Abstract
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%.
매 학기마다 반복되는 대학의 강의시간표 작성 방법은 대학 상황에 따라 다르며, 교육환경의 변화에 따라 그 복잡도와 문제의 크기가 증가되는 NP-hard 문제로 알려져 있다. 그 동안, 효과적인 강의자원 배분을 위한 강의시간표 자동생성의 필요성으로 대학 강의시간표 작성에 관한 여러 방법의 연구가 진행되어 왔다. 일반적으로 교양과목 강의시간표는 대학행정부서에서, 전공과목은 학과에서 작성하는데 각 학과 단위의 전공강의시간표작성지원시스템은 학생들의 편의를 도모하고 수업의 효과와 전공강의자원의 효과적인 배분를 위해 중요한 역할을 한다. 이를 위하여 본 연구는 한신대학교의 새로운 강의시간표 작성체계에 따라, 사례 기반의 템플릿을 생성하고, 이로부터 규칙 기반의 상호대화형으로 효과적인 강의자원 배분이 가능한 전공강의시간표를 작성하는 두 단계 지원시스템을 제안하였으며, 사례 데이터를 이용한 프로토타입으로 그 효과를 검정하였다. 과거 사례와의 유사도는 학과 평균 41.72%로 템플릿의 유용성을 볼 수 있으며, 민감도 분석 결과에서 동일 시간 개설과목 허용 임계치를 90% 이상 설정한다면 강의시간표가 더 고른 분포를 갖게 됨을 검정하였다.