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International Conference on Science and Technology 2019

Journal of Physics: Conference Series 1569 (2020) 022074

IOP Publishing

doi:10.1088/1742-6596/1569/2/022074

1

Subject Scheduling Using Genetic Algorithms (Case Study:

SMK Negeri 1 Labang-Madura-Indonesia)

Eka Mala Sari Rochman1, Muhammad Ali Syakur2, Imamah3, Aeri Rachmad4

Faculty of Engineering, University of Trunojoyo Madura. Raya Telang Road P.O. BOX 2 Kamal, Bangkalan-Madura,Indonesia

1ekamala.sari@yahoo.com, 4aery_r@yahoo.com

Abstract. The manually scheduling system is considered less effective and efficient because it

requires a long time. Problems will become more complex if the number of components or data

used is increasing. The schedule is expected not only not to experience clashes, but also to adjust

to some limitations that must be met. Genetic Algorithm is one of the heuristic search algorithms

that are very well used in solving optimization problems. The problem of scheduling genetic

algorithms is considered to have good performance in finding the optimal solution. Genetic

Algorithms implement an evolutionary process by randomly producing chromosomes from each

population These chromosomes produce a solution to the problem raised, namely scheduling

subjects. The conclusion of this study is to be able to arrange the schedule of subjects efficiently,

by overcoming obstacles such as clashing schedules without eliminating the constraints that must

be met. Keywords: Schedulilng System, optimization problems Genetic Algorithm.

1. Introduction

The definition of a schedule is the division of time based on a work order arrangement plan; list or table

of activities or plan of activities with a detailed division of the time of implementation, while the

definition of scheduling is a process, method, action schedule or include in the schedule [1]. So

scheduling is something that must be present in every activity. Scheduling techniques vary depending

on the size, complexity, duration of the activity [2] [3]. One activity that requires scheduling is an

activity in the world of education in the form of a schedule of subjects. The lesson schedule is used as a

guideline by teachers, students or principals in carrying out the teaching and learning process.

Understanding of the lesson schedule is a set of learning sequences that are used as guidelines and must

be followed in the process of teaching and learning activities. Labang 1 State Vocational School is a vocational high school that has a problem in terms of unique

scheduling which has 27 classes, there are 6 vocational majors with 4 types of subjects namely

normative, adaptive, mulok (Local Content) and vocational subjects. In the process of teaching and

learning activities SMK Negeri 1 Labang has a total of 50 lesson hours per week for each class with a

total of teachers. There are several aspects that must be considered to get an effective and efficient lesson

schedule. The related aspects of scheduling include: no occurrence of clash of subjects in the same class

and at the same time, no teacher who teaches subjects more than one different class at the same time

and the number of hours of subjects in accordance with total time of week.

The method for making lesson schedules that has been done so far is still manual, that is by doing it

by searching for any columns that are still empty, then placing a schedule in that column. The schedule

International Conference on Science and Technology 2019

Journal of Physics: Conference Series 1569 (2020) 022074

IOP Publishing

doi:10.1088/1742-6596/1569/2/022074

2

produced in this way takes a long time and tends to ignore these various aspects. Therefore it is necessary

to develop a lesson scheduling system that can accommodate various aspects that are considered above.

There are several methods and algorithms that can be used to solve scheduling problems where each

algorithm has advantages and disadvantages. One method and algorithm is Genetic Algorithm. Genetic

Algorithm is one algorithm that adopts the mechanism of natural genetics that was developed to find

solutions to problems such as scheduling [4] [5]. Genetic algorithms find solutions, namely in the

initialization process. Processing is done to get a solution improvement [6]. With the use of genetic

algorithms, scheduling will be obtained in accordance with the appropriate aspects.

2. Methodology

2.1. Data Collection

The data used in this study include subject data, teacher data, class data, study hours and data

assignments of teaching teachers in the 2017-2018 school year at 1 Labang Vocational High School.

Table 1 shows the input data used.

Table 1 Data

No Data Input Jumlah

1 Teacher 44 Teachers

2 Subjects 20 Subjects

3 Class 9 classes

4 Time allocation 50 hours / week

2.2. Genetic Algorithm

Genetic Algorithm is an optimization method to find the optimal solution to a problem. Genetic

algorithms are search algorithms that are based on natural system mechanisms namely genetic and

natural selection [7] [8] [5]. In contrast to conventional search techniques, genetic algorithms depart

from a set of randomly generated solutions.

Figure 1. Flowchart of genetic algorithms for scheduling

This set is called a population. Whereas every individual in a population is called a chromosome which

is a representation of a solution. Chromosomes evolve in a continuous iterative process called

generation. In each generation, chromosomes are evaluated based on an evaluation function. After

several generations the genetic algorithm will converge on the best chromosome, which is expected to

be the optimal solution. Genetic Algorithms have a simple optimization methodology as follows:

1. Determine the population of a certain number of solutions

Start

Schedule Data

GA Process:

1. Chromosome Representation

2. Generating the initial population

3. Selection

4. Crossover

5. Mutation

End

Schedule of subjects

International Conference on Science and Technology 2019

Journal of Physics: Conference Series 1569 (2020) 022074

IOP Publishing

doi:10.1088/1742-6596/1569/2/022074

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2. Calculating fitness value functions all solutions in the population

3. Choose several solutions with the highest function fitness value

4. Perform optimization by means of mutations and crossover as much as needed

5. Determine the best solution as a solution to the problem being optimized

Finish Steps:

1) Initial Parameters

The parameters specified in the genetic algorithm are:

a. Fitness function (objective function) that is owned by each candidate scheduling to determine the

individual's fitness level with the criteria to be achieved.

b. Population number of individuals involved in each generation through a selection process.

c. The maximum number of generations that occurs

d. The probability of a cross (pc) in a generation.

e. The probability of a mutation (pm) in each individual.

2) Encoding Techniques

The coding technique is a method of coding / initializing genes from chromosomes. Each

chromosome contains a number of genes containing information stored on the chromosome. In this

study using coding techniques in the form of string bit / varchar which is used in genetic

programming.

3) Set Population and Chromosome Representations

Determining the initial population is the process of generating a number of chromosomes randomly.

Chromosomes represent one possible alternative solution. Chromosomes can be said to be the same

as individuals. Population size depends on the problem to be resolved. After population size is

determined, then initial population generation is carried out by initializing possible solutions into a

number of chromosomes. The length of one chromosome is determined based on the problem under

study.

The length of one chromosome is the multiplication of the number of lesson hours per week with

the number of classes available. One gene contains information on subjects, classes, and lesson

hours. For example for initialization of chromosome formation, for example there is a distribution

of subjects in table 2, distribution of time in table 3.

4) Calculation of Fitness Value

Individuals in the population have been formed, the next step is to calculate the fitness value of each

individual. Fitness will be calculated based on the number of violations found in the individual. The

value generated from the function indicates how optimal the solution is. In the case of subject

scheduling, the smaller the number of violations produced, the better the solution will be.

F = 1 / 1 + (∑ BG + ∑ BK + ∑ BJ) (1) Keterangan :

BG : Teacher clashes at the same time

BK : Clash of classes at the same time

International Conference on Science and Technology 2019

Journal of Physics: Conference Series 1569 (2020) 022074

IOP Publishing

doi:10.1088/1742-6596/1569/2/022074

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BJ : Clash of lesson hours

Limits used to calculate fitness values:

1. Teachers may not teach more than once at the same time

2. One class may not be scheduled more than once at the same time

3. One subject may not be scheduled more than once at the same time

5) Selection

In this study the method used is roulette wheel selection. In this selection, individuals are selected based

on their fitness values to choose which individuals will experience the marriage process or crossovers,

the better the quality of an individual the greater the chance to be chosen. In the roulette wheel selection

process, the cumulative value of the fitness probability of each individual will be calculated. Examples

of selection steps using roulette wheel:

a. Calculate the total fitness value

b. Calculate the probability of each chromosome, how: fitness value / total fitness

c. Look for intervals for each chromosome

d. Generate 0-1 random numbers as many as existing chromosomes Eg 0.75; 0.25; 0.9; 0.5

e. Search for each random number at which chromosome interval.

f. Then the results of the new population obtained from the selection are

Then the results of the new population obtained from the selection are

Chromosome 1 Chromosome 3

Chromosome 2 Chromosome 1

Chromosome 3 Chromosome 4

Chromosome 4 Chromosome 2

g. Use the selected population for the next process

6) Crossover

Crossover is done by crossing 2 mothers to produce offspring. In the crossing process, the method used

is one-cut-point crossover by taking several genes from the first parent which are then combined with

the genes in the second parent. The child number of the reproductive process is determined by

determining the pc value (crossover probability) which is random from a value between 0 and 1.

Examples of crossover steps:

a. Determine pc value

b. Generate random numbers for each chromosome

c. Search for random numbers that are less than a pc

d. Awaken random numbers (1 to the length of the chromosome) to determine the cut point.

e. Perform crossover, for example the crossover that will be done is chromosome 2 and 4, with cut point

2

Chromosome 1 Chromosome 2

PAI6 TKJ2 T1 MUL4 TKJ2 T21

BIG4 TKJ1 T9 PJS3 TKJ2 T18

MUL3 TKJ2 T5 FIS5 TKJ2 T15

FIS3 TKJ1 T9 BIG1 TKJ1 T15

BIG6 TKJ2 T15 P1D4 TKJ1 T15

BIG3 TKJ1 T19 FIS2 TKJ1 T3

P1D2 TKJ1 T17 PAI6 TKJ2 T23

FIS1 TKJ1 T19 SIM1 TKJ1 T15

f. Use the crossover population for the next process

International Conference on Science and Technology 2019

Journal of Physics: Conference Series 1569 (2020) 022074

IOP Publishing

doi:10.1088/1742-6596/1569/2/022074

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7) Mutations

Mutation is a process of reproduction by modifying the arrangement of genes from a parent. From one

mutation process to one parent will produce one child. Before the reproduction process is carried out

using mutations, it is necessary to determine the value of pm (probability of mutation), which is

generated from a value between 0 and 1, which is the function of pm to determine how many children

must be produced in the mutation process. The steps of the mutation process:

a. Calculate total genes, total genes = many genes on one x chromosome many chromosomes in the

population

b. Many genes are transferred = total gene x pm. For example, the total genes = 16 and pm = 0.1, many

genes that are mutated are 1.6 ≈ 2

c. Generate random numbers 0 to 1 as many genes as possible

d. Search for genes with random numbers < pm

e. If the results are less than mutated genes, then all are used. If more than the maximum mutated gene,

random to take as many genes that are mutated.

f. Perform the mutation process, by changing the time component in the gene

Before mutation BIG4 TKJ1 T9

After mutation BIG4 TKJ1 T3

g. Use the mutation population for the next process

8) Stop Conditions

Iteration will continue to run and will stop if one of the following conditions has been fulfilled

a. After several successive generations the best fitness value of the population has not changed

b. The maximum number of generations has been reached

c. If the minimum best fitness value has been reached. If there is no violation of the chromosome

3. Result and Discussion

In this test the author uses several parameters that will be applied to the genetic algorithm process. Test

parameters can be seen in the following table 4 below:

Table 4 Testing Parameters

Parameter Value

Number of Individuals 10

Crossover probability 0.7

Mutation Probability 0.1

Many Generation 10

Figure 2. Data Figure 3. Generate Schedule

International Conference on Science and Technology 2019

Journal of Physics: Conference Series 1569 (2020) 022074

IOP Publishing

doi:10.1088/1742-6596/1569/2/022074

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Figure 4. Generate Results

CONCLUSIONS

Based on the results and discussion, the conclusions that can be obtained from this study are as follows:

1. The performance of genetic algorithms is good enough for subject scheduling

2. To achieve optimization it is best influenced by several parameters applied

3. The more number of generations that are raised, the fewer the number of crashes that occur, the better

the solution will be.

Table 5 Accuracy

Generation Total Crash Accuracy

10 32 93.03 %

20 31 93.13 %

50 23 93.17 %

80 19 94.00 %

100 16 95.88 %

ACKNOWLEDGMENT The authors state that there is no issue of interest with the agencies listed in this paper. We would like

to thank our colleagues at the University of Trunojoyo Madura - Indonesia, the Laboratory of Network

and Multimedia team who helped author in completing this research. It gave the author opportunities

in using the equipment of the laboratory

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[5] S. D. KUMAR RITWIK, "A GENETIC ALGORITHM-BASED APPROACH FOR

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ICST 2019 International Conference on Science and Technology (ICST) is a scientific forum to discuss the development and latest research on exact science, engineering and technology. The following topics of thid conference are Physical Sciences and Chemistry, Mathematics and Statistics, Informatics and Computer Science, Aerospace Engineering, Biomedical Engineering, Chemical Engineering, Civil Engineering, Computer Engineering, Electrical Engineering and Electronics, Power and Energy Engineering, Environmental Engineering, Geological and Geophysical Engineering, Industrial Engineering, Manufacturing and Mechanical Engineering, Engineering Physics and Materials Engineering, Mining and Petroleum Engineering. Technology-based applications such as learning media for education can also be accepted at this Conference. Selected papers that have been through the peer review will be published in IOP and indexed by Scopus. We respectfully request that you join us to ICST 2019. We look forward to welcoming you to Surabaya! In 2019, ICST is focusing on Science, Technology and Engineering related to the 4th industrial revolution known as Industry 4.0. Therefore, the theme of this conference is

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1.1. COMMITTEES • Honorary General Chairs: • Prof. Ir.

Renanto Handogo, M.Sc., Ph.D., Institut Teknologi Sepuluh Nopember Surabaya, Indonesia • Prof. dr. ir. G.J. (Bart) Verkerke, Rijksuniversiteit Groningen, The Netherland • Assoc. Professor Hadi Susanto, M.Sc., Ph.D., University of Essex, United Kingdom • Dr. Jamari, S.T., M.T., University of Diponegoro, Indonesia • General Chairs: • Prof. Dr. Arif Muntasa., S.Si., M.T.,

University of Trunojoyo Madura, Indonesia • Advisory Board:

• Prof. Nobuo Funabiki, Ph.D., Okayama University, Japan

• Prof. Dr. Ir. Muhammad Idrus Alhamid, University of Indonesia, Indonesia • Prof. Dr. Madlazim, M.Si, Universitas Negeri Surabaya, Indonesia • Prof. Dr. rer. nat. Ir. A. P. Bayuseno, M.Sc., University of Diponegoro, Indonesia • Prof. Dr. Sari Edi Cahyaningrum, M.Si., Universitas Negeri Surabaya, Indonesia • Prof. Dr. Ir. Rachmad Hidayat., M.T., IPU., AER., University of Trunojoyo Madura, Indonesia • Prof. T. M. Indra Mahlia, Ph.D., University of Technology Sidney, Australia • Prof. Dr. Revolson A. Mege, M.S., State University of Manado, Indonesia • Roman Podraza, Ph.D., Warsaw University of Technology, Poland • Dr. Dani Harmanto, University of Derby, United Kingdom • Dr. Ario Sunar Baskoro, S.T, M.T, M.Eng., University of Indonesia, Indonesia • Dr. Dra. Jariyah, MP., UPN “Veteran” East Java, Indonesia • Dr. Ir. Ni Ketut Sari, M.T., UPN “Veteran” East Java, Indonesia • Dr. Ir. Reda Rizal, M.Si., UPN "Veteran" Jakarta, Indonesia • Dr. Maspiyah, M.Kes., Universitas Negeri Surabaya, Indonesia • Saiful Anwar, STP, MP., State Polytechnic of Jember, Indonesia • Lita Asyriati Latif, S.T., M.TM., Universitas Khairun Ternate, Indonesia • Ir. Made Mudhina, M.T., Bali State Polytechnic, Indonesia

• Daniel Parenden, S.T., M.T., University of Musamus Merauke , Indonesia • Scientific Committee (also reviewer):

• Wahyudi Agustiono, S.Kom., M.Sc., Ph.D, University of Trunojoyo Madura, Indonesia • Dr. Hakam Muzakki, S.T., M.T., University of Trunojoyo Madura, Indonesia • Chandra Ade Irawan, Ph.D., University of Nottingham Ningbo, China • Abdul Malek Bin Yakoob, Ph.D., Universiti Utara Malaysia, Malaysia • I Dewa Made Cipta Santosa, ST, M.Sc, PhD., Bali State Polytechnic, Indonesia • Muhammad Yusuf, S.T., M.MT., Ph.D., University of Trunojoyo Madura, Indonesia • Dr. Basuki Rahmat, S.Si., M.T., UPN "Veteran" East Java, Indonesia • Dr. Iis Hamsir Ayub Wahab, S.T., M.Eng., Universitas Khairun Ternate, Indonesia • Reviewers (Out of Scientific Committee):

• Prof. Dr. Arif Muntasa, S.Si., M.T., University of Trunojoyo Madura, Indonesia • Prof. Dr. Madlazim, M.Si., Universitas Negeri Surabaya, Indonesia • Prof. Dr. Revolson A. Mege, M.S., State University of Manado, Indonesia • Dr. Dani Harmanto, University of Derby, United Kingdom • Dr. Ario Sunar Baskoro, S.T., M.T., M.Eng., University of Indonesia, Indonesia • Dr. Indah Agustien S., S.Kom. M.Kom., University of Trunojoyo Madura, Indonesia • Dr. Dra. Jariyah, MP., UPN “Veteran” East Java, Indonesia • Dr. Ir. Ni Ketut Sari, M.T., UPN “Veteran” East Java, Indonesia • Dr. Ir. Reda Rizal, M.Si., UPN "Veteran" Jakarta, Indonesia • Dr. Maspiyah, M.Kes., Universitas Negeri Surabaya, Indonesia • Dr. Akhmad Sabaruddin, S.T., M.T., University of Trunojoyo Madura, Indonesia • Dr. Muhammad Amin, S.T., M.T., University of Samudra, Indonesia • Dr. Iis Hamsyir Ayub Wahab, S.T., M.Eng., Universitas Khairun Ternate, Indonesia • Dr. Mufti Amir Sultan, M.T., Universitas Khairun Ternate, Indonesia • Dr. Damora Rhakasywi, S.T., M.T., UPN "Veteran" Jakarta, Indonesia • Dr. Ir. Halim Mahfud, M.Sc., UPN Veteran Jakarta, Indonesia • Dr. Dira Ernawati, S.T., M.T., UPN "Veteran" East Java, Indonesia • Dr. I Gede Susrama, M.Kom., UPN "Veteran" East Java, Indonesia • Dr. Philipus Betaubun, M.T., Universitas Musamus Merauke, Indonesia • Dr. Ir. Budi Hariono, M.Si., State Polytechnic of Jember, Indonesia • Dr. Lilik Anifah, S.T., M.T., Universitas Negeri Surabaya, Indonesia • Dr. Yeni Kustiyahningsih, S.Kom., M.Kom., University of Trunojoyo Madura, Indonesia • Dr. Noor Ifada, S.T., MISD., University of Trunojoyo Madura, Indonesia • Dr. Edy Winarno, S.T., M.Eng., Unisbank, Semarang, Indonesia • Dr. Ir. Lilik Sudiajeng, M.Erg., Bali State Polytechnic, Indonesia • Dr. Anak Agung Ngurah Gde Sapteka, S.T., M.T., Bali State Polytechnic, Indonesia • Dr. Fuad Hasan, S.P., M.P., University of Trunojoyo Madura, Indonesia • Dr. Erina Rahmadyanti, S.T., M.T., Universitas Negeri Surabaya, Indonesia • Rusli Yosfiah, Ph.D., Universiti Teknologi Malaysia, Malaysia • Euis Nurul Hidayah, S.T., M.T., Ph.D., UPN Veteran East Java, Indonesia • Ida Bagus Irawan Purnama, S.T., M.Sc., Ph.D., Bali State Polytechnic, Indonesia • I Gst.Ngr.A. Dwijaya Saputra, S.T., M.T., Ph.D., Bali State Polytechnic, Indonesia • Putu Wijaya Sunu, S.T., M.T., Bali State Polytechnic, Indonesia • Mahrus Khoirul Umami, S.T., M.Sc., Ph.D., University of Trunojoyo Madura, Indonesia • Eppy Yundra, S.Pd., M.T., Ph.D., Universitas Negeri Surabaya, Indonesia • Cahyo Indarto, S.TP., M.P., Ph.D., University of Trunojoyo Madura, Indonesia • Dr. Kukuh Winarso, S.Si, M.T., University of Trunojoyo Madura, Indonesia