International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 1 – Oct 2014
A Hybrid Approach for optimal solution of Job shop
Scheduling
1
B. Preethi Devi,2M.V. Rajesh
1
Final MTech Student,2Associate Professor & HOD
Dept of Computer Science,Pragati Engineering College,Surampalem , E.G Dist, A.P
2
Dept of Information Technology,Pragati Engineering College,Surampalem , E.G Dist, A.P
1
Abstract:Usage of computational resources is always an
interesting research issue in the field of Grid computing.
Job shop scheduling is a combinatorial optimization
problem; it finds possible number of solution for optimal
solution. In this paper we are proposing a hybrid approach
of genetic algorithm and GELS algorithm for identifying
missed task or optimal solution from set of samples or
chromosomes which contains jobs, operation and time
span.
I. INTRODUCTION
Shop scheduling problems belong to the class of multistage scheduling problems,where each job consists of a set
of operations. For describing these problems, we use the
standard3-parameter classification a j b j g introduced in
[42]. The parameter indicates the machine environment, the
parameter b describes job characteristics, and the parameter
g gives the optimization criterion. In such a shop
scheduling problem, a set of n jobs J1,J2,…..,Jan has to be
processed one set of m machines M1,M2………,Mm. The
processing of a job Jib on a particular machine Mjis denoted
as an operation and abbreviated by (I,j). Each job Ji
consists of a number n iof operations. For the deterministic
scheduling problems, the processing time pi j of each
operation (i; j) is given in advance.
Among the shop scheduling problems, there are
three basic types: a flow-shop, a jobshopand an open-shop.
In a flow shop problem (a = F), each job has exactly m
operations, and the technological route (or machine order)
in which the job passes through the machines is the same
for any job. Without loss of generality, we assume that the
technological route for any job is given by
M1M2…..Mm. In a job shop problem (a = J), a
specific technological route Mj1Mj2….Mjni is given for
each job Ji,1≤ i ≤ n. Note that the number of operations per
job in is equal to m for the classical job shop problems, but
this number may be also smaller than m or larger than m
(recirculation; in this case we may use the notation (I,j,k)
for the k-th processing of job Ji on machine Mj). In an open
shop problem (a = O), no technological routes are imposed
on the jobs. Usually, it is assumed that each job has to be
processed on any machine [1].
ISSN: 2231-5381
Genetic algorithms have been originally
developed by [3] they work witha population composed of
individuals. The genetic structure of a biological individual
is composed of several chromosomes. Each of these
chromosomes is composed of several genes each of which
consists of a number of alleles. In combinatorial
optimization, an individual is usually identified with a
chromosome. A chromosome is further split into number of
genes (in some papers a gene is also identified with an
allele). Before applying genetic algorithm to scheduling
problems, an appropriate encoding (or representation) of
the solution must be introduced.
Representation of a solution In many genetic
algorithms, often a binary encoding is used, i.e., each gene
of an individual contains either the number 0 or the number
1. Of course, integers can be converteda representation but
for permutation problems, this is often not favorable. For
flow shop problems with the permutation condition a
standard way of representing feasible solution is the
permutation code, i.e., an individual consists of a string of
lengthen, and the ith gene contains the index of the job at
position i, so an individual describes the job sequence
chosen on all machines. In the case of a regular criterion, a
permutation is decoded into a feasible solution by
construction the resulting semi-active schedule.
For job shop scheduling problems, the situation is
a bit different. Here several encoding strategies exist, and it
is not clear in advance which is the best. Many authors
distinguish between a direct and an indirect representation.
In the first case, a solution is directly encoded into the
genotype (i.e., the schedule itself is encoded), but in the
second case not(this means that an indirect representation
encodes the instructions to a schedule builder).
II. RELATED WORK
Select Operation: Here, tournament operator was used to
choose the chromosomes. After accounting the fitness of
each chromosome, a chromosome which has more fitness
than the others is selected for applying combination
operators on it. Crossover operation: The crossover
operator used in this algorithm is a basic two-point
crossover which works as follows: Two random
chromosomes were selected by previous phase and
exchanges a random part of those. Combination Operator:
Since in mutation operator, the points which the changes
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International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 1 – Oct 2014
are applied on this are chosen randomly, so in proposed
method instead of this operator, chromosomes changes
were done through GELS algorithm for making the
neighbor solutions, because the dynamically varying the
ways in this algorithm isn't randomly. When each
chromosome was selected by previous phase, was
controlled by GELS algorithm until the solution of its
neighbor was obtained.
Each gene on chromosome is considered as a
dimension of the problem. In fact the problem’s
dimensions are just the neighboring solutions which are
obtained by changing the current solution. Initial velocity
is given to each of the TDGA algorithm combines the
duplication scheduling heuristic (DSH) algorithm [22] and
a GA. This algorithm first sorts tasks in descending order
and then repeats the parent task on all processors so that the
children can execute earlier, because the transportation cost
between processors becomes zero. By repeating the parent
task, overload and communication delays are reduced and
total execution time is minimized.
The resource fault occurrence history (RFOH)
[23] algorithm is used for job scheduling fault-tolerant
tasks in computational grid. This method stores resource
fault occurrence histories in a fault occurrence history table
(FOHT) in the grid information server. Each row of the
FOHT table represents are source and includes two
columns. One column shows the failure occurrence history
for the resource and the other shows the number of tasks
executing on the resource. The broker uses information in
this table in the GA when it schedules tasks. This reduces
the possibility of selecting resources with more occurrences
of failures. The chaos-genetic algorithm [24] is a GA for
solving the problem of dependent task/job scheduling. This
algorithm uses two parameters, time and cost, to evaluate
quality of service (QOS), and chaos variables are used
rather than randomly producing the initial population. This
combination of the advantages of GAs and chaos variables
to search the search space inhibits premature convergence
of the algorithm andproduces solutions more quickly, with
a faster convergence.
The integer genetic algorithm (IGA) [25] is a
genetic algorithm for solving dependent task/job
scheduling that simultaneously considers three QOS
parameters: time, cost, and reliability. Since these
parameters conflict with one
Another and cannot be simultaneously optimized—as
improvement of one reduces the quality of another—
weights are assigned to each parameter, either by the user
or randomly. If the user provides the weighting, the
parameter that is more
Important to the user is given more weight than the others.
III. PROPOSED WORK
In this paper we are proposing an efficient hybrid
approach for generation of optimal solution from set of
solutions or schedules generated from input samples. In
this approach we initiallygenerate schedules, every
schedule includes set of operations and time span or time
required to complete individual task and we generate a
random set of schedules initially and computes the fitness
function for all the schedules, here fitness function gives
the time span to complete operations in a schedule. The
following example shows sets of schedules with some
operation and time span required to complete those
operations as follows
Job1:
Op1
5
Op2
Op3
6
4
Op4
3
8
Op5
Op6
4
Job2
Op2
6
Op3
Op9
5
OP1
7
OP6
5
OP10
4
5
OP6
6
OP5
6
OP2
4
10
Job3
OP1
8
OP3
5
OP9
OP indicates operation and corresponding value shows
time span which is required to complete operation. Now
the above figures are the schedules or jobs which contain
some set of operations, we need to find the optimal
schedules from set of samples with our hybrid approach.
ISSN: 2231-5381
The following algorithm shows sequential steps to find
optimal solution.
In genetic algorithm every schedules is assumed as
chromosome and every chromosome is set of genes, here
genes are operations in the schedule and time span
indicates the object value or velocity value in GELS and
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International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 1 – Oct 2014
updates maximum velocity value, chromosome can be
treated as velocity vector.
Initially set of chromosomes can be generated
randomly and assigned with some set of operations or
velocities and time spans of the operations, In this
approach fitness value or objective function can be
calculated for every chromosome and applies cross over
operation between the best parents of each iteration to
generate a child chromosome and computes the fitness
function for time required to complete the task then same
chromosome can be forwarded to mutation operation, here
mutation operation can be done by the flip bit and
compute the fitness value again, if the current fitness value
greater than existing chromosomes add to list of optimal
chromosomes.
In this paper we are using the feature of gravitational
attraction from GELS algorithm to modify the existing
mutation operation, in traditional approach we will flip one
bit position of based on the percentage but in our approach
we initially flip bit positions of the chromosome then
computes fitness function,if it is not optimal then we
check for next flip bit position instead of termination .
IV. CONCLUSION
We are concluding our research work with
efficienthybrid approach of genetic algorithm GELS
approach where mutation performed. Our proposed
approach searches the optimal solution from set of possible
solutions by performing cross over operation and GELS
based mutation operation over chromosomes or schedules.
References:
Algorithm for combinatorial optimization:
Step1: Initialize K number of chromosomes
[1] GENETIC ALGORITHMS FOR SHOP SCHEDULINGPROBLEMS:
A SURVEY Frank Werner_
Step2: Compute fitness values of the individual
chromosomes
[2]Abdelmaguid, R. Representations in genetic algorithm for the job shop
schedulingproblem: A computational study. J Software Engineering &
Applications, 2010, 3,1155 - 1162.
Step3: For i:0I<max_iterations : i++
[3] Holland, J.A. Adaptation in natural and artificial systems. Ann Arbor:
University ofMichigan, 1975.
[4] H. El-Rewini, T. G. Lewis, H. H. Ali, Task Scheduling in Parallel
andDistributed Systems, Prentice-Hall, 1994, ISBN:0-13-099235-6.
Child: = Cross over (Parent1, Parent2)
If (fitness (child) > current solution) then
[5] L. Khanli, M. Etminan Far , A. Ghaffari, "Reliable Job Scheduler
usingRFOH in Grid Computing," Journal of Emerging Trends in
Computingand Information Sciences, Vol. 1, No. 1, pp. 43- 47, 2010.
Add to child_list
[6] G. Gharoonifard, F. Moeindarbari, H. Deldari, A. Morvaridi,
"Scheduling of scientific workflows using a chaos- genetic
algorithm,"Procedia Computer Science, Elsevier, Vol. 1, No.1, pp. 14451454,2010.
Next
Step4: while (child_list. Count > 0)
[7] Q. Tao, H. Chang, Y. Yi, CH. Gu, "A Grid Workflow Scheduling
Optimization approach for e-Business Application," Proceedings of
the10th International Conference on E-Business and E-Government, pp.
168-171, 2010.
Child_count :=0
For j=0; j<child_list[i].length; j++
If (fitness (child_list[i]) > current
solution) then
Add
optimal_chromozomes_list
child_list:= child_list-1;
End while
Step5: Return optimal_chromozomes_list.
ISSN: 2231-5381
to
[8] Abdulal. W, Jadaan. O. A, Jabas. A, Ramachandram. S, "An
ImprovedRank-based Genetic Algorithm with Limited Iterations for
GridScheduling", IEEE Symposium on Industrial Electronics
andApplications,
pp.
215-220,
October
2009.
DOI:http://10.1109/ISIEA.2009.5356468
[9] Tamilarasi. A, Ananthakumar. T, "An enhanced genetic algorithm
withsimulated annealing for job-shop scheduling", International Journal
ofEngineering, Science and Technology, Vol. 2, No. 1, pp. 144- 151,2010.
DOI:
http://www.doaj.org/doaj?func=openurl&genre=article&issn=21412820da
te=2010&volume=2&issue=1&spage=144
[10] Omaraa. F. A, Arafa. M. M,” Genetic algorithms for task
schedulingproblem”, Journal Parallel Distributed Computing, Vol. 70, Iss.
1, pp.13-22, 2010.DOI: http://dx.doi.org/10.1016/j.jpdc.2009.09.009.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 16 Number 1 – Oct 2014
BIOGRAPHIES
M V RAJESH received the M Tech
degree in Computer Science from
JNTUCEK, Jawaharlal Nehru
Technological University, and
Hyderabad in 2006. Currently he is
working as Associate Professor &
HOD in Department of Information
Technology in PRAGATI Engineering College,
Surampalem, Andhra Pradesh, India. He has seven years of
experience in teaching and five years of experience in
software industry. Previously he has worked with
SIEMENS Information Systems Ltd, Bangalore as
Associate Consultant in the role of Software Developer in
the HealthCare domain. His research interests include
Object Oriented Programming, Artificial Intelligence and
Cloud Computing.
B.Preethidevi pursuing her M.Tech in
Computer
Science
at
Pragati
Engineering College, Surampalem,
Kakinada, Andhra Pradesh. Her areas
of
Interest
is
Mobile/wireless
Computer
Networks,
Artificial
Intelligence and Software engineering
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