Proposing a New Job Scheduling Algorithm in Grid Environment Using a Combination of Imperialist Competition Algorithm (ICA) and Gravitational Emulation Local Search (GELS)

International Journal of Computer Applications Technology and Research
Volume 5–Issue 10, 641-647, 2016, ISSN:-2319–8656
www.ijcat.com 641
Proposing a New Job Scheduling Algorithm in Grid
Environment Using a Combination of Imperialist
Competition Algorithm (ICA) and Gravitational Emulation
Local Search (GELS)
Arman Alizadeh
Department of Computer
Science and Research Branch
Islamic Azad University, Kish, Iran
Ali Harounabadi
Islamic Azad University
Central Tehran Branch
Mehdi Sadeghzadeh
Islamic Azad University
Mahshahr,Iran
Abstract: Grid computing is a hardware and software infrastructure and provides affordable, sustainable, and reliable access. Its aim is
to create a supercomputer using free resources. One of the challenges to the Grid computing is scheduling problem which is regarded
as a tough issue. Since scheduling problem is a non-deterministic issue in the Grid, deterministic algorithms cannot be used to improve
scheduling. In this paper, a combination of imperialist competition algorithm (ICA) and gravitational attraction is used for to address the
problem of independent task scheduling in a grid environment, with the aim of reducing the makespan and energy. Experimental results
compare ICA with other algorithms and illustrate that ICA finds a shorter makespan and energy relative to the others. Moreover, it
converges quickly, finding its optimum solution in less time than the other algorithms.
Keywords: Grid computing, scheduling, artificial intelligence algorithm, imperialist competition algorithm (ICA), Local search
algorithm following the gravitational attraction
1. INTRODUCTION
Application of a new technology, or scientific evolution,
requires scientific proof and practical implementation. Because
it is time-consuming to implement practical research and
mistakes can arise because of in attention to problems in
theoretical subjects, there is a need to use simulations in some
contexts instead of real implementations. The computations that
are needed to simulate and study all aspects of scientific research
projects require a significant amount of computational power
that a single computer would take too much time to provide.
Superscalar computers, vector processors, and pipeline
processing were proposed to address this problem. Although
they provide more computational power and greater speed than
a single computer, technological limitations related to speed and
the high cost of their design and manufacture make them
available only to users with no financial limitations. Grid
computations, which are based on distributed systems, were
proposed to solve such problems. Grid systems have been
proposed as a solution overcoming the limitations of hardware
availability and computer locations, so that unused computers
and their computational power can be exploited [1]. Grid
computing systems are well-known for solving complicated
large-scale problems in science, engineering, and finance [2],
and have provided a wide range of heterogeneous and
distributed resources for data-intensive computations [3].
In recent years, grid computing has been the subject of much
research and has been used in commercial environments [4]. A
resource management system (RMS) is the most important
component of grid computing; it has a significant role in
controlling and supervising the usage of resources. The most
important function of an RMS is to schedule incoming tasks,
assigning them to available compatible resources [5]. However,
the heterogeneous and dynamic state of resources in grid
systems poses difficulties, particularly when combined with
complex task scheduling. Deterministic algorithms don’t have
the necessary efficiency to solve these scheduling problems, so
a considerable amount of research has been devoted to using
heuristic algorithms such as genetic algorithms (GAs) [6],
simulated annealing (SA)[7], particle swarm optimization (PSO)
[8], ant colony optimization (ACO) [9], Queen-Bee Algorithm
[10], tabu search (TS) [11], and various combinations of these
[12, 13, 14, 15, 16] to produce better results in reasonable time.
The heuristic ICA [17], proposed in 2007, was inspired by the
sociopolitical evolution of imperial phenomena and has been
used for solving many optimization problems in continuous
space. This paper proposes a discrete version of ICA for solving
the independent task scheduling problem in grid computing
systems. The present paper converts ICA from a continuous state
algorithm to a discrete state algorithm by changing the
assimilation stage. The resulting algorithm is compared with GA
and other heuristic algorithms and is shown to produce better
results than these. This algorithm simultaneously considers
makespan and completion time and energy by using appropriate
weights in the mean total cost function.
2. BACKGROUND
2.1 Scheduling Method
The scheduling task issue is considered as a tough challenge
which is composed of n tasks and m resources. Each task must
be processed by a machine and does not top until the end of the
performance. We used ETC matrix model described in [18]. The
system assumes that the expected execution time for each task i,
on every resource j is predetermined and is located in the matrix
ETC, ETC [i, j]. Here, makespan is regarded as the maximum
completion time in CompleteT [i, j], calculated in the following
equation (1) [19]:
Makespan = Max (completeT [i,j]) 1 ≤I≤ N, 1 ≤j≤ M (1)
In the above equation, CompleteT[i, j] is equal to the time when
the task i on the source j is completed and it is calculated in
equation (2):
completeT [i,j] = Ready [M] + ETC [i,j] (2)

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2.2 Imperialist Competition Algorithm
The imperialist competition algorithm (ICA) proposed by
(Atashpaz -Gargari and Lucas 2007) is a mathematical modeling
of imperialist competitions. Similar to other evolutionary
algorithms, the ICA algorithm begins with a number of initial
random populations. Each random population is called a
country. The possible solutions for ICA are called countries. A
number of the best elements of the population are selected as
imperialists, others which are governed by Imperialists are
called colonies. By applying an assimilation policy in the
direction of various optimization axes, imperialists gain the
favor of their colonies. The total power of each empire is
modeled as the sum of the imperialist power and a percentage of
the mean power of its colonies. After the initial formation of
empires, imperialistic competition starts among them. Any
empire that has no success in the imperialistic competition with
nothing to add to its power is eliminated from the competition.
So the survival of an empire depends on its power to assimilate
competitor’s colonies. As a result, the power of greater empires
is gradually increased in imperialistic competitions and weaker
empires will be eliminated. Empires have to make
improvements in their colonies in order to increase their power.
For this reason, colonies will eventually become like empires
from the point of view of power, and we will see a kind of
convergence. The stopping condition of the algorithm is having
a single empire in the world.
2.3 Local Search Algorithms Following
Gravitational Attraction
In 1995, Voudouris and his colleagues [20] suggested GLS
algorithm for searching in a searching space and NP-hard
solution for the first time. In 2004, Vebster [21] presented it as
a strong algorithm and called it GELS algorithm. This algorithm
is based on gravitational attraction and it imitates the process of
nature for searching within a searching space. Each response has
different neighbors which can categorize based on a criteria
which is depended on the problem. Obtained neighbors in each
group are called neighbors in that dimension. For each
dimension, a primary velocity was defined which each
dimension has much primary velocity has more appropriate
response for problem. GELS algorithm calculated gravitation
force within responses in a searching space in two ways. In the
first method, a response is selected from local neighbor space of
current response and the gravitation force between these two
responses was calculated. In the second method, the gravitation
force among all of the neighbor responses in a neighbor space of
current response was calculated and it is not limited to one
response. In the movement into searching space, GELS
algorithm implements in two methods: the first method is
allowed movement from current response to in local neighbor
spaces of current response, the second method is allowed
movement to the responses out of local neighbor spaces of
current response in addition to allowed neighbor responses of
current response. Each of these transference methods can be
applied with each accounting methods gravitation force, thus,
four models are created for GELS algorithm.
2.3.1 Parameters Used in GELS Algorithm
(a) Max velocity: Defines the maximum value that any element
within the velocity vector can have used to prevent velocities
that became too large to use.
(b) Radius: Sets the radius value in the gravitational force
formula; used to determine how quickly the gravitational force
can increase (or) decrease.
(c) Iterations: Defines a number of iterations of the algorithm
that will be allowed to complete before it is automatically
terminated (used to ensure that the algorithm will terminate).
(d) Pointer: It is used to identify the direction of movement of
the elements in the vectors.
2.3.2 Gravitational Force (GF)
GELS algorithm uses the formula (3) for the gravitational force
between the two solutions as
𝐹 = 𝐺 +
(𝐶𝑈−𝐶𝐴)
𝑅2 (3)
Where
G = 6.672 (Universal constant of gravitation)
CU = objective function value of the current solution
CA = objective function value of the candidate solution
R = value of radius parameter
3. PREVIOUS RESEARCH
A large number of heuristic algorithms have been proposed for
grid scheduling. Most of them try to minimize the maximum
completion time of tasks, or makespan. Each task has its own
deadline, and we try to decrease the makespan in order to
prevent tasks from failing to execute because of their deadlines.
That is, decreasing the makespan results in the ability to execute
more tasks in the network. It also helps to provide efficient
resource allocation and energy utilization.
The hierarchic genetic strategy (HGS) algorithm was proposed
in [22] for scheduling independent tasks in a grid system and is
implemented in dynamic grid environments in batch mode. This
algorithm simultaneously considers optimization of flow time
and makespan. The authors generate root nodes based on two
other algorithms: longest job to fastest resource and shortest job
to fastest resource (LJFR-SJFR) [23] and minimum completion
time (MCT) [24], and they generate the rest of the population
stochastically. In LJFR-SJFR, initially, the highest workload
tasks are assigned to machines that are available. Then the
remaining unassigned tasks are assigned to the fastest available
machines. In MCT [24], tasks are assigned to machines that will
yield the earliest completion time.
Balanced job assignment based on ant algorithm for computing
grids called BACO was proposed by [25]. The research aims to
minimize the computation time of job executing in Taiwan
UniGrid environment which focused on load balancing factors
of each resource. By considering the resource status and the size
of the given job, BACO algorithm chooses optimal resources to

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process the submitted jobs by applying the local and global
pheromone update technique to balance the system load. Local
pheromone update function updates the status of the selected
resource after job has been assigned and the job scheduler
depends on the newest information of the selected resource for
the next job submission. Global pheromone update function
updates the status of each resource for all jobs after the
completion of the jobs. By using these two update techniques,
the job scheduler will get the newest information of all resources
for the next job submission. From the experimental result,
BACO is capable of balancing the entire system load regardless
of the size of the jobs. However, BACO was only tested in
Taiwan UniGrid environment.
4. THE PROPOSED ALGORITHM
The proposed algorithm for task scheduling is a combination of
ICA and GELS which is used for scheduling of independent
tasks in computational grid environment. According to ICA’s
high performance in scheduling problems, a simple method for
country representation is taken into consideration firstly. Natural
numbers are used to encrypt countries. The value in each country
is resource number ranging from 1 to M, where M is the number
of all resources. Fig.1 illustrates an example of countries
representation where 9 tasks are assigned to 3 resources. As
Figure depicts, for example task 4 (T4) is running on resource
1(R1).
Fig. 1. Country representation in ICA-GELS Algorithm.
Fig. 2. The amount of consumed energy for each task time unit.
Pj,i is considered as a 1*M array where M is the number of
resources. The value in each entry represents the amount of
consumed energy for executing a task. Fig 2 shows a sample
matrix where the consumed energy per each task time unit in
second resource (R2) is 250 J. The initial population of countries
in the ICA is generated randomly. A random number between 1
and M is generated which is the resource number and the
intended task will be execute on it. The independent task
scheduling problem includes M tasks and M machines. Each
task should be processed by one of the machines in way that
makespan get minimum. Proposed algorithm takes two QoS
parameters such as energy and time limitation into
consideration. Each task can be execute on one resource and will
not stop until execution is completed. Our algorithm applies
ETC matrix model. Considering that proposed scheduling
algorithm is static, it is assumed that expected execution time is
determined for each task on each resource at prior and it is stored
in ETC [i, j]. Also, Ready time [M] determines the time that
machine M completes the previous assigned task. Makespan is
considered as maximum completion time (completeT(i, j)),
which is computed using equation (4).
Makespan = Max (completeT [i, j]) (4)
completion _time [i, j] is the time when task i completes on
resource j and it is computed using equation (5) and TransferC
and wait (i, j) are respectively the data transfer time and waiting
execution time.
completeT (i, j) = ETC [i, j] + TransferC + wait (i, j) (5)
The objective of scheduling in the proposed algorithm is to map
each task to each resource in way that makespan and total loosed
tasks get minimum. For example, ETC matrix (table (1))
presents 9 tasks and 3 resources.
Table 1. ETC matrix
Task/Resource P1 P2 P3
T1 2 3 1
T2 2 5 3
T3 1 3 4
T4 4 5 6
T5 8 5 6
T6 3 5 4
T7 4 2 4
T8 4 6 7
T9 2 3 1
4.1 The objective and fitness function in
proposed algorithm
The main idea behind task scheduling is to minimize the
makespan, which is the total execution time for all tasks. To
solve task scheduling by ICA, a country is more suitable that
minimize makespan and total consumed energy for all tasks.
Equation (6) describes the first fitness function for each country.
Also, equation (7) and (8) compute the energy consumption for
each solution.
Fitness1 (Ci) = α ×
1
FTime (Ci)
+ (1 − α) ×
1
E (Ci)
(6)
E (Ci) = ∑ ∑ Ei,j
N
i=1
M
j=1 (7)
Ei,j = (Pj,i−Ij)ETC [i , j] (8)
Where E is the total consumed energy to execute all tasks in
country i and Pj,i is the consumed energy for executing task i on
resource j. Also Ij is the consumed energy of resource i when the
resource is ideal. It can be concluded from equation (6) that
when the consumed enregy and makespan are minimzied, the
fitness function is maxmized and shows the more suitable
solution to the problem. Also the coeffiction α determines the
impact of each parameter on fitness value. For example Fig. 3
illustrates a solution to the scheduling problem. Considering the

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ETC matrix in table (1), the makespan equals to 12. Fig. 3 shows
the total scheduling length for countries.
Fig. 3. Total scheduling length for countries
4.2 Second fitness function
As stated before, the main objective of task scheduling is to
minimize the makespan. It is possible to have several countries
with similar total scheduling time but with different workload
on their resources. Therefore, second fitness function takes this
factor into consideration. Such that, after achieving solutions
with minimum makespan, second fitness function will be
applied to them aiming at acquiring balanced solution in terms
of workload. To gain maximum balanced workload, the fitness
value should be computed for resources. To achieve the value of
balanced workload we are have to compute sum of standard
deviation. It is clear that we should compute the fitness for
resources firstly. Equation (9) shows the second fitness function
for balanced workload computing.
Fitness2(Counteryi) =
1
RUi
(9)
At fires maximum exaction time is specified using equation (10).
E = Max {Tij + τij} (10)
To compute E’s value in highest path, we use Tij and τij which
are equal to data transmission time RMS and processing time,
respectively. If we use ui to represent fitness value of resource i
for execting task j, we have:
ui =
Tij+τij
E
(11)
To compute fitness value for each resource we use the equation
process which is used for computing E value. In other words, the
value of E is specified firstly, then using equation (10) the fitness
value for each resource is computed. To compute standard
deviation, we are have to compute total fitness value at first.
Consider the two solutions for task scheduling in Fig. 2 and Fig.
3, the scheduling total time for this solutions is equal to 12.
Fig. 4. Total scheduling time with respect to load balancing.
4.3 The assimilation and revolution
operations in our proposed algorithm (ICA-
GELS)
4.3.1 Assimilation operator
Historically, the assimilation policy was developed with the
purpose of moving the culture and social
structure of colonies toward the culture of the central
government. In the proposed algorithm some cells
approximately 40% (Duki, et al. 2010) of the Imperialist array
are randomly selected (cells 1, 4, 8, and 9 in the Fig. 5 are
imperialist and others are colony ).
Fig. 5. Assimilation operator representation
4.3.2 Revolution operator
To perform this operation, two cells are first selected in the
colony in a random manner and their values are exchanged. This
stages (random exchange or revolution operation) is repeated
based on the percentage of the total number of tasks. If the new
colony is better than the old one, it replaces the old colony;
otherwise, this procedure is repeated. This operation is
illustrated in Fig. 6.
Fig. 6. Revolution operator representation
4.3.3 Local search algorithm parameters
imitating the gravitational attraction
In the last execution step of ICA, due to the poor performance
of the algorithm in local search, the solutions which are similar
in scheduling length are given to the GELS algorithm to generate
a neighbor solution (response) for them.

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4.3.3.1 Solution dimensions (space)
Unlike other algorithms, GELS algorithm does not perform fully
randomly to obtain neighbor solution from the current solution.
Each solution has many neighbors which are computed by a
variable type in the current solution. All achieved neighbors are
based on this variable type. The proposed approach assumes that
solution dimensions and countries features are equal (solution
dimensions are solution neighbors which are achieved by
changing the current solution). Solution dimensions are equal to
the size of input tasks.
4.3.3.2 Initial velocity vector
The number of initial velocity vectors elements are equal to
number of solution dimensions. Initial velocity vector elements
will be initialized to random numbers ranging from 1 to
maximum initial velocity.
4.3.3.3 Neighborhood
Neighbor solution of the current solution is equivalent to
solution which assigned task is changed. The value is between 1
and maximum initial velocity. A feature from country which has
a maximum velocity is chosen, then its value changes randomly
(from 1 to M). For example Fig. 7 presents a solution in which
the property with maximum velocity is chosen and a neighbor
solution is generated for it.
Fig. 7. Representing a neighbor solution.
4.3.3.4 Calculating gravitational force in
ICA-GELS algorithm
After acquiring neighbor solution for current solution, the fitness
for neighbor solution is computed using equation (3). If the
neighbor solution is better than the current solution, then it will
be replaced its parent country in the new population; otherwise
it is not copied in the new population. The amount of force
between neighbor solution and current solution is computed
using equation (12) and its value will be added to the initial
velocity vector from which the neighbor solution is acquired to
updated the initial velocity vector (it is possible to have negative
gravitational forces). It is worth to noting that if the value of
elements in initial velocity vector exceeds the specified ranges;
their values is tuned to a number within the range.
F = G ×
Fitness1 (Candidate_C𝑖)−Fitness2 (Current_Ci)
R2 (12)
Candidate_C and Current_C in above equation are neighbor
solution and current solution, respectively. The value for G is
fixed and it is equal to 6.672 and R is the neighbor radius for to
objects in searching space which is fixed as so. The algorithm
ends when it reaches the maximum specified threshold. The
Pseudo-code of the proposed algorithm is shown below.
Step 1 : Initialization
Step 2 : 2.1. Generate the k number of random country with
length n
2.2. Speed_vector[1..n] = The initial velocity for
each dimension
2.3. Location_vector[1..n] = The value of the
initial position of each particle
2.4.Setting the Maximum: Maximum-Time (Mt)
and Maximum-energy (Me) according to the
user’s requirement.
Step 3 : 3.1. Create initial empires.
Steo 4 : 4.1. Assimilation & Revolution
4.2. Assimilation: Colonies move towards
imperialist.
4.3. Revolution: Random change occur in the
characteristics of some countries.
Step 5 : Position exchange between a colony and imperialist
Step 6 : Compute Makespan and energy for all country
Step 7 : 7.1. Imperialistic Competition
7.2. Eliminate the powerless empires. Weak
empires lose their power their power gradually
and they will finally be eliminated.
Step 8 : The best country from the imperialist competitive
algorithm as a solution to it current GELS will be
producing a neighboring country
Step 9 :
9.1. Direction = max (speed_vector [...])
9.2. change the velocity_vector[index] of
current_solution with random integer between 1
and Max Velocity.
9.3. Fitness of the neighboring country by
equation (3) is calculated and saving the worst fitness
9.4. if direct country < neighbor country
Neighbor country is selected as the best solution
Step 10:
10.1. Calculated the mass of each particle with using
formula (22)
10.2. Calculate Acceleration for 'k' factors.
Step 11 :
11.1. Update Velocity_Vector for each dimension by
gravitational force of country.
Figure 8. Pseudo-code of the proposed algorithm.
5. DISCUSSION
In this section, aiming at evaluating performance of the proposed
work, the simulation results will be presented. Our simulations
are conducted on OPNET Modeler simulator (Modeler 2009).
We have conducted several simulations to verify the
effectiveness of our proposed algorithms. Our experiments are
conducted in a system equipped with 4 GB of RAM and 1600
MHz CPU which is run Windows Xp. The performance of the
proposed algorithm is compared with several task scheduling
algorithms considering the simulation parameters demonstrated
in table (2). The iteration parameter shows that to achieving the
application execution time using existing algorithms, 100
iteration are performed and the average of the values are
computed. Also the initial value for parameters which are used
in ICA and GELS and GA algorithms are shown in table (2),
respectively.

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Table (2). Initial values for parameters for algorithms
ICA
Assimilation rate 2
Revolution rate 0.1
α rate 0.8
ICA-
GELS
Assimilation rate 2
Revolution rate 0.1
α rate 0.8
Initial velocity
Between 1 and
Max Velocity
Constant
Gravitation (G)
6.672
GA
P-Crossover 0.85
P-Mutation 0.02
Figure 9. Comparison of makespan of algorithms
Fig.10 compares the algorithms in terms of consumed
energy. As results show the consumed energy increases as
tasks passes. The consumed energy for our algorithm is
lower than other algorithms.
Fig. 10. Comparing consumed energy for task execution
5. CONCLUSIONS
In the proposed method, the researchers have combined
imperialist competitive algorithm with gravitational emulation
local search algorithm which has been used for scheduling in
grid environment. The proposed algorithm, in which a weighted
objective function is used considering the degree of importance
of time and energy of user’s projects, gives more freedom for
specifying the time and energy of users’ projects. In the use of
this algorithm, similar to the objective function, the time and the
energy, along with their weight, are considered based on the
user's perspective. The purposes of the proposed scheduling are
to minimize completion time and energy of implementation of
tasks for different tasks of users simultaneously.
The proposed scheduling is compared with two algorithms of
ICA and GA with regard to the parameters of time and energy.
The results are investigated based on cost and energy requests in
different charts. They show that if we have limited number of
resources as well as high number of duties, the proposed
scheduler has the best performance compared to the other three
schedulers in reducing the overall time and energy of
scheduling. The results of experiments show that the hybrid
imperialist competitive algorithm and the gravitational
attraction can reach a high performance regarding creation of a
balance between energy and tasks implementation scheduling.
Further research can be conducted with regard to the practice of
resource allocation to works in the proposed algorithm through
using an approach based on fuzzy logic and using of fuzzy
inference system.
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Proposing a New Job Scheduling Algorithm in Grid Environment Using a Combination of Imperialist Competition Algorithm (ICA) and Gravitational Emulation Local Search (GELS)

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Proposing a New Job Scheduling Algorithm in Grid Environment Using a Combination of Imperialist Competition Algorithm (ICA) and Gravitational Emulation Local Search (GELS)