International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 11, November 2018, pp. 416–428, Article ID: IJMET_09_11_041 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=11 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed A CRITICAL REVIEW ON THE OPTIMIZATION METHODS IN SOLVING EXAM TIMETABLING AND SCHEDULING Elizabeth Amudhini Stephen Associate Professor, Mathematics, Karunya institute of technology and science, Coimbatore, India ABSTRACT The Examination Timetabling problem regards the scheduling for the exams of a set of university courses, avoiding the overlapping of exams having students in common, fairly spreading the exams for the students, and satisfying room capacity constraints. This paper review different optimization techniques used to solve a general time tabling problems. The basic approach can readily handle a wide variety of exam timetabling problem constraints, and is therefore likely to be of great practical usefulness. The approach relies for its success on the use of specially designed mutation operators which greatly improve upon the performance. Keywords: Exam Timetabling; Iterative Improvement Methods, Simulated Annealing, Great Deluge Algorithm, Tabu Search, Evolutionary Algorithms, Memetic Algorithms, Ant Colony Optimization, Hybrid Approaches. Cite this Article Elizabeth Amudhini Stephen, a Critical Review on the Optimization Methods in Solving Exam Timetabling and Scheduling, International Journal of Mechanical Engineering and Technology, 9(11), 2018, pp. 416–428. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=11 1. INTRODUCTION The oxford advanced learner’s dictionary defines a timetable as ‘a list of showing the times at which particular events will happen’. Wren(1996) described timetabling as a special type of scheduling. He defined timetabling as follows;“Timetabling is the allocation, subject to constraints, of given resources to objects being placed in space time, in such a way as to satisfy as nearly as possible a set of desirable objectives.’ Since the early 1960’s an enormous number of research papers reporting work on timetabling problems have appeared in the literature. After more than 50 years, research in this area is still very active and new research directions are continuing to emerge. Educational timetabling is a major administrative activity for a wide variety of Universities. A time tabling problem can be defined to be the problem of assigning a number of events into a limited number of time periods. University exam timetabling problem is modeled as an optimization problem The Examination Timetabling problem is a combinatorial problem that commonly arises in http://www.iaeme.com/IJMET/index.asp 416 [email protected] Elizabeth Amudhini Stephen Universities: One has to schedule a certain number of examinations in a given number of time slots in such a way that no student is involved in more than one exam at a ime. The assignment of exams to days and to time slots within the day is also subject to constraints on availabilities, fair spreading of the student workload, and room capacities. Different variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of constraints and objectives involved. Constraints involve room capacity and teacher availability, whereas objectives mainly regard student workload. In this paper, we present an ongoing research on the development a of solution algorithm for a set of variants of the Examination timetabling problem using different methods of optimization. 2. UNIVERSITY EXAM TIME TABLING Examinations in a university take place five times a year. At the end of each semester and at the end of every trimester there is a normal four week examination period where all the courses offered during the semester/trimester are examined. Generally students have complete freedom in taking the exams at any exam period (in which they are scheduled) within their course of studies. In every examination day there are two different periods (9:30 AM– 12:30P.M and 2:00 P.M – 5:00 P.M).Since students are allowed to have increased flexibility in selecting courses, all the courses offered by the department must be examined at different periods. Even in its simplest form this task is not easy. In each department, about 50 courses are offered and therefore atleast two examinations per dept must be scheduled in each examination day. The basic exam timetabling problem is to assign examinations to limited number of time units(periods), normally lasting up to three hours, in such a way that: 1. There are no conflicts., i.e., no students is called to take more than one examination at a time 2. All the exams are assigned to periods 3. The seating capacity is not exceeded in any period 4. Only one compulsory course from each department must be examined in each examination day 5. The compulsory course of a university stream must be evenly spread over the examination period: and 6. The exam period has the smallest possible length 3. THE GENERAL FRAMEWORK Hertz (1991) stated that approaches developed to solve timetabling problems usually consist of two phases. Normally, in Phase 1:Sequential Constructive Algorithm, a solution is (or solutions are) constructed by using a sequential construction algorithm. The constructed solutions can be feasible or infeasible. If a solution is infeasible, it can be ‘corrected’ during the iterative improvement phase (Phase 2). In Phase 2: Iterative improvement, the initial solution is modified in order to improve the solution while ensuring the feasibility of the solution. The improvements can be implemented by using any search algorithm such as Genetic Algorithms (Holland, 1992), Tabu Search (Glover,1986), Simulated Annealing (Kirkpatrick et al., 1983) or the Great Deluge Algorithm (Dueck, 1993) (to name just a few approaches). In the first part of this research, the focus is on the construction process, as constructing feasible solutions is a difficult task especially for large, real-world timetabling problems (Hertz, 1991). The use of a sequential constructive algorithm is amongst the earliest approaches used to tackle the examination timetabling problem http://www.iaeme.com/IJMET/index.asp 417 [email protected] A Critical Review on the Optimization Methods in Solving Exam Timetabling and Scheduling in an automated way (Broder, 1964; Cole, 1964; Foxley and Lockyer, 1968). In this approach, the concept of ‘failed first’ was implemented. The basic idea was to first schedule the exams that might cause problems if they were to be left to later in the scheduling process. By doing so, the overall aim was to avoid the assignment of exams to time slots which might later lead to an infeasible solution. An infeasible solution is reached when at least one exam remains unscheduled. In many cases this is because exams placed earlier have invalidated all the potentially valid time slots. In such a situation, a different ordering may enable a feasible solution to be found. Approaches which order the events prior to assignment to a period have been discussed by several authors including Boizumault et al. (1996), Brailsford et al. (1999), Burke and Newall (2004), Burke, Kingston and de Werra (2004b), Burke and Petrovic (2002), and Carter et al. (1996). In the context of the exam timetabling benchmark data sets used in this research, this sequencing strategy has been implemented by Carter et al. (1996), Burke and Newall (2004), and Burke et al. (2007). Usually, the unscheduled exams are ordered in a sequence that represents how difficult it is judged that they will be to place in the timetable (most difficult first). A number of commonly used strategies have been adopted from the graph colouring problem. Many studies employ graph theory to calculate the ‘difficulty to schedule an exam’. The following list describes the most common graph colouring based heuristic orderings used in timetabling research: Largest Degree (LD) First. Exams are ranked in descending order by the number of exams in conflict — i.e. priority is given to exams with the greatest number of exams in conflict. Largest Enrolment (LE) First. Exams are ranked in descending order by the number of students enroled in each of the exams — i.e. exams with the highest number of students are given the highest priority. Least Saturation Degree (SD) First. Exams are ranked in increasing order by the number of valid time slots remaining in the timetable for each exam — priority is given to exams with fewer time slots available. Largest Colored Degree (LCD) First. This heuristic is based on LD. For this heuristic, only exams which have been already assigned to the schedule are considered as the exams which will cause conflict. Weighted Largest Degree (WLD) First. This heuristic is also based on LD. Besides the number of exams in conflict, the total number of students involved in the conflicts are taken into account as well. In general, heuristic orderings are divided into two categories: static and dynamic. Static heuristic orderings are predetermined before the start of the assignment process and their values remain the same throughout the process. For the heuristic orderings described above, LD, LE and WLD are categorized as static heuristic orderings. The number of exams in conflict with each exam and the number of students enrolled for each exam only need to be calculated once by analysing the specific problem structure. On the other hand, SD and LCD are considered to be a dynamic heuristic orderings because the number of valid time slots available for unscheduled exams and the number of exams assigned to time slots may change each time an exam is assigned to a valid time slot; in which case, the unscheduled exams need to be reordered. In 1961, Appleby et al. implemented graph colouring techniques in the preparation of school timetables. Since then, the use of graph based heuristic orderings has been extended to other types of timetabling problem.