A Contention-Oriented Timeslot Selection Heuristic for School Timetabling

A double evolutionary pool memetic algorithm is proposed to solve the examination timetabling problem. To improve the performance of the proposed algorithm, two evolutionary pools, that is, the main evolutionary pool and the secondary evolutionary pool, are employed. The genetic operators have been specially designed to fit the examination timetabling problem. A simplified version of the simulated annealing strategy is designed to speed the convergence of the algorithm. A clonal mechanism is introduced to preserve population diversity. Extensive experiments carried out on 12 benchmark examination timetabling instances show that the proposed algorithm is able to produce promising results for the uncapacitated examination timetabling problem.


 
 
 
 Abstract:
 Aim: This study is on tackling Examination Timetabling Problem (ETP) of the Faculty of Economics And Administrative Sciences (FEAS) of the Ankara HBV University summer school, where the courses of fall and spring semesters are offered simultaneously and regulations on restricting enrollments in inter-department electives or in-department courses of distinct years are relaxed. Thus, the complexity of the nature of the ETP problem is exacerbated. The direct heuristics based on successive assignments that the university normally adopts was proven inadequate for assuming standard regulations hence, another approach we explain in this paper was needed.
 Design / Research methods: The ETP was formulated as a Linear Mixed-Integer Program (LMIP) and decomposed into three stages; timetabling exams, room assignment, student allocation. To manage the conflict between the stakeholders of the examination procedure, a lexicographic optimization process based on the priority of the parties was undertaken.
 Conclusions / findings: After a recursive timetabling process based on a trial-and-error method a clash-free timetable was generated and, a room assignment plan that minimizes the total number of proctoring duties, usage of higher floor rooms and total crowdedness of rooms respectively was put into action. Therefore no student group experienced any clashing exams, the faculty members saved time that can be spent on research instead, since the room usage was better planned the costs (elevator usage, lighting, air conditioning, the labor of the janitors) were assumed to be decreased.
 Originality / value of the article: Each examination period bares a different ETP due to its problem-specific nature (number of courses offered, structure of student enrollments, availability of rooms, etc.). Summer schools provide a more irregular structure that demands special attention, a trial-and-error reformulation of the ETP in our case. In addition, the traditional formulations of the ETP, to the extent we have been able to scan, do not include the minimization of the crowdedness of the rooms. Thus, in creating a more comfortable environment, easier to monitor exams and, ability in handling unexpected dysfunctionalities (broken classroom equipment, etc.) this study is novel.
 Limitations of the research: The algorithms to solve an ETP formulated as an LMIP are of high complexity therefore, we are not able to assert the optimality of our suggested solutions acquired within time limitations.
 
 
 
 
 Keywords: examination timetabling, group decision making, lexicographic optimization, linear mixed-integer programming
 JEL: C44, C61, M12
 
 
 

Solving a real-world university examination timetabling is an intractable problem. Examination timetabling problems (ETP) can be defined as a problem of assigning a set of final examinations schedules to a given number of timeslots and rooms subject to a set of constraints. These constraints are usually divided into hard and soft constraints. Hard constraints must be satisfied under any circumstances. Whilst, soft constraints are not only essential but also should be satisfied as much as possible. Due to the complexity of the problem, it is usually impossible to have solutions that satisfy all soft constraints. The quality of the timetable is measured based on soft constraints violation. A weighted penalty/value is attached to each violation of the soft constraint and the objective is to minimize the total penalty value of these violations. Although there have been a numerous approaches in solving the ETP, but this paper only focus on Genetic Algorithm (GA) method based on the fact that it is robust and can fits into complex problem space. This paper gives a summary of the GA method on ETP and it aims in helping other researcher to shorten their time in understanding the application of GA in the selected problem.

In general, uncapacitated exam timetabling is conducted manually, which can be time-consuming. Many studies aim to automate and optimize uncapacitated exam timetabling. However, pinpointing the most efficient algorithm is challenging since most studies assert that their algorithms surpass previous ones. To identify the optimal algorithm, this research evaluates the performance of four algorithms: Hill climbing (HC), simulated annealing (SA), great deluge (GD), and tabu search (TS) in addressing the exam timetabling problem. The Kempe chain operator’s influence on optimization solutions is also examined. A simple random method is employed to select the low-level heuristic (LLH). The Carter (Toronto) dataset served as the test material, with each algorithm undergoing 200,000 iterations for comparison. The results indicate that the TS algorithm is superior, providing the best solution in 13 instances. The use of a tabu list enhanced the search process’s efficiency by preventing redundant modifications. The Kempe chain LLH exhibited a tendency towards achieving better solutions.

At all educational institutions, timetabling is a conventional problem that has always caused numerous difficulties and demands that need to be satisfied. For the examination timetabling problem, those matters can be defined as complexity in scheduling exam events or non-deterministic polynomial hard problems (NP-hard problems). In this study, the latest approach using an ant colony optimisation (ACO) which is the ant system (AS) is presented to find an effective solution for dealing with university exam timetabling problems. This application is believed to be an impressive solution that can be used to eliminate various types of problems for the purpose of optimising the scheduling management system and minimising the number of conflicts. The key of this feature is to simplify and find shorter paths based on index pheromone updating (occurrence matrix). With appropriate algorithm and using efficient techniques, the schedule and assignation allocation can be improved. The approach is applied according to the data set instance that has been gathered. Therefore, performance evaluation and result are used to formulate the proposed approach. This is to determine whether it is reliable and efficient in managing feasible final exam timetables for further use.

We present one general high-level hyper-heuristic approach for addressing two timetabling problems in the health care domain: the patient admission scheduling problem and the nurse rostering problem. The complex combinatorial problem of patient admission scheduling has only recently been introduced to the research community. In addition to the instance that was introduced on this occasion, we present a new set of benchmark instances. Nurse rostering, on the other hand, is a well studied operations research problem in health care. Over the last years, a number of problem definitions and their corresponding benchmark instances have been introduced. Recently, a new nurse rostering problem description and datasets were introduced during the first Nurse Rostering Competition. In the present paper, we focus on this nurse rostering problem description. The main contribution of the paper constitutes the introduction of a general hyper-heuristic approach, which is suitable for addressing two rather different timetabling problems in health care. It is applicable without much effort, provided a set of low-level heuristics is available for each problem. We consider the instances of both health care problems for testing the general applicability of the hyper-heuristic approach. Also, improvements to the previous best results for the patient admission scheduling problem are presented. Solutions to the new nurse rostering instances are presented and compared with results obtained by an integer linear programming approach.

The examination timetabling problem involves assigning exams to a specific or limited number of timeslots and rooms with the aim of satisfying all hard constraints (without compromise) and satisfying the soft constraints as far as possible. Most of the techniques reported in the literature have been applied to simplified examination benchmark data sets. In this paper, we bridge the gap between research and practice by investigating a problem taken from the real world. This paper introduces a modified and extended great deluge algorithm (GDA) for the examination timetabling problem that uses a single, easy to understand parameter. We investigate different initial solutions, which are used as a starting point for the GDA, as well as altering the number of iterations. In addition, we carry out statistical analyses to compare the results when using these different parameters. The proposed methodology is able to produce good quality solutions when compared with the solution currently produced by the host organisation, generated in our previous work and from the original GDA.

The timetabling problem is well known to be an NP-complete combinatorial problem. The problem becomes even more complex when addressed to individual timetables of students. The core of dealing with the problem in this application is a timetable builder based on mixed direct-indirect encoding evolved by a genetic algorithm with a self-adaptation paradigm, where the parameters of the genetic algorithm are optimized during the same evolution cycle as the problem itself. The aim of this paper is to present an encoding for self-adaptation of genetic algorithms that is suitable for timetabling problems. Compared to previous approaches we designed the encoding for self-adaptation of not only one parameter or several ones but for all possible parameters of genetic algorithms at the same time. The proposed self-adaptive genetic algorithm is then applied for solving the real university timetabling problem and compared with a standard genetic algorithm. The main advantage of this approach is that it makes it possible to solve a wide range of timetabling and scheduling problems without setting parameters for each kind of problem in advance. Unlike common timetabling problems, the algorithm was applied to the problem in which each student has an individual timetable, so we also present and discuss the algorithm for optimized enrollment of students that minimizes the number of clashing constraints for students.

Hyper-heuristics can be identified as methodologies that search the space generated by a finite set of low level heuristics for solving search problems. An iterative hyper-heuristic framework can be thought of as requiring a single candidate solution and multiple perturbation low level heuristics. An initially generated complete solution goes through two successive processes (heuristic selection and move acceptance) until a set of termination criteria is satisfied. A motivating goal of hyper-heuristic research is to create automated techniques that are applicable to a wide range of problems with different characteristics. Some previous studies show that different combinations of heuristic selection and move acceptance as hyper-heuristic components might yield different performances. This study investigates whether learning heuristic selection can improve the performance of a great deluge based hyper-heuristic using an examination timetabling problem as a case study.

University examination timetabling problem is a complicated, multi-constraint combinatorial optimization problem. The current grouping genetic algorithm could get a better optimistic solution. Although the block encoding technique was applied in, the probabilities of crossover and mutation operation were still based on simple genetic algorithm. So the universality of this algorithm is not very well because the same probabilities of crossover and mutation operation could obtain different effects in different cases of examination arrangements. To find a more general algorithm, an Improved Adaptive Genetic Algorithm (IAGA) for practical applications was presented in this paper. IAGA can reconstruct the probabilities of crossover and mutation operation according to different cases of examination arrangements. To make further improvement of its convergence speed and overcome premature problem, IAGA appropriately adjusts mutation operation by Population's Maturity in addition. Moreover, the Memory Operator was added into the Algorithm to ensure getting the global optimization solution. Finally, IAGA was tested in function optimization and Examination Timetabling problems, and the experiments show that the results are promoted very well.

An informed genetic algorithm for the examination timetabling problem

An examination timetabling problem at a large American university is presented. Although there are some important differences, the solution approach is based on the ITC 2007 winning solver which is integrated in the open source university timetabling system UniTime. In this work, nine real world benchmark data sets are made publicly available and the results on four of them are presented in this paper. A new approach to further decreasing the number of student conflicts by allowing some exams to be split into multiple examination periods is also studied.

A survey of the state-of-the-art of optimisation methodologies in school timetabling problems

This paper addresses the school timetabling problem, which consists of defining the date and time in which classes will be given by teachers in educational institutions. For this purpose, a tool that uses Operational Research (OR) techniques was developed, focused on generating and optimizing Elementary and High School timetables, taking into account teachers’ preferences for certain days or for sequenced (twinned) classes. Conductive to solving the problem, a Non Linear Binary Integer Programming mathematical model (NLBIP) and Local Search (LS) and Iterated Local Search (ILS) procedures were comparatively applied. A real problem with 14 timetables of public schools in the city of Araucária (in Paraná State, Brazil) was analyzed. The results indicate that the computational time required by the mathematical model is feasible for the problems in question. The ILS technique has the potential for testing larger scale problems, as it presents a dispersion of 3.5% to 7.7% relative to the optimal solution (obtained by the NLBIP) and a computational time that is 15 to 338 times faster.

Hybrid bee colony optimization for examination timetabling problems