University Timetabling Problem Research Articles

Optimization Techniques in University Timetabling Problem: Constraints, Methodologies, Benchmarks, and Open Issues

University timetabling problems are a yearly challenging task and are faced repeatedly each semester. The problems are considered non-polynomial time (NP) and combinatorial optimization problems (COP), which means that they can be solved through optimization algorithms to produce the aspired optimal timetable. Several techniques have been used to solve university timetabling problems, and most of them use optimization techniques. This paper provides a comprehensive review of the most recent studies dealing with concepts, methodologies, optimization, benchmarks, and open issues of university timetabling problems. The comprehensive review starts by presenting the essence of university timetabling as NP-COP, defining and clarifying the two formed classes of university timetabling: University Course Timetabling and University Examination Timetabling, illustrating the adopted algorithms for solving such a problem, elaborating the university timetabling constraints to be considered achieving the optimal timetable, and explaining how to analyze and measure the performance of the optimization algorithms by demonstrating the commonly used benchmark datasets for the evaluation. It is noted that meta-heuristic methodologies are widely used in the literature. Additionally, recently, multi-objective optimization has been increasingly used in solving such a problem that can identify robust university timetabling solutions. Finally, trends and future directions in university timetabling problems are provided. This paper provides good information for students, researchers, and specialists interested in this area of research. The challenges and possibilities for future research prospects are also explored.

A Mixed-Integer Linear Programming approach for university timetabling problem with the multi-section courses: an application for Hacettepe University Department of Business Administration

University course timetabling is an NP-Complete problem type which becomes even more difficult due to the specific requirements of each university. In this study, it was aimed to solve a university course timetabling problem by using integer programming and to develop assignment models that can be easily adapted to similar problems. The models that we developed for the solution are based on the integer programming model of Daskalaki et al. [1]. In addition, the models were developed taking into account the fact that there was an availability of multi-section courses, the minimum overlap of elective courses, and the ability to divide courses into sessions in terms of effective use of the capacity. In this framework, two different models (model 1 and model 2) were developed. Whereas model 1 assumes that all courses are processed as a single session (If a course has 3 time periods per week, then it is taught as a single session), model 2 assumes courses can be assigned by divided into multiple sessions (If a course has 3 time periods per week, then it can be divided into 1+1+1 or 2+1 sessions.). In model 2, a structure in which the model itself could determine how to split the courses in the framework of predetermined options was developed. Both models were formulated in such a way as to maximize the satisfaction of the lecturers. Finally, a larger scale problem was derived from the first problem and the performance of these two models were compared for both problems. The results showed that the optimal solution was obtained within the specified constraints, and the solution time significantly increased with an increase in the size of the problem.

A graph-based MIP formulation of the International Timetabling Competition 2019

The International Timetabling Competition 2019 (ITC 2019) posed a university timetabling problem involving assigning classes to times and rooms for an entire semester while assigning students to required classes. We propose a new mixed integer programming (MIP) formulation of the problem. The MIP formulation takes advantage of different graph structures in conflict graphs to construct a strong formulation of the constraints. In addition, we introduce a reduction algorithm that removes redundancies from the input data. We show that the reduction algorithm, combined with the graph-based MIP formulation, outperforms the MIP formulated by Holm et al. (A MIP formulation of the International Timetabling Competition 2019 problem, 2020) and thus becomes the new state-of-the-art MIP formulation for the ITC 2019. This paper reports the graph-based MIP formulation, which we used during the ITC 2019, and discusses additional approaches that one can use to strengthen the MIP.

A mixed-integer programming approach for solving university course timetabling problems

This article presents a mixed-integer programming model for solving the university timetabling problem which considers the allocation of students to classes and the assignment of rooms and time periods to each class. The model was developed as part of our participation in the International Timetabling Competition 2019 and produced a ranking of second place at the competition. Modeling a timetabling problem as a mixed-integer program is not new. Our contribution rests on a number of innovative features adapted to this problem which allow for a reduction in the number of variables and constraints of the mixed-integer program to manageable levels achieving a reasonable computational performance. The proposed algorithm consists of a first-stage method to obtain an initial feasible solution and a second-stage local search procedure to iteratively improve the solution value, both of which involve the optimization of mixed-integer programming problems.

An SHO-based approach to timetable scheduling: a case study

ABSTRACT University timetable scheduling, which is a typical problem that all universities around the world have to face every semester, is an NP-hard problem. It is the task of allocating the right timeslots and classrooms for various courses by taking into account predefined constraints. In the current literature, many approaches have been proposed to find feasible timetables. Among others, swarm-based algorithms are promising candidates because of their effectiveness and flexibility. This paper investigates proposing an approach to university timetable scheduling using a recent novel swarm-based algorithm named Spotted Hyena Optimizer (SHO) which is inspired by the hunting behaviour of spotted hyenas. Then, a combination of SA and SHO algorithms also investigated to improve the overall performance of the proposed method. We also illustrate the proposed method on a real-world university timetabling problem in Vietnam. Experimental results have indicated the efficiency of the proposed method in comparison to other competitive metaheuristic algorithm such as PSO algorithm in finding feasible timetables.

On a conjecture for the university timetabling problem

The University timetabling is a generalization of the well-known class-teacher timetabling model, where in addition to lectures given by a single teacher to a single class, there are some lectures given by a single teacher to a group of classes simultaneously. One looks for a minimum number of periods in which to complete all lectures without conflicts. The problem is NP-hard in the strong sense even if the number of groups is three, but it is polynomially solvable for two groups. In the latter case, it has been conjectured that the minimum number of periods in which to complete all lectures without conflicts equals ⌈T⌉, where T is the optimal value of an LP-relaxation. The LP-relaxation permits fractions of periods in feasible solutions. We prove this conjecture in this paper.

A general ontological timetabling-model driven metaheuristics approach based on elite solutions

Timetabling is a managerial problem that recurringly appears in various domains such as education, transport, sports, and staff management. The combinatorial nature of this problem poses solution challenges that aggravate with an increase in the problem size. While heuristics and metaheuristics initially offered promise, the progress plateaued as attempts to solve even bigger problems showed exorbitant costs while sampling feasible solutions. This issue is criticized for the lack of exploiting the underlying problem structure and the prevailing fragmentation in modeling and solution approaches. To address these issues, we first propose a novel timetabling ontology that serves as a common modeling basis, resolving the existing heterogeneity across various application domains. This ontology facilitates mapping the anatomy of any real timetabling problem onto its general structure. Second, it offers a unique two-stage solution approach for solving this generalized problem. The first stage of this approach entails generating elite initial solutions by exploiting this general problem structure, while the second stage uses a metaheuristic to improve these solutions at a very low computational cost. Using a university timetabling problem, we demonstrate the applicability of this approach. The numerical results show that the proposed algorithm converges within a fraction of computational costs incurred by other techniques for comparable problem sizes. This research paves the way for consolidating efforts for the development of generalizable cross-domain timetabling approaches.

A systematic mapping study on solving university timetabling problems using meta-heuristic algorithms

Since university timetabling is commonly classified as a combinatorial optimisation problem, researchers tend to use optimisation approaches to reach the optimal timetable solution. Meta-heuristic algorithms have been presented as effective solutions as proven on their leverage over the last decade. Extensive literature studies have been published until today. However, a comprehensive systematic overview is missing. Therefore, this mapping study aimed to provide an organised view of the current state of the field and comprehensive awareness of the meta-heuristic approaches, by conducting meta-heuristic for solving university timetabling problems. In addition, the mapping study tried to highlight the intensity of publications over the last years, spotting the current trends and directions in the field of solving university timetabling problems, as well as having the work to provide guidance for future research by indicating the gaps and open questions to be fulfilled. Primary studies on mapping study that have been published in the last decade from 2009 until the first quarter of 2020, which consist of 131 publications, were selected as a benchmark for future research to solve university timetabling problems using meta-heuristic algorithms. The majority of the articles based on the publication type are hybrid methods (32%), in which the distribution of meta-heuristic algorithms the hybrid algorithms represent the higher application (31%). Likewise, the majority of the research is solution proposals (66%). The result of this study confirmed the efficiency and intensive application of the meta-heuristic algorithms in solving university timetabling problems, specifically the hybrid algorithms. A new trend of meta-heuristic algorithms such as grey wolf optimiser, cat swarm optimisation algorithm, Elitist self-adaptive step-size search and others with high expectations for reliable and satisfying results can be proposed to fill this gap.

Applying genetic algorithm to university classroom arrangement problem

University classroom arrangement problem is considered as a sub-question of the university timetabling problem, which has been proved to be an NP-hard problem in combinatorial optimization field. In this paper, we firstly analyzed the relevant factors and set up a model of the problem. Then the genetic algorithm was applied to optimize the arrangement of classroom considering the moving distance of students between courses, which was caused by room changing. The experimental results have shown that the genetic algorithm could generate feasible solutions and optimize the classroom arrangement.

Model-based problem solving for university timetable validation and improvement

Abstract Constraint satisfaction problems can be expressed very elegantly in state-based formal methods such as B. But can such specifications be directly used for solving real-life problems? In other words, can a formal model be more than a design artefact but also be used at runtime for inference and problem solving? We will try and answer this important question in the present paper with regard to the university timetabling problem. We report on an ongoing project to build a curriculum timetable validation tool where we use a formal model as the basis to validate timetables from a student’s perspective and to support incremental modification of timetables. In this article we describe the problem domain, the formalization in B and our approach to execute the formal model in a production system using ProB .

A study on university course and exam timetabling problems and methods: an optimization survey

The objective of this paper was to retrieve the overview approaches that have been proposed and classification constraints related to previ-ous papers of timetabling problems. Optimisation and scheduling are essential problems in every type of timetabling that can be considered as a non-deterministic polynomial. The objective of this paper to investigate the course and exam timetabling problem by presented classifi-cation table of set of constraints and describes the most reliable method that has been used to solve university timetabling problem. The re-sult of study concerned the two most successfully method that widely used for optimising course and exam timetable. The contribution of this study also help to provide knowledge and idea for further surveys.

Genetic Algorithm Analysis using the Graph Coloring Method for Solving the University Timetable Problem

The Timetable Problem is one of the complex problems faced in any university in the world. It is a highly-constrained combinatorial problem that seeks to find a possible scheduling for the university course offerings. There are many algorithms and approaches adopted to solve this problem, but one of the effective approaches to solve it is the use of meta-heuristics. Genetic algorithms were successfully useful to solve many optimization problems including the university Timetable Problem. In this paper, we analyse the Genetic Algorithm approach for graph colouring corresponding to the timetable problem. The GA method is implemented in java, and the improvement of the initial solution is exhibited by the results of the experiments based on the specified constraints and requirements.

University-timetabling problem and its solution using GELS algorithm: a case study

University-timetabling problem and its solution using GELS algorithm: a case study

University-timetabling problem and its solution using GELS algorithm: a case study

Course scheduling includes a large volume of data with numerous constraints and unchangeable specifications and each university deals with several times a year. Course scheduling is a NP-hard problem and using traditional methods to solve it is very difficult. But evolutionary algorithms suggest good solutions for this type of problems. In this paper we used gravitational emulation local search algorithm to solve the course scheduling problem which is an evolutionary algorithm. Results demonstrate the good quality of time table provided by the proposed algorithm and also decreased time against other algorithms.

An integer program and a hybrid genetic algorithm for the university timetabling problem

The university timetabling problem (UTP) has been studied by numerous research groups for decades. In addition to addressing hard and soft constraints, we extend the UTP by considering consecutiveness and periodicity constraints of multi-session lectures, which are common in many eastern Asian universities. Because schedulers can decide the consecutiveness and periodicity constraints for the multi-session lectures within a limited ratio, we consider these novel decision variables in our model. We develop a mixed integer linear program for the UTP. For the analysis, we convert the UTP into the three-dimensional container packing problem (3DCPP) and create a hybrid genetic algorithm (HGA), which has been shown to be efficient in solving the 3DCPP. We also develop a tabu search algorithm based on the existing UTP literature and compare the findings with that of our HGA. The results show that our HGA obtains a better solution than the tabu search algorithm in a reasonable amount of time.

Memetic Algorithm and its Application to the Arrangement of Exam Timetable

This paper looks at Memetic Algorithm for solving timetabling problems. We present a new memetic algorithm which consists of global search algorithm and local search algorithm. In the proposed method, a genetic algorithm is chosen for global search algorithm while a simulated annealing algorithm is used for local search algorithm. In particular, we could get an optimal solution through the .NET with the real data of JiangXi Normal University. Experimental results show that the proposed algorithm can solve the university exam timetabling problem efficiently.

A Utilization-based Genetic Algorithm for Solving the University Timetabling Problem (UGA)

Building university timetables is a complex process that considers varying types of constraints and objectives from one institution to another. The problem solved in this paper is a real one featuring a number of hard and soft constraints that are not very conventional. The pursued objective is also novel and considers maximizing resource utilization. This paper introduces a genetic algorithm that uses some heuristics to generate an initial population of feasible good quality timetables. The algorithm uses a simple weighted sum formula to respect professors’ preferences and handle conflicts. In order to reduce waste, a crossover type focusing on the utilization rates of learning spaces is introduced. A targeted mutation operator that uses a local search heuristic is also employed. The algorithm applies a composite fitness function that considers space utilization, gaps between events and a maximum number of lectures per day. A large dataset with real data from the Faculty of Commerce, Alexandria University in Egypt was used to test the contributed algorithm. The algorithm was also tested against two difficult benchmark problems from the literature. Testing proved that the developed algorithm is an effective tool for managing timetables and resources in universities. It performed remarkedly well on the large datasets of the two benchmark problems and it also respected more constraints than those stated in the initial problem statement of the two benchmark datasets.

TTGELS: a new approach for solving university exam timetabling problem by using gravitational emulation local search algorithm

University exam timetabling problem is one of the NP-hard problems that challenge universities all over the world. Thus, different methods have been proposed to solve this problem by using heuristic algorithm. In this paper, a new method named TTGELS has been proposed to solve the university exam timetabling problem by using gravitational emulation local search algorithm. The proposed method is compared with other methods and results indicate that the proposed method could produce better results but it needs more time to execute, that's because of using neighbourhood production process and multiple stepping method to produce better solutions.

A multi-stage IP-based heuristic for class timetabling and trainer rostering

We consider a timetabling and rostering problem involving periodic retraining of large numbers of employees at an Australian electricity distributor. This problem is different from traditional high school and university timetabling problems studied in the literature in several aspects. We propose a three-stage heuristic consisting of timetable generation, timetable improvement, and trainer rostering. Large-scale integer linear programming models for both the timetabling and the rostering components are proposed, and several unique operational constraints are discussed. We show that this solution approach is able to produce good solutions in practically acceptable time.

A Hybrid Swarm-Based Approach to University Timetabling

This paper is concerned with the application of an automated hybrid approach in addressing the university timetabling problem. The approach described is based on the nature-inspired artificial bee colony (ABC) algorithm. An ABC algorithm is a biologically-inspired optimization approach, which has been widely implemented in solving a range of optimization problems in recent years such as job shop scheduling and machine timetabling problems. Although the approach has proven to be robust across a range of problems, it is acknowledged within the literature that there currently exist a number of inefficiencies regarding the exploration and exploitation abilities. These inefficiencies can often lead to a slow convergence speed within the search process. Hence, this paper introduces a variant of the algorithm which utilizes a global best model inspired from particle swarm optimization to enhance the global exploration ability while hybridizing with the great deluge (GD) algorithm in order to improve the local exploitation ability. Using this approach, an effective balance between exploration and exploitation is attained. In addition, a traditional local search approach is incorporated within the GD algorithm with the aim of further enhancing the performance of the overall hybrid method. To evaluate the performance of the proposed approach, two diverse university timetabling datasets are investigated, i.e., Carter’s examination timetabling and Socha course timetabling datasets. It should be noted that both problems have differing complexity and different solution landscapes. Experimental results demonstrate that the proposed method is capable of producing high quality solutions across both these benchmark problems, showing a good degree of generality in the approach. Moreover, the proposed method produces best results on some instances as compared with other approaches presented in the literature.