Analysis of selection schemes for solving job shop scheduling problem using genetic algorithm

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 02 Issue: 11 | Nov-2013, Available @ http://www.ijret.org 775
ANALYSIS OF SELECTION SCHEMES FOR SOLVING JOB SHOP
SCHEDULING PROBLEM USING GENETIC ALGORITHM
A.Ranjini 1
, B.S.E.Zoraida 2
1
Research Scholar, Bharathidasan University, Tiruchirappalli, Tamilnadu, India, ranjini.anbu@gmail.com
2
Assistant Professor, Bharathidasan University, Tiruchirappalli, Tamilnadu, India, b.s.e.zoraida@gmail.com
Abstract
Scheduling problems have the standard consideration in the field of manufacturing. Among the various types of scheduling
problems, the job shop scheduling problem is one of the most interesting NP-hard problems. As the job shop scheduling is an
optimization problem, Genetic algorithm was selected to solve it In this study. Selection scheme is one of the important operators
of Genetic algorithm. The choice of selection method to be applied for solving problems has a wide role in the Genetic algorithm
process. The speed of convergence towards the optimum solution for the chosen problem is largely determined by the selection
mechanism used in the Genetic algorithm. Depending upon the selection scheme applied, the population fitness over the
successive generations could be improved. There are various type of selection schemes in genetic algorithm are available, where
each selection scheme has its own feasibility for solving a particular problem. In this study, the selection schemes namely
Stochastic Universal Sampling (SUS), Roulette Wheel Selection (RWS), Rank Based Roulette Wheel Selection (RRWS) and Binary
Tournament Selection (BTS) were chosen for implementation. The characteristics of chosen selection mechanisms of Genetic
algorithm for solving the job shop scheduling problem were analyzed. The Genetic algorithm with four different selection schemes
is tested on instances of 7 benchmark problems of different size. The result shows that the each of the four selection schemes of
Genetic algorithm have been successfully applied to the job shop scheduling problems efficiently and the performance of
Stochastic Universal Sampling selection method is better than all other four selection schemes.
Keywords: Genetic Algorithm, Makespan, Selection schemes
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1. INTRODUCTION
Scheduling is an optimization process intended to make the
best possible use of the limited resources by making suitable
allotment of the said resources over a period of time [5].
There are several techniques that have been applied to solve
the scheduling problems namely time tabling problem, flow
shop scheduling, etc... One important problem of scheduling
is the job-shop scheduling problem (JSSP). It is a famous
problem in the field of industries especially, in manufacturing
companies and transportation companies. Job shop
scheduling is one of the combinatorial optimization
problems, where the set of possible solutions is very large
and the goal is to find the best possible solution.Traditional
methods can be also be used to solve the job shop problem.
But, the time complexity is there with them. This is because,
when the problem size is small, the traditional methods for
solving JSSP are able to explore the entire search state in
order to obtain the optimal solution within reasonable time.
But it is not the case for the most real world problems.
Therefore, a non-traditional method known as “Genetic
Algorithm” can be utilized in the scheduling of the
manufacturing system. It is a very effective algorithm to
search for solutions for an optimization problem. The
solutions are usually optimum solutions or solutions near by
the optimum value for the chosen problem.
A lot of work has been already carried out for solving the job
shop problem. R.Thamilselvan and P.Balasubramanie [1]
introduced three new crossover operators namely Order
Preserving Multipoint Crossover, Unordered Subsequence
Exchange Crossover and Ordered Partially Mapped
Crossover in the Genetic Algorithm for solving the JSSP.
They analyzed the effectiveness of each of the three
crossover operators by testing them on the known benchmark
problems. From their results, it is proved that the Unordered
Subsequence Exchange Crossover operator provides the
remarkable performance than the other two operators.
R.Sivaraj and Dr.T.Ravichandran [2] presented an overview
of Genetic Algorithm and the various selection schemes used
in the Genetic Algorithm. Tamer F.Abdelmaguid [3]
provided a computational study to compare impact of
chromosome representation in Genetic Algorithm for solving
the JSSP. The performance of the Genetic Algorithm under
six different chromosomes representations was presented in
the paper.It is found that the machine-based representation is
capable of achieving the lowest optimality gap, but with the
highest computational time. Omar Al Jadaan,
LakishmiRajamani[4] and C. R. Rao introduced a new
selection method namely Rank Based Roulette Wheel
selection in their work. The result shows that by introducing
this selection scheme in the Genetic Algorithm the gain of
diversity among population is increased and the uncertainty
in selection process is decreased. Kumar Ritwik and Sankha
Deb [5] developed a new encoding scheme for chromosome
representation. The proposed encoding scheme is compared
with other schemes on the basis of the Lamarkian property,
complexity of decoder and memory requirement. The
proposed scheme was compared with the existing operation
based representation. When the number of operations is

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small, the proposed scheme performs better than the
operations based scheme. But, when the number of
operations is increased, the proposed scheme tends to lose its
effectiveness. S.M.Kamrul, RuhulSarker and David
Cornforth [6] had presented a hybrid Genetic Algorithm for
solving the JSSP. The proposed Genetic Algorithm includes a
heuristic job ordering with the Genetic Algorithm and they
incorporated a new, but simple local search method.
NorainiMohdRazali and John Geraghty [7] presented the
comparison of Genetic Algorithm performance using
different parent selection strategy in solving travelling
salesman problem. Therefore, the selection strategy has
notable impact for the problem using Genetic Algorithm.
This factor is analyzed in this paper.
2. PROBLEM DESCRIPTION
The classical job-shop scheduling problem can be formulated
as follows [1-5]: A set of n jobs and a set of m machines are
given. The n jobs are to be scheduled on the m machines,
where each job is divided into a set of operations. Each
operation is needed to be processed by the required machine
with the fixed processing time. There are several constrains
on jobs and machines:
1. Every job has to be processed on all machines.
2. Each job must visit each machine exactly once.
3. Each machine can process only one job at a time.
4. The processing order of the set of operations for
each job is pre-specified, which is known as
“precedence constraint” or “technology constraint”.
5. There are no precedence constraints among the
operations of different jobs.
6. All operations are not preemptive. That is, each
operation needs to be processed on the required
machine without interruption for the given period of
time.
7. The operations of the same job cannot be processed
concurrently.
8. We assume that there is no machine failure.
9. Neither release times nor due dates are specified.
The maximum completion time of all the jobs is known as
„Makespan‟. The execution sequence of all operations of all
jobs on the given machines is referred as a schedule. A
schedule is said to be feasible schedule only if it satisfies all
the above stated constraints. The objective of the JSSP is to
find a feasible schedule of minimum length, that is, the
schedule must minimize the makespan.
3. GENETIC ALGORITHM
Genetic Algorithms are bio-inspired search algorithms based
on the evolutionary ideas of natural selection and genetics
that are used successfully to solve problems in many different
disciplines. Genetic Algorithm uses the technique that
resembles natural selection in the biological process. Genetic
Algorithm was developed by John Holland, his colleagues,
and his students at the University of Michigan in the 1960s
and the 1970s. Due to the robustness of Genetic Algorithms
on problems of high complexity, it has an increasing number
of applications in the fields of artificial intelligence, numeric
and combinatorial optimization, business, management,
medicine, computer science, engineering etc.
4. GENETIC ALGORITHM FOR JSSP
4.1 Operation based representation
In the scheduling problems, the popular representation is
operation-based representation for the chromosome. In this
study also, the operation based representation is adopted for
implementation. This representation encodes a schedule as a
sequence of operations where each gene stands for one
operation. All operations of the same job are represented by
the same symbol and they are interpreted according to the
order of their occurrence in the chromosome sequence. Using
the representation, each job number occurs m times in the
chromosome. By scanning the chromosome from left to right,
the k-th occurrence of a job number refers to the k-th
operation in the technological sequence of this job.
As in Fig- 1, an example chromosome for 3 X 5 JSSP is
given as [2 2 1 3 1 2 2 3 1 3 3 1] for the three jobs and five
machines problem. As each job consists of five operations,
the job number occurs exactly five times in the chromosome.
The fourth gene represents the first operation of job 3
because number 3 has been occurred at the first time.
Similarly, the sixth gene in the chromosome implies third
operation of job 2.
4.2 Permutation encoding
There are many chromosome encoding methods are
available. Since the permutation encoding is only for
ordering problem, this encoding is applied in this paper.
4.3 Initial population
In this paper, the initial population is created by means of
random permutation of the operation sequence. It is proved
that the initial solution methods affect the speed of
convergence solution and so the better initial solutions might
provide better results.
4.4 Fitness calculation
The fitness function for the JSSP can be defined as fitness =
1/(makespan).
4.5 Selection
The selection strategy determines which of the chromosomes
in the current generation will be used to reproduce offspring
with the hope that the next generation will have higher
fitness. Different selection strategies have different methods
of calculating selection probability. All the differing selection
techniques develop solutions based on the principle of
survival of the fittest. In this paper, selection schemes namely
Stochastic Universal Sampling, Roulette Wheel Selection,

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Rank Based Roulette wheel selection and Binary Tournament
selection were implemented.
4.6 Unordered subsequence exchange crossover
The Unordered Subsequence Exchange Crossover (USXX) is
adopted in this work that children inherit subsequences on
each machine as far as possible from parents [1]. Fig- 2
shows the method for performing the Unordered
Subsequence Exchange Crossover and the procedure to do it
is as follows.
Step 1: Choose two parent individual randomly, namely
Parent1 and Parent2.
Step 2: Select random subset of operations (genes) from
Parent1 and copy it into Child1 with the same
context dependent.
Step 3: Starting from the first crossover point from Parent1,
look for elements within the subsequence in Parent2
and remove those from Parent2.
Step 4: The remaining operations of Parent2 are copied into
Child1 so as to maintain their relative ordering.
Step 5: Change the Parents and go to Step 1 to generate
Child2 in the same manner.
4.7 Swap mutation
In this study, the swap mutation is applied. It randomly takes
two positions in a chromosome and then the alleles in those
positions are swapped. Fig -3 shows the procedure for
performing the swap mutation for an example chromosome
for 3 X 4 JSSP.
4.8 Procedure For Genetic Algorithm For JSSP
A simple and basic Genetic Algorithm cycle for solving the
JSSP is shown in Fig- 4 as follows:
5. RESULTS AND DISCUSSION
The implementation work is carried out using Matlab
software. In order to analyze the effectiveness of various
selection schemes in this paper, the following factors are
taken to be measuredfor each of the four selection schemes.
 Frequency of occurrence of optimum solution
 Fitness Evolution History and
 Quality of solution
Eight well known benchmark problems namely LA1, LA5,
LA6, LA7, LA8, LA11, FT10 and LA13 are tested to
measure these factors.
Frequency of occurrence of optimum solution
The frequency of occurrence of optimum solution refers to
the number of occurrences of known optimum solution out of
a number of trial runs. The result obtained for this factor is
given in Table 1.
Table 1: Frequency Of Occurrence Of Optimum Solution

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LA1 LA5 LA6 LA7 LA8 LA11 LA13
0
1
2
3
4
5
6
7
8
9
Benchmark Problems
FrequencyOfOccurence
FREQUENCY OF OCCURENCE OF OPTIMUM SOLUTION
SUS
RRWS
RWS
BTS
Fig -5. Frequency of occurrence of optimum solution
The Fig -5 is drawn using the data given in the Table 1. From
this figure, it is known that the Stochastic Universal
Selection(SUS) scheme has the high frequency of occurrence
of optimum solution for the Rank Based Roulette Wheel
Selection (RBWS), Roulette Wheel Selection (RWS) and
Binary Tournament Selection (BTS). The empty spaces
between the bars in the bar stack of a problem shows the zero
frequency.
Fitness evolution history
The fitness evolution history shows the fitness value
calculated for each iteration of the Genetic algorithm cycle. It
is also used to refer the number of iterations that take to reach
the optimum solution.

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From the Fig - 6, 7, 8, 9, 10, 11 and 12 it is known that the
SUS scheme has reached the optimum solution with the less
number of iteration when compared to all other three
schemes.
Quality of Solution
The quality of solution is used to measure the deviation of
obtained solution from the optimum solution of the problem.
The result obtained for this factor is given in Table 6 and the
Fig -13 is drawn using the data given in the Table 2.
Table 2: Quality of Solution
SUS RRWS RWS BTS
0
2
4
6
8
10
12
Selection Schemes
DeviationFromOptimumSolution
QUALITY OF SOLUTION
Fig -13: Deviation from optimum solution
From the Fig -13, it is shown that SUS scheme provides the
minimum deviation from the optimum solution given than
other three schemes.
CONCLUSION
From the experimental result, it is concluded that out of the
four selection schemes for the tested benchmark problem, the
Stochastic Universal Sampling selection scheme gave the
high frequency of occurrence of optimum solution for all
problems. The average makespan value and the deviation
from the optimum solution given by the scheme are also
lesser it than the other selection schemes. Thus, the
Stochastic Universal Sampling selection is well suited for
solving the JSSP using Genetic Algorithm.
FUTURE WORK
The future work will concentrate on making the various
parameters of Genetic Algorithm namely the population size,
crossover probability and mutation probability can be made
as dynamic. Some other techniques namely Simulated
Annealing, Neighborhood search can also be incorporated as
a local search technique in the Genetic Algorithm to improve
its performance. The work can be extended for flexible job
shop scheduling environment also.
ACKNOWLEDGEMENT
The authors are thankful to the Department of Computer
Science, Engineering and Technology, Bharathidasan
University, Trichy and all the people who help to make this
study as a successful one.
REFERENCES
[1] R.Thamilselvan and P.Balasubramanie, “Analysis of Various
Alternate Crossover Strategies for Genetic Algorithm to Solve
Job Shop Scheduling Problems” European Journal of Scientific
Research ISSN 1450-216X Vol.64 No.4 (2011), pp. 538-554©
EuroJournals Publishing, Inc. 2011
[2] R.Sivaraj and Dr.T.Ravichandran, “A Review Of Selection
Methods In Genetic Algorithm” International Journal of
Engineering Science and Technology (IJEST) ISSN: 0975-5462
Vol. 3 No. 5 May 2011
[3] Tamer F. Abdelmaguid, “Representations in Genetic
Algorithm for the Job Shop Scheduling Problem: A
Computational Study”, Journal of Theoretical and Applied
Information Technology(2005-2008)
[4]Omar Al Jadaan, Lakishmi Rajamani, C. R. Rao,” Improved
Selection Operator For Ga”, International Journal of computer
science and technology (2006)
[5] Kumar Ritwik and Sankha Deb, “A Genetic Algorithm-
Based Approach For Optimization Of Scheduling In Job Shop
Environment” Journal of Advanced Manufacturing Systems Vol.
10, No. 2 (2011) 223–240c_World Scientific Publishing
Company DOI: 10.1142/S0219686711002235
[6] S. M. Kamrul Hasan, Student Member, IEEE, Ruhul Sarker,
Member, IEEE, and David Cornforth, “Hybrid Genetic
Algorithm for Solving Job-Shop Scheduling Problem”,
Proceedings of the World Congress on Engineering 2011 Vol II
WCE 2011, July 6 - 8, 2011, London, U.K. ISBN: 978-988-
19251-4-5 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
[7] Sivanandam S.N. and Deepa S.N. 2008. Introduction to
Genetic Algorithms, Springer, Berlin, New York.
[8] Goldberg D.E. (2003), “Genetic Algorithms in Search,
Optimization, and Machine Learning” (Addison Wesley,
Reading g, MA,)
[9]
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Analysis of selection schemes for solving job shop scheduling problem using genetic algorithm

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