• Title/Summary/Keyword: Course Timetabling Problem

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A Constraint Programming-based Automated Course Timetabling System

  • Hwang, Junha
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.4
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    • pp.27-34
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    • 2019
  • The course timetabling problem is a kind of very complex combinatorial optimization problems, which is known as an NP-complete problem. Sometimes a given course timetabling problem can be accompanied by many constraints. At this time, even if only one constraint is violated, it can be an infeasible timetable. Therefore, it is very difficult to make an automated course timetabling system for a complex real-world course timetabling problem. This paper introduces an automated course timetabling system using constraint programming. The target problem has 26 constraints in total, and they are expressed as 24 constraints and an objective function in constraint programming. Currently, we are making a timetable through this system and applying the result to the actual class. Members' satisfaction is also much higher than manual results. We expect this paper can be a guide for making an automated course timetabling system.

The University Examination And Course Timetabling Problem With Integer Programming

  • Chung, Yerim;Kim, Hak-Jin
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.9
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    • pp.9-20
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    • 2019
  • In this paper, we study the university timetabling problem, which consists of two subproblems, the university course timetabling problem and the examination timetabling problem. Given a set of classrooms, students, teachers, and lectures, the problem is to assign a number of courses (and examinations) to suitable timeslots and classrooms while satisfying the given set of constraints. We discuss the modeling and solution approaches to construct course and examination timetables for one of the largest Korean university. By using binary integer programming formulations, we describe these two complex real-world problems. Then, we propose a solution method, called NOGOOD, to solve the examination timetabling model. The computation results show that NOGOOD finds the optimal examination schedule for the given instance. Although we consider a specific instance of the university timetabling problem, the methods we use can be applicable to modeling and solving other timetabling problems.

Constraint Programming Approach for a Course Timetabling Problem

  • Kim, Chun-Sik;Hwang, Junha
    • Journal of the Korea Society of Computer and Information
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    • v.22 no.9
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    • pp.9-16
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    • 2017
  • The course timetabling problem is a problem assigning a set of subjects to the given classrooms and different timeslots, while satisfying various hard constraints and soft constraints. This problem is defined as a constraint satisfaction optimization problem and is known as an NP-complete problem. Various methods has been proposed such as integer programming, constraint programming and local search methods to solve a variety of course timetabling problems. In this paper, we propose an iterative improvement search method to solve the problem based on constraint programming. First, an initial solution satisfying all the hard constraints is obtained by constraint programming, and then the solution is repeatedly improved using constraint programming again by adding new constraints to improve the quality of the soft constraints. Through experimental results, we confirmed that the proposed method can find far better solutions in a shorter time than the manual method.

A Template-based Interactive University Timetabling Support System (템플릿 기반의 상호대화형 전공강의시간표 작성지원시스템)

  • Chang, Yong-Sik;Jeong, Ye-Won
    • Journal of Intelligence and Information Systems
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    • v.16 no.3
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    • pp.121-145
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    • 2010
  • University timetabling depending on the educational environments of universities is an NP-hard problem that the amount of computation required to find solutions increases exponentially with the problem size. For many years, there have been lots of studies on university timetabling from the necessity of automatic timetable generation for students' convenience and effective lesson, and for the effective allocation of subjects, lecturers, and classrooms. Timetables are classified into a course timetable and an examination timetable. This study focuses on the former. In general, a course timetable for liberal arts is scheduled by the office of academic affairs and a course timetable for major subjects is scheduled by each department of a university. We found several problems from the analysis of current course timetabling in departments. First, it is time-consuming and inefficient for each department to do the routine and repetitive timetabling work manually. Second, many classes are concentrated into several time slots in a timetable. This tendency decreases the effectiveness of students' classes. Third, several major subjects might overlap some required subjects in liberal arts at the same time slots in the timetable. In this case, it is required that students should choose only one from the overlapped subjects. Fourth, many subjects are lectured by same lecturers every year and most of lecturers prefer the same time slots for the subjects compared with last year. This means that it will be helpful if departments reuse the previous timetables. To solve such problems and support the effective course timetabling in each department, this study proposes a university timetabling support system based on two phases. In the first phase, each department generates a timetable template from the most similar timetable case, which is based on case-based reasoning. In the second phase, the department schedules a timetable with the help of interactive user interface under the timetabling criteria, which is based on rule-based approach. This study provides the illustrations of Hanshin University. We classified timetabling criteria into intrinsic and extrinsic criteria. In intrinsic criteria, there are three criteria related to lecturer, class, and classroom which are all hard constraints. In extrinsic criteria, there are four criteria related to 'the numbers of lesson hours' by the lecturer, 'prohibition of lecture allocation to specific day-hours' for committee members, 'the number of subjects in the same day-hour,' and 'the use of common classrooms.' In 'the numbers of lesson hours' by the lecturer, there are three kinds of criteria : 'minimum number of lesson hours per week,' 'maximum number of lesson hours per week,' 'maximum number of lesson hours per day.' Extrinsic criteria are also all hard constraints except for 'minimum number of lesson hours per week' considered as a soft constraint. In addition, we proposed two indices for measuring similarities between subjects of current semester and subjects of the previous timetables, and for evaluating distribution degrees of a scheduled timetable. Similarity is measured by comparison of two attributes-subject name and its lecturer-between current semester and a previous semester. The index of distribution degree, based on information entropy, indicates a distribution of subjects in the timetable. To show this study's viability, we implemented a prototype system and performed experiments with the real data of Hanshin University. Average similarity from the most similar cases of all departments was estimated as 41.72%. It means that a timetable template generated from the most similar case will be helpful. Through sensitivity analysis, the result shows that distribution degree will increase if we set 'the number of subjects in the same day-hour' to more than 90%.

Design of a Multiagent-based Lecture-timetabling Automation System using the Properties of Distributed Constraint Satisfaction (분산 제약조건 만족 특성을 이용한 다중 에이전트 기반 강의 시간표 자동화 시스템 설계)

  • 황경순;전중남;이건명
    • Proceedings of the Korean Information Science Society Conference
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    • 2002.04b
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    • pp.283-285
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    • 2002
  • 강의시간표 문제(Lecture timetabling Problem)는 일주일을 기본으로 하는 특정 시간대 별로 학생(Course-class), 교수, 그리고 강의실과 같은 자원에 대한 스케줄링 문제로서 각각의 자원에 대하여 적절한 조합으로 제약조건들 사이의 충돌을 최소화하여 자원을 배치하는 할당문제이다. 강의시간표 문제는 수천 명 학생들에 대하여 개개인의 시간표를 작성해야 하므로 기하급수적으로 증가하는 탐색공간에 대하여 최악의 경우 탐색 시간이 지수적으로 증가하는 NP-complete Problem이다. 이러한 거대하고 복잡한 강의시간표 문제는 계층적으로 분할하여 기능별로 처리하면서 제약조건을 협상하도록 하는 각 모듈 단위의 에이전트를 구성하므로 좀 더 작고 단순한 문제로 변환될 수 있다. 본 논문에서는 방대한 탐색 공간과 과잉-제약조건(Over-constraint)문제의 하나인 강의시간표 작성 문제를 분산제약조건 만족 문제 특성을 이용하고 다중 에이전트 구조를 사용하여 해결하는 강의시간표 자동화 시스템 설계를 제안한다.

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A Novel and Effective University Course Scheduler Using Adaptive Parallel Tabu Search and Simulated Annealing

  • Xiaorui Shao;Su Yeon Lee;Chang Soo Kim
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.18 no.4
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    • pp.843-859
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    • 2024
  • The university course scheduling problem (UCSP) aims at optimally arranging courses to corresponding rooms, faculties, students, and timeslots with constraints. Previously, the university staff solved this thorny problem by hand, which is very time-consuming and makes it easy to fall into chaos. Even some meta-heuristic algorithms are proposed to solve UCSP automatically, while most only utilize one single algorithm, so the scheduling results still need improvement. Besides, they lack an in-depth analysis of the inner algorithms. Therefore, this paper presents a novel and practical approach based on Tabu search and simulated annealing algorithms for solving USCP. Firstly, the initial solution of the UCSP instance is generated by one construction heuristic algorithm, the first fit algorithm. Secondly, we defined one union move selector to control the moves and provide diverse solutions from initial solutions, consisting of two changing move selectors. Thirdly, Tabu search and simulated annealing (SA) are combined to filter out unacceptable moves in a parallel mode. Then, the acceptable moves are selected by one adaptive decision algorithm, which is used as the next step to construct the final solving path. Benefits from the excellent design of the union move selector, parallel tabu search and SA, and adaptive decision algorithm, the proposed method could effectively solve UCSP since it fully uses Tabu and SA. We designed and tested the proposed algorithm in one real-world (PKNU-UCSP) and ten random UCSP instances. The experimental results confirmed its effectiveness. Besides, the in-depth analysis confirmed each component's effectiveness for solving UCSP.