International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 10, October 2013
ISSN 2319 - 4847
A hybrid algorithm for grid task scheduling
problem
AtenaShahkolaei1, Hamid Jazayeriy2
1
Department of computer engineering, Islamic Azad University, Science and Research Ayatollah Amoli branch, Amol, Iran
2
Babol Noshirvani University of Technology, Iran
Abstract
At the beginning the Grid computing and Grid technologies was used for scientific and technical jobs where computers were
distributed geographically, connected through internet, are used in order to invent virtual supercomputers with high computing
competency. The goal of inventing such a virtual supercomputer was solving complex scientific problems in less time than before.
The goal of task scheduling in Grid systems is decreasing the total completion time of the all tasks with providing a timetable to
perform all existing tasks. The problem of task scheduling in grid systems has large solution space and is considered as a kind of
NP-Hard problems. In this paper a new method for solving task scheduling in Grid computing system is proposed by combining
Genetic Algorithm with Tabu Search Algorithm. The goal of proposed algorithm is to combining the global search abilities of
Genetic Algorithm with local search of Tabu Search, and creating a stable algorithm that highly guarantees the accessing of the
global optima. The proposed algorithm is compared with other heuristic algorithms and experimental results showed that the
proposed algorithm has high efficiency for solving task scheduling in Grid computing.
Keywords:Computational Grids,ETC Matrix, Genetic Algorithm, Tabu Search.
1. INTRODUCTION
Grid computing and its technologiescreates at first for technical and scientific activities in computers where
geographicallydistributed, connected through internet, and used to createvirtual supercomputers with high computing
abilities. The purpose of creating these virtual supercomputers is solving complex scientific problems in less time than
before. Afterwards, Grid Computing was applied for helping and reaching improvements in meteorology, physics,
medicine and other computing-intensive scientific fields. Examples of such works in large scale including optimization
and data-intensive computing are studied in [1]–[7].
The current definition of Grid was introduced for first time by [8] in 1998 as following: "A computational grid is a
hardware and software infrastructure that provides dependable, consistent, pervasive, and inexpensive access to high-end
computational capabilities."
Task scheduling in Grid Computing contains a set of tasks that should be run on a limited set of resources. The purpose
of task scheduling in Grid systems is offering a time table for executing all tasks and decreasing the execution time of all
tasks. The problem of task scheduling in grid systems has large solution space and is considered as a kind of NP-Hard
problems [9], [10].In the past few years, many researches were performed for solving Grid Task Scheduling problems
based on GA [11]–[14] and TS [11], [16]–[18].A hybrid GA (TS) algorithm for the problem of independent scheduling in
computational grids presented in [15]. In their proposed algorithm the hybridization follows a low level approach in
which GA is the main flow and TS is subordinated to it. The experimental evaluation showed that GA (TS) outperforms
both GA and TS for small and medium size grid scenarios but achieves worse value for large size scenario. In this paper,
the proposed algorithm utilize GA and TS together to maintain the global search abilities of Genetic Algorithm and local
search of Tabu Search. In GA(TS) algorithm [15] the TS algorithm used instead of mutation operation, but in this paper,
in the proposed algorithm the TS algorithm execute separately after Crossover and Mutation operations, to optimize
some percent of individuals in GA population.
2. GRID TASK SCHEDULING
The Grid Task Scheduling is including of a set of tasks that should run on limited set of resources. The purpose of task
scheduling in Grid systems is offering a time tablefor executing all tasks, so that the execution time of all tasks minimized
and the computational load of all system divided between all resources equally.
For simulating grid environment, a static environment used that contained at×mmatrix called ETC (expected time to
compute); the model offered by [11] is used. Any row in ETC matrix shows the estimated execution times for a given task
on each machine. Thus, for an arbitrary taskti and an arbitrary machine mj the entryETC(ti ,mj)is the estimated execution
time of running task i on machine j.
In simulated model, the purpose of heuristic algorithm is minimizing the metatask execution time that is called
themakespan. Consider that the earliest time machine can complete the execution of all the tasks that have previously
been assigned to it, called Machine availability time. Thus, the completion time for a new task on machine will
define by relation (1):
Volume 2, Issue 10, October 2013
Page 343
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 10, October 2013
ISSN 2319 - 4847
(1)
ct ( t i , m j )  mat ( m j )  ETC (t i  m j )
Where matis machine availability time for machinemjandctis the completion time for taskti on machinemj. With having
the amount of
for each task, the metatask execution time (makespan) will calculate by relations (2).
makespan
 max


i
t
m


 ct ( t i  m j ) 

 0 j  0

(2)
3. PROPOSED ALGORITHM
In this paper a new method for solving task scheduling in Grid computing system is proposed by combining Genetic
Algorithm with Tabu Search Algorithm that will describe in this section. For displaying chromosomes a 1 × t vector is
used[15], where t is equal by the number of all available tasks for processing. Each chromosome in the proposed
algorithm shows apossible mappingfor all tasks of users. In the proposed algorithm parents are selected using
therankingmethod, and the chosen operator for generating new children is single point crossover. After generating new
children the mutation operator is used for making diversity in children population. Swap and Transfer are two types of
methods that selected for mutation. The main purpose of these mutations is changing tasks between different machines to
process the tasks with more suitable machines.
In Population Optimizations step, some percentages of available chromosomes optimized by Tabu Search algorithm and
added to the genetic population as new children. Tabu Search algorithm receive one genetic chromosome as base solution,
and try to optimize the chromosome with its operators in some iterations.
In the proposed Tabu Search algorithm, at first a solution will create in neighborhood of current solution. Then, the index
of tasks that has a role in generating the new neighbor will locate in the tabu list, to forbidden these tasks to participate in
generating new neighbors. In following, if the generated neighbor be better than the best solution produced so far, the
generated neighbor will select as the best solution and the structures of memory will updated. This cycle of generating
neighborhood will repeat in numbers that was determined before, and finally the Tabu Search algorithm will return its
best solution to Genetic Algorithm.
The proposed algorithm get terminated if no improvement observed in chromosomes in a predefine number of generation.
Figure 1 shows the flowchart of the proposed algorithm.
Figure1: Flowchart of the proposed algorithm
4. EXPERIMENTAL RESULTS
To evaluate the performance of the proposed algorithm, it is compared with other heuristic algorithms in [11]. The
proposed algorithm was implemented in C# 2010 and the tests were made on a Pentium IV 3.00GHz processor with 1.00
GB of RAM.For testing the proposed algorithm in simulated environment, 9 test data set based on different type of ETC
matrices are designed, each of them consisting of 100 instances. They are labeled as Test_X_YZ_N where X is the type of
ETC matrices(C - consistent, I – inconsistent and p means partially consistent), Y and Z indicate the task and machine
heterogeneity. Their value could be H for maximum heterogeneity and L for the minimum heterogeneity. N is used to
number the corresponding test. For example, if a test labeled as Test_C_HH_10, it means that, in this test a consistent
matrices is used with maximum heterogeneity for tasks and machines.In test of the proposed algorithm, all test data sets
are composed from 512 jobs and 16 machines. Various GA and TS options used are:
Population size = 100
Crossover probability = 0.75
Volume 2, Issue 10, October 2013
Page 344
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 10, October 2013
ISSN 2319 - 4847
Mutation probability = 0.25
Tabu Search neighborhood size = 20
tabu_tenure = 5
The proposed algorithm for any test performed 100 times and the average of fitness values is calculated by the proposed
algorithm. Figure 2 shows the output of Test_C_HH_1 in Gant chart. This Chart is consisting of 16 rows and 512 colorful
rectangles that any one of them is showing one of the 16 machines and 512 works in the simulated system.
Figure2: Gant chart of Test_C_HH_1
In Figure 3 the chart of movements of best chromosome in genetic population is shown,that represents high speed of
algorithm in achieving to optimal solution. In this chart tilt of curve will decrease during the time, and finally it’s stopped
in local optima.
Figure3: Fitness of the best chromosome in Genetic Population
Table1 shows the result of several tests that obtained to optimal solutions. In Table 1, the first column presents test name,
and other results such as the best iteration that optimal solution obtained, the total running time for the proposed
algorithm, the time that optimal solution obtained, and fitness of the optimal solution are presented in other columns
respectively.
Table 1: The result of some tests
Test Data
Best Iteration
Run Time
Best time
Best fitness
Test_C_HH_
1
40115
785
767
7234264
Test_I_HH_1
69897
1358
1339
3103133
Volume 2, Issue 10, October 2013
Page 345
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 10, October 2013
ISSN 2319 - 4847
Test_P_HH_1
57390
1104
1086
4425099
Figure 4 shows the chart of average running time for the proposed algorithm and other heuristic algorithms [11]. In
Figure 4 the average running time of proposed algorithm shown with red color.
Figure4: Average run time of the proposed and other heuristic algorithms
Figure 5 shows the comparison of makespan obtained by the proposed algorithm and other heuristic algorithms [11]. As
you can see in Figure 5 the proposed algorithm obtained better optimal solution in comparison with other heuristic
algorithms.
Figure5: Comparison of makespan versus other algorithms in the literature
5. CONCLUSION
In this paper a new method for solving task scheduling in Grid computing system is proposed by combining Genetic
Algorithm with Tabu Search Algorithm. The goal of proposed algorithm is to minimizing the execution time of all tasks
and dividing the computational load of the whole system between all resources equally. To evaluate the performance of
the proposed algorithm, it is compared with other heuristic algorithms, and experimental results showed that the proposed
algorithm has high performance for solving task scheduling in Grid computing. For future works, the effect of selecting
other type of operations and parameters on the quality of solving problem in proposed algorithm could be examine.
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 10, October 2013
ISSN 2319 - 4847
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AUTHOR
AtenaShahkolaei received her B.S. in IT Engineering from University of Ghaemshahr, Iran and received her
M.S. degree in Software Engineering from Science and Research University of Amol, Iran. She is a reader in
Grid Computing, Cloud Computing and she has done a lot of researches about Grid Computing in recent years.
Hamid Jazayeriy is a lecturer at the faculty of electrical and computer engineering, NIT, IRAN. He received
his B.Sc. of computer engineering from university of Tehran in 1996 and his master of software engineering
from university of Isfahan in 2000. In 2011, he received his Ph.D. from university Putra Malaysia, UPM. He is
a reader in multi-agent systems, swarm intelligence and graph theory.
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