Reshuffling and arranging classroom based on the capacity of the audience, complete facilities, lecturing time and many more may lead to a complexity of classroom scheduling. While trying to enhance the efficiency in classroom planning, this paper proposes a heuristic approach for timetabling optimization. A new algorithm was produced to take care of the timetabling problem in a university. The proposed of heuristics approach will prompt a superior utilization of the accessible classroom space for a given time table of courses at the university. Genetic Algorithm through Java programming languages were used in this study and aims at reducing the conflicts and optimizes the fitness. The algorithm considered the quantity of students in each class, class time, class size, time accessibility in each class and lecturer who in charge of the classes

Ahmad, Izah R.

Ali, Maselan

Mohd Razali, Siti Noor Asyikin

Sufahani, Suliadi

English

Ahmad, Izah Rafidah

Sufahani, Suliadi Firdaus

Journals of Universiti Tun Hussein Onn Malaysia (UTHM)

Journal of Science and Technology, Vol. 9 No. 3 (2017) p. 10-15  *Corresponding author: izah.fida@gmail.com 2017 UTHM Publisher. All right reserved.                                                                                                            10 penerbit.uthm.edu.my/ojs/index.php/jst  A Heuristics Approach for Classroom Scheduling using Genetic Algorithm Technique  Izah R. Ahmad*, Suliadi Sufahani, Maselan Ali and Siti N.A.M. Razali  1*Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology,  Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Johor, Malaysia       Received 30 September 2017; accepted 4 December 2017; available online 12 December 2017     1. Introduction  Scheduling of timetable is an important thing that should be done in any academic institution or even un-academic institution also. This to make sure syllabus of the lesson can be completed on time or the scheduling project or activity done in the given time. According to dictionary, scheduling can be defined as a plan of procedure, usually written, for a proposed objective, especially with reference to the sequence of and time allotted for each item or operation necessary to its completion. According to Bethel et al. [1], scheduling is the phase of production control which rates the works in order of its priority and then provides for its release to the plant at the proper time and in the correct sequence. Based on Jha [2], the meeting of people will be the events and the timetable must specify the people need to be met, the location and also the time they need to have the meeting. The most and famous scheduling timetable is educational timetable. In 2007, based on Burke et al. [3], it can happen that probably, educational timetabling is the most widely studied. There are many types of scheduling problem such as job-shop scheduling [4], transportation scheduling [5], staffing scheduling [6], sport scheduling [7] and home health care scheduling [8]. For this paper, a general problem of timetable problem in an academic institution will be solved. To schedule the timetable many constraints should be considered such as the size of class with the capacity of students, time for each slots and class, number of class in a day, subject involved and the lecturer as well. The most suitable approach to solve problem is a genetic algorithm (GA). Genetic algorithm is such a popular algorithm technique used to solve the scheduling problem. This genetic algorithm, was first invented from University of Michigan which is Prof. John Holland in 1975. Java programming is used to solve the problem.  2. Timetable Problem Description      There are many timetable problem in this world such as transport, nurse-rostering, sport, job shop and also timetable of student. To make a best timetable, all the conflicts arise should be well managed. The example of conflicts are the rooms, the lecturer or instructors, the size of room or capacity of the rooms, the subject, the class size, and sometimes the number of subject in a day also can be one of the conflict. Some students Abstract:  Reshuffling and arranging classroom based on the capacity of the audience, complete facilities, lecturing time and many more may lead to a complexity of classroom scheduling. While trying to enhance the efficiency in classroom planning, this paper proposes a heuristic approach for timetabling optimization. A new algorithm was produced to take care of the timetabling problem in a university. The proposed of heuristics approach will prompt a superior utilization of the accessible classroom space for a given time table of courses at the university. Genetic Algorithm through Java programming languages were used in this study and aims at reducing the conflicts and optimizes the fitness. The algorithm considered the quantity of students in each class, class time, class size, time accessibility in each class and lecturer who in charge of the classes.  Keywords: Genetic Algorithm; Heuristics Approach; Timetable Scheduling Journal of Science and Technology, Vol. 9 No. 3 (2017) p. 10-15  11  consider only 4 class in a day while other consider 5. Usually the conflicts can be divided into two which are hard constraints and soft constraints.  2.1 Problem definition  Following are the participant in the timetable scheduling problem: I is an instructor or lecturer 𝒊𝟏,𝒊𝟐, 𝒊𝟑, 𝒊𝟒 and MT is a Meeting Time 𝒎𝒕𝟏, 𝒎𝒕𝟐, 𝒎𝒕𝟑, 𝒎𝒕𝟒 and C is a course 𝒄𝟏, 𝒄𝟐, 𝒄𝟑, … , 𝒄𝟕 and R is a room 𝒓𝟏, 𝒓𝟐, 𝒓𝟑 and D is a department of dept1, dept2, dept3 I is the lecturer involve in the timetable. The meeting time and the day of the class has been set in the program. The course also until 7 course and the available room is only 3 that has been set the capacity of each room. 2.2 Constraints Involved In the timetable scheduling, there are a constraints should be followed which are:  No two subjects in one class at the same time.  Instructor having no more than one class in the same time  No room should be double book  All the allocated rooms must can hold the number of student To get the feasible solution, the constraints should be followed. This paper should satisfy as many soft constraints as possible so that, the good quality of timetable can be obtained. The soft constraints generally is just to get the best timetable that can make all the students and also instructors satisfy and happiest. This paper has constructed a lecturer timetable by using the genetic algorithm techniques. A natural chromosomes representation was chosen and genetic operators was also be build. A chromosome is made up of groups as genes.  3. Genetic Algorithm     Genetic algorithm is a method for solving both constrained and unconstrained optimization problems based on a natural selection process that mimics biological evolution. According to Michael D. V. [9], the simple genetic algorithm is definitely about two thing which are the search space and identifying the heuristic function. The algorithm repeatedly modifies a population of individual solution. The best point in the population approaches an optimal solution. A population is maintained and the fittest timetables are selected to form the basis of the next generation or iteration. In GA there are three basic operator which are selection, crossover and mutation. This three operator is applied to get the best results. The initialization of a population, the evaluation, and the genetic operator were implemented and controlled by using programming. The GA will assign course in what class, at what time and the instructor involved. Initial population is generated randomly. In the figure 1 below shows the genetic algorithm cycles.  Fig. 1 Genetic Algorithm cycle  3.1 Chromosome Representation  The chromosome is usually representations as a bit string. All the possible information should be contains in the chromosome such as;    Journal of Science and Technology, Vol. 9 No. 3 (2017) p. 10-15  12  𝑓 ∶ 𝐼 × 𝑀𝑇 × 𝐶 × 𝑅 × 𝐷  →   {0,1} Where f (i, mt, c, r, dept) = 1 if and only if course c has I has an instructor in the given class and time. A gene in this representation may also be considered as an element with 5-dimensional matrix, with an allele value of 0 if false and 1 if true. 3.2 Initialize Population  A population of a solution is initialize randomly. For a timetable to be produced, the core course should be considered first. The course is selected in random order, and each course is assigned to a randomly chosen meeting time with the number of students in the course with the available room capacity without violated the constraints. 3.3 Evaluate Fitness  Fitness function is an objective function of problem. Fitness will give the value that then will specify the solution is the best solution or not. This evaluation of fitness also will make sure the looping process in genetic algorithm to be stopped or not. In others word, fitness will control and maintain the process flow of genetic algorithm. The option of the next generation will be control and maintain and will not go further from it. The fitness function for this timetable problem is the inverse of the number of students with class conflicts. This give a meaning, the lesser the number of students with class conflicts, the more fit the class is. The fitness function can be; f =  11 + x  Where, x is a submission of conflicts or constraints. 𝑥 = 𝐼 + 𝑀𝑇 + 𝐶 + 𝑅 + 𝐷 I is an instructor, the instructor will assign value of 0 in number if there is only i instructor at meeting time mt in class course c in room r from department dept. The value will be equal to 1, if there is clash of any meeting time mt, class course c, room r, department dept or even with other lecturer. This situation is same with other 4 criteria which are meeting time, class course, room and department. There should have no clash and the value is 0, if there are clash, value of 1 will be assign, show there is a conflict. 3.4 Selection  Selection is one of the Genetic Algorithm operators and it’s usually will be applied first. According to [2], reproduction or selection usually will be the first operator being applied on a population. After the fitness value is calculated, the most fitter will be selected. 3.5 Crossover and Mutation       Crossover is a phase where there is a recombination of two string to get a better string. The crossover process being done to vary a chromosome from one generation to the next generation. Such an example of crossover is; Parent 1: 1   1   1   0   0 Parent 2: 0   1   0   1   1 Choose a crossover point Parent 1: 1   1   1   0   0 After crossover  Offspring 1: 1   1   0   1   1 Offspring 2: 0   1   1   0   0 At this point, the fitness value will be calculated, and if it’s not fit enough, the mutation process will go through.       Mutation is a process of altering one or more gene values in chromosomes from its initial state. This phase will be used to maintain genetic diversity from one generation. Example of mutation process is: Before: 1   1   0   0   1 After: 1   1    0    1    1       After the mutation process, the fitness value will be calculated, if its fitter, then it will stop and get the best solution, but if it’s not fitter, the process will begin from evaluate to selection, crossover and mutation until it Journal of Science and Technology, Vol. 9 No. 3 (2017) p. 10-15  13  satisfy stopping criteria or objective function achieved. 3.6 GA Implementation The timetabling is perform in Java programming for this paper of GA. From this paper, the timetable produced is based on the best fitness value which has a low in conflicts. 4. Computational Results The data is get from the simulation and not from the real data. The timetable can be represented as a class, dept, course, room, instructor, and meeting time. In the table 1, its shows the fitness value and conflicts of the program after some iteration. The table 1 explaining about list of possible result based on conflict and fitness value. The table start from less fitness value and higher conflict and stop with higher fitness value and lowest conflict. Its gives a fitness of 1.0000 and 0 conflicts at the end of result. Therefore, the iteration stop as it’s satisfy objective function and give the best result of timetable. While in table 2, showing the timetable with more proper arrangement and more easy to be seen with its separation. Table 2 explaining about the optimal solution with 0 conflict and fitness value of 1. The result show that all the constraints is satisfy The separation is made into course with number and maximum of students, room with capacity, the instructor’s name and the meeting time as well. Table 1  Solution showing fitness value and conflicts Schedule Classes [dept,class,room, instructor,meeting-time] Fitness Conflict 0 [MATH,C1,R2,I2,MT2],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I2,MT3],[EE,C4,R3,I3,MT3],[EE,C5,R3,I4,MT2],[PHY,C6,R2,I1,MT4],[PHY,C7,R2,I2,MT1] 1.00000 0 1 [MATH,C1,R2,I2,MT4],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I2,MT3],[EE,C4,R3,I3,MT3],[EE,C5,R3,I4,MT2],[PHY,C6,R1,I1,MT3],[PHY,C7,R2,I2,MT1] 0.50000 1 2 [MATH,C1,R2,I2,MT2],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I2,MT3],[EE,C4,R3,I3,MT3],[EE,C5,R3,I4,MT2],[PHY,C6,R1,I1,MT3],[PHY,C7,R2,I2,MT1] 0.50000 1 3 [MATH,C1,R2,I2,MT4],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I2,MT3],[EE,C4,R3,I3,MT3],[EE,C5,R3,I4,MT2],[PHY,C6,R2,I1,MT3],[PHY,C7,R2,I2,MT1] 0.50000 1 4 [MATH,C1,R2,I2,MT4],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I2,MT3],[EE,C4,R1,I4,MT4],[EE,C5,R3,I4,MT2],[PHY,C6,R1,I1,MT3],[PHY,C7,R2,I2,MT1] 0.33333 2 5 [MATH,C1,R2,I2,MT2],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I2,MT3],[EE,C4,R3,I3,MT3],[EE,C5,R3,I4,MT2],[PHY,C6,R1,I3,MT3],[PHY,C7,R2,I2,MT1] 0.33333 2 6 [MATH,C1,R2,I2,MT2],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I2,MT3],[EE,C4,R1,I4,MT3],[EE,C5,R1,I4,MT1],[PHY,C6,R2,I1,MT3],[PHY,C7,R2,I2,MT1] 0.25000 3 7 [MATH,C1,R2,I2,MT2],[MATH,C3,R1,I1,MT2],[EE,C2,R2,I3,MT3],[EE,C4,R3,I3,MT2],[EE,C5,R3,I4,MT2],[PHY,C6,R3,I3,MT4],[PHY,C7,R3,I4,MT3] 0.25000 3 8 [MATH,C1,R2,I2,MT4],[MATH,C3,R1,I1,MT2],[EE,C2,R1,I2,MT3],[EE,C4,R1,I4,MT4],[EE,C5,R3,I4,MT2],[PHY,C6,R1,I1,MT3],[PHY,C7,R2,I2,MT1] 0.20000 4       Journal of Science and Technology, Vol. 9 No. 3 (2017) p. 10-15  14  Table 2 The timetable Class  Dept  Course (number, max # of students) Room (capacity) Instructor (Id) Meeting time (Id) 01 Math  325K (C1, 25) R2(45) Mr B (I2) MWF 10:00 – 11:00 (MT2) 02 Math  462k (C3, 25) R1(25) Dr A (I1) MWF 10:00 – 11:00 (MT2) 03 EE 319K (C2, 35) R2(45) Mr B (I2) TTH 09:00 – 10:30 (MT3) 04 EE 464K (C4, 30) R3(35) Dr C (I3) TTH 09:00 – 10:30 (MT3) 05 EE 360C (C5, 35) R1(25) Mrs D (I4) MWF 10:00 – 11:00 (MT2) 06 Phy  303K (C6, 45) R2(45) Dr A (I1) TTH 10:30 – 12:00 (MT4) 07 Phy  303L (C7, 45) R2(45) Mr B (I2) MWF 09:00 – 10:00 (MT1)  From the table, it show that only three department are involve which are mathematics, physics and electrical engineering. The course also only 7 course involve with 4 instructor. All the three rooms available has been using with the time set.  Conclusions This research has concentrated on a scheduling of timetable. This problem of scheduling being solve by using a genetic algorithm. This paper shown that genetic algorithm is the best choices to solve a problem regarding of student timetable. In this paper, the meeting and day has been set. The GA operators also is very helping in getting the best solutions and efficient. Selection, crossover and also mutation give the best solution and variation. References  [1]  Lawrence L. & Bethel, (1956), Industrial Organization and Management, Mc Graw-Hill Publisher. [2]  Jha S. K., (2014), Exam timetabling problem using genetic algorithm, International Journal of Research in Engineering and Technology, 3(5), 649-654. [3]  Burke E. K., McCollum B., Meisels A., Petrovic S., & Qu, (2007), R. A graph-based hyper-heuristic for educational timetabling problem, European Journal of Operational Research, 176, 177-192. [4]  Kacem I., (2003), scheduling flexible job-shops: a worst case analysis and an evolutionary algorithm, International Journal of Computational Intelligence and Applications, 3(4), 437-452. [5] Sauer J., Appelrath H.-J. (2000), Integrating transportation in a multi-site scheduling environment, published in the Proceedings of the Hawai’i International Conference On System Sciences, Maui. [6]  Labidi M., Mrad M., Gharbi A., and Louly M. A. (2014), Scheduling IT staff at a bank: a mathematical programming approach, The Scientific World Journal. [7]  Ribeiro C. C. (2012), Sports scheduling :problems and applications, International Transactions In Operational Research, 19 (1-2), pp. 201-226. [8]  Yuan Z., Fugenschuh (2003), Home health care scheduling: A case study, European Journal of Operational Research, 151(3), pp. 447-460, 6. [9] Michael D. V., (1999), The Simple Genetic Algorithm: Foundations and Journal of Science and Technology, Vol. 9 No. 3 (2017) p. 10-15  15  Theory, A Bradford Book, The MIT Press, London, England.   

A Heuristics Approach for Classroom Scheduling using Genetic Algorithm Technique

This study explored the impact of sintering temperature variations on the synthesis and characteristics of mullite ceramics derived from a composite blend of kaolinite clay, silica (silicon dioxide), and feldspar. Sintering temperatures ranging from 1100 to 1200 °C were systematically examined to analyze alterations in shrinkage, density, microstructure, elemental composition, and phase formation. The study revealed that an increase in sintering temperature led to decreased shrinkage due to improved particle packing and reduced porosity. Ceramic density showed a direct relation with sintering temperature, reaching the optimal density at 1175 °C and indicating efficient particle packing and compaction. Analysis through field emission scanning electron microscopy (FESEM) provided insights into microstructural changes, including alterations in grain morphology, porosity, and connectivity. Energy dispersive X-ray spectroscopy (EDS) clarified element distribution within the microstructure, offering valuable information on compositional variations. X-ray diffraction (XRD) examinations unveiled temperature-dependent phase transformations, which confirmed the successful formation of mullite during the sintering process. A sintering temperature of 1175 °C yielded the optimal ceramic quality and cost-effectiveness for high-temperature heating processes

Jalaluddin, Mohamed Lokman

Umar Al-Amani Azlan, Umar Al-Amani Azlan

Abd Rashid, Mohd Warikh

Tamin, Norfauzi

UTHM Institutional Repository

Effect of sintering temperatures on the physical, structural properties and microstructure of mullite-based ceramics

An empirical study of the implementation of green supply chain management practices in the electrical and electronic industry and their relation to organizational performance,

An inter-sectoral comparison of green supply chain management in China: drivers and practices”,

Are supplier selection criteria going green? Case studies of companies in Brazil.

Barriers and stimuli for ecodesign in SMEs”,

Designing the green supply chain&quot;,

Do green supply chains lead to competitiveness and economic performance?”,

Drivers for the participation of small and medium-sized suppliers in green supply chain initiatives. Supply Chain Management:

Emerald Article Conducting a literature review Conducting a Literature Review,

Emerging Logistics Strategies: Blueprints for the Next Century&quot;,

Environmental performance as an operations objective”,International

Green Supply Chain Initiatives: Investigation on the Barriers in the Context of SMEs in

Green value chain practice in the furniture industry,Journal of

Greening production: a South-East Asian experience”,

Management of Technology: The Key To Competitiveness and Wealth creation”.

Research Methods for Business, A Skill Building Approach (4th Edition)

S.(2009), “Going Green though Green Supply Chain Initiatives towards Environmental Sustainability” ”,

Strategic Assets and Organizational Rent”,Strategic

supply chain efficiency from a green perspective.

Supporting environmental improvements in SMEs in the UK”,

A heuristics approach for classroom scheduling using genetic algorithm technique

https://publisher.uthm.edu.my/ojs/index.php/JST/article/download/2030/1236

A heuristics approach for classroom scheduling using genetic algorithm technique

Abstract

Similar works

Full text

Available Versions

Journals of Universiti Tun Hussein Onn Malaysia (UTHM)

UTHM Institutional Repository

UTHM Institutional Repository