to these 30 resources in less waiting time for each task in the queue of each resources. Moreover, while we
have tested 50 tasks in 10 resources (50, 10) in SA algorithm, we have seen makespan has just upper than
130 units but rest of them has less than this amount. When resources increase, Queen-Bee algorithm declines
makespan more than half of its amount compared to other algorithms (just upper than 40 units).
35
Runtime Comparison (in 100 Iterations)
30
(task, resource)
25
(500,10)
(500,20)
(500,30)
20
15
10
5
0
SA
GA
GSA
Queen
Figure 9: Runtime Comparison among algorithms for 100 iterations
Figure 9 illustrates runtime of GA, SA, GSA, and Queen Algorithms for 500 tasks in different
resources in 100 iterations. In Figure 9, GSA is the worst time consumer and SA is the least time consumer.
Although, SA has the best solution among these algorithms but it produce worst makespan, because, it would
locally in problem space and it could not search space of the problem clearly, hence, it could not produce an
optimum result for makespan, so, we do not consider this method among others. As a result, Queen is the
best method among others in runtime. As is shown, while free resources are grown, all algorithms takes more
time to search and allocate tasks among the queue of resources. The rate of increment in Queen is less than
others (approximately 4 seconds). For example, in (500, 20) state, runtime in GSA is 30 seconds; in GA just
upper than 20 seconds, and in Queen is just lower than 20 seconds.
Title of manuscript is short and clear, implies research results (First Author)
180
5.
ISSN: 2252-8938
CONCLUSION
Nowadays, increase the complexity and the necessity to improve the calculating power is
considered as a characteristic of scientific issues. Therefore, creating and optimizing the computing grid
systems have been considered very much. Scheduling in the grid is one of the most important problems in
determining the efficacy. Considering that the grid scheduling is a nondeterministic problem, hence,
deterministic algorithms are not suitable. There are many heuristic methods to improve scheduling in the grid
that could be utilized.
In this paper, Queen-Bee algorithm was used for scheduling the independent tasks and was
compared with four other offered algorithms. The calculation results showed that the proposed algorithm
produces less makespan then GA, SA, GSA algorithms and it is also more suitable regarding the execution
time.
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IJ-AI Vol. 1, No. 4, Dec 2012 : 171 – 181
IJ-AI
ISSN: 2252-8938
181
BIBLIOGRAPHY OF AUTHORS
Zahra pooranian received her Msc in Computer Architecture degree as honor student in Dezful
Islamic Azad University since 2011. She is an instructor in Sama University in Dezful and
Ahvaz since 2009. Her research interest in Grid computing specially in resource allocation and
scheduling. She has worked on several papers in decreasing time and makespan in grid
computing by using several AI methods such as GA, GELS, PSO, and ICA. She has published
more than 5 papers especially in grid scheduling and resource allocation in various conferences,
such as WASET 2010-11, ICCCIT 2011, and ICEEE 2011.
Mohammad Shojafar Received his Msc in Software Engineering in Qazvin Islamic Azad
University, Qazvin, Iran in 2010.Also, he Received His Bsc in Computer Engineering-Software
major in Iran University Science and Technology, Tehran, Iran in 2006. Mohammad is
Specialist in Network Programming in Sensor field and Specialist in Distributed and cluster
computing (Grid Computing and P2P Computing) and AI algorithms (PSO, LA, GA). He
Published two Journals in IEEE, 4 papers in IEEE, 2 papers in WASET, and two papers in
WORLDCOMP Conferences Series held in USA till now. Now, Mohammad is a Faculty of
Somesara Islamic Azad University in Iran. Moreover, He is a system analyzer in FFSDB project
in Exploration Directorate in N.I.O.C.
Dr Bahman Javadi is a Lecturer in Networking and Cloud Computing at the University of
Western Sydney. Prior to this appointment, he was a Research Fellow at the University of
Melbourne, Australia. From 2008 to 2010, he was a Postdoctoral Fellow at the INRIA RhoneAlpes, France. He received his MS and PhD degrees in Computer Engineering from the
Amirkabir University of Technology in 2001 and 2007 respectively. He has been a Research
Scholar at the School of Engineering and Information Technology, Deakin University, Australia
during his PhD course. He has served on program committees for multiple international
conferences and workshops and was co-guest editor of a special issue of the Journal of Future
Generation Computer Systems on Desktop Grids.
Title of manuscript is short and clear, implies research results (First Author)