Examination Timetabling Research Articles

On the computation of robust examination timetables: methods and experimental results

AbstractWith ever-rising student numbers and an increasing shift towards more interdisciplinary study programs, the requirements for finding schedules for courses and exams become ever more complex. In real-world scenarios, the models used for calculating solutions to the course and the examination timetabling problem often must be provided to the students at the time of registration. In the field of curriculum-based course timetabling, timetables are calculated based on the structure of the study programs. For the examination timetabling problem, only a few papers focus on scheduling exams without registration data, as the requirements for exams are often more strict, or partial information is known from course registrations. In this paper we show that with the use of robustness techniques, we can also define the examination timetabling problem based on curricula. We introduce three robustness measures that address the inherent uncertainty when using the curriculum-based model. These robustness measures, along with other quality measures, are analyzed using a multi-objective simulated annealing algorithm. The results are compared on the Pareto front approximations found. We present a case study showing that, without a significant loss in solution quality, the chance is significantly reduced that rescheduling will be required after the exact numbers for the model are known.

The performance analysis of hyper-heuristics algorithms over examination timetabling problems

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.

A proven optimal result for a benchmark instance of the uncapacitated examination timetabling problem

AbstractExamination timetabling is a problem well known to the scheduling community. Its simplest version, which is the uncapacitated examination timetabling problem, is easily described and comprehended. Nevertheless, proof of optimality is notoriously difficult even for moderate size problems. In this paper, we describe the effort that our team exercised in finally proving the optimality of the sta83 instance of Carter’s dataset. The problem was decomposed naturally in three parts and for each part a different approach managed to prove optimality of the currently best known solution. This work also presents optimal solutions to subproblems that exist in various public datasets problems and two best known solutions of such problems.

An Integer Linear Programming Model for the Examination Timetabling Problem: A Case Study of a University in Thailand

This paper considers the examination timetabling problem (ETTP) at the College of Industrial Technology (CIT) of the King Mongkut’s University of Technology North Bangkok in Thailand. A new integer linear programming (ILP) formulation for the ETTP at the CIT is presented. The objectives were to minimize both the number of examination days (the main objective) and the number of rooms used throughout the entire examination period (the secondary objective). In this paper, a course can have multiple sections, and an examination room can accommodate exams for more than one course section. To illustrate the proposed ILP model, real data on courses acquired from the CIT were used to generate two test problems: a small problem and a large problem. The small problem included 32 courses with 69 sections. The large problem included 73 courses with 341 sections, which was the real data required for generating the midterm examination timetable for all first‐year courses in the first semester of 2021. Both problems were solved using the CPLEX solver software. The results show that the proposed model could find an optimal examination timetable for the small problem with a computational time of 2 min and 46 s. It also could find a good feasible midterm examination timetable that satisfied the requirements of the CIT for the large problem within the 2‐h time limit, much less time than that compared to manual scheduling by the CIT’s administrative staff. The obtained midterm examination timetable required five examination days and could reduce 104 examination rooms compared to assigning each course section to a separate examination room. The proposed ILP model can be used in a real‐life situation and can be a good option to generate an optimal schedule or a good feasible schedule for examinations at the CIT or other institutions that have similar requirements.

A hybrid modified cuckoo search algorithm for the uncapacitated examination timetabling

A hybrid modified cuckoo search algorithm for the uncapacitated examination timetabling

Generic University Examination Timetabling System with Steepest-Ascent Hill Climbing Hyper-heuristic Algorithm

A common problem encountered in various educational institutions is the scheduling of exams, which involves allocating resources such as time and space, as well as considering student schedules within defined hard and soft constraints. This scheduling problem falls under the category of NP-Hard Problems, making it challenging to solve perfectly, and manual scheduling becomes even more difficult. One approach commonly used to address this issue is the Hyper-heuristic method, which generally provides above-average solutions. In this study, the Steepest-Ascent Hill Climbing algorithm is employed to optimize the initial solution generated by the Graph Coloring algorithm. The optimization process, using the Steepest-Ascent Hill Climbing algorithm, was tested over data set from Department of Information Systems, ITS University. The results showed improved timetabling compared to the Simple Hill Climbing algorithm, with lower penalty values. After 10,000 iterations, Steepest-Ascent Hill Climbing achieved an average penalty value of 2.783, whereas Simple Hill Climbing resulted in an average penalty value of 3.943.

Multi-neighbourhood simulated annealing for the ITC-2007 capacitated examination timetabling problem

Multi-neighbourhood simulated annealing for the ITC-2007 capacitated examination timetabling problem

Fifty years of operational research: 1972–2022

In July 2022, I received the EURO Gold medal at the 32nd EURO Conference held in Espoo, Finland. This paper is based on the presentation I made at the medal award ceremony. It covers 10 topics on which I have worked throughout my career. These are the seriation problem, rotating work schedules, deterministic vehicle routing, stochastic vehicle routing, examination timetabling, districting, waste management, metro network design, green transportation, and humanitarian logistics.

Exact and metaheuristic methods for a real-world examination timetabling problem

Exact and metaheuristic methods for a real-world examination timetabling problem

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 hybrid modified cuckoo search algorithm for the uncapacitated examination timetabling

A hybrid modified cuckoo search algorithm for the uncapacitated examination timetabling

An introduction of preference based stepping ahead firefly algorithm for the uncapacitated examination timetabling.

In recent times, there has been a growing attention to intelligent optimization algorithms centred on swarm principles such as the firefly algorithm (FA). It was proposed for the continuous domain that mimics the attraction of fireflies to flashing light and has been used in discrete domains via modification. A discrete domain that is a major challenge in most higher education institutes (HEI) is examination timetabling. This article presents a new methodology based on FA for uncapacitated examination timetabling problems (UETP) where the proposed method is an extension of earlier work by the authors on the continuous domain. UETP is considered in this article as it is a university examination timetabling problem, which is still an active research area and has not been solved by FA algorithm as per authors knowledge. The proposed method concentrates on solving the initial solution using discrete FA where it consolidates the reordering of examinations and slots through a heuristic ordering known as neighborhood search. Three neighborhoods are employed in this research, where one is used during the initialization phase while two are utilized during solution improvement phase. Later, through preference parameters, a novel stepping ahead mechanism is used, which employs neighborhood searches built on previous searches. The proposed method is tested with 12 UETP problems where the preference based stepping ahead FA creates comparative results to the best ones available in the literature for the Toronto exam timetabling dataset. The results obtained are proof of concept at the preliminary stage and require further experiments on other educational datasets such as the second international timetable competition benchmark sets. The newly introduced preference based stepping ahead mechanism takes advantage of the current best solution space where it exploits the solution space for better solutions. This paves the way for researchers to utilize the mechanism in other domains such as robotics, etc.

A Variant Genetic Algorithm for a Specific Examination Timetabling Problem in a Japanese University

Background: Examination Timetabling Problem which tries to find an optimal examination schedule for schools, colleges, and universities, is a well-known NP-hard problem. This paper presents a Genetic Algorithm variant approach to solve a specific examination timetabling problem common in Japanese colleges and universities. Methods: The proposed algorithm uses direct chromosome representation Genetic Algorithm and implements constraint-based initialization and constraint-based crossover operations to satisfy the hard and soft constraints. An Island model with varying crossover and mutation probabilities and an improvement approach called pre-training are applied to the algorithm to further improve the result quality. Results: The proposed model is tested on synthetic as well as real datasets obtained from Sophia University, Japan and shows acceptable results. The algorithm was fine-tuned with different penalty points combinations and improvement combinations. Conclusion: The comparison results support the idea that the initial population pre-training and the island model are effective approaches to improve the result quality of the proposed model. Although the current island model used only four islands, incorporating greater number of islands, and some other diversity maintenance approaches such as memetic structures are expected to further improve the diversity and the result quality of the proposed algorithm on large scale problems.

University Examination Timetabling Using a Hybrid Black Hole Algorithm

University timetabling construction is a complicated task that is encountered by universities in the world. In this study, a hybrid approach has been developed to produce timetable solution for the university examination timetabling problem. Black Hole Algorithm (BHA), a population-based approach that mimics the black hole phenomenon has been introduced in the literature recently and successfully applied in addressing various optimization problems. Although its effectiveness has been proven, there still exists inefficiency regarding the exploitation ability where BHA is poor in fine tuning search region in reaching for good quality of solution. Hence, a hybrid framework for university examination timetabling problem that is based on BHA and Hill Climbing local search is proposed (hybrid BHA). The aim of this hybridization is to improve the exploitation ability of BHA in fine tuning the promising search regions and convergence speed of the search process. A real-world university examination benchmark dataset has been used to evaluate the performance of hybrid BHA. The computational results demonstrate that hybrid BHA capable of generating competitive results and recording best results for three instances, compared to the reference approaches and current best-known recorded in the literature. Other than that, findings from the Friedman tests show that the hybrid BHA ranked second and third in comparison with hybrid and meta-heuristic approaches (total of 27 approaches) reported in the literature, respectively.

Intelligent university timetable scheduling system using sudoku grid with magic square

Examination timetabling is problem faced by many academic educational institutions. The situation formulated as artificial intelligence problems as Sudoku grid with Magic square. Problem assigning a set of examinations to a fixed number of examination periods so that no student is required to take more than one examination at a time. The research describes two proposed heuristic algorithms to create university examination timetabling and avoiding the overlapping of exams. We proposed two algorithms, the first algorithm is based on Sudoku grid, a number of hard constraints as well as a number of soft constraints are proposed. We assigned exams as 9 to period as 27 slot times and to 3 rooms, with 3 classes. Each student in each class takes 9 exams While, the second algorithm simulates the classic manual methods while observing the hard and soft constraints of the problem. The heuristic approach used to further optimize the result to include hard constraints with soft. The proposed methodology for creating the Exam timetabling problem has been implemented in Matlab and closing the gap between classical methods and intelligent methods. The results obtained with very less computational effort through two algorithms.

School Timetabling Optimisation Using Artificial Bee Colony Algorithm Based on a Virtual Searching Space Method

Although educational timetabling problems have been studied for decades, one instance of this, the school timetabling problem (STP), has not developed as quickly as examination timetabling and course timetabling problems due to its diversity and complexity. In addition, most STP research has only focused on the educators’ availabilities when studying the educator aspect, and the educators’ preferences and expertise have not been taken into consideration. To fill in this gap, this paper proposes a conceptual model for the school timetabling problem considering educators’ availabilities, preferences and expertise as a whole. Based on a common real-world school timetabling scenario, the artificial bee colony (ABC) algorithm is adapted to this study, as research shows its applicability in solving examination and course timetabling problems. A virtual search space for dealing with the large search space is introduced to the proposed model. The proposed approach is simulated with a large, randomly generated dataset. The experimental results demonstrate that the proposed approach is able to solve the STP and handle a large dataset in an ordinary computing hardware environment, which significantly reduces computational costs. Compared to the traditional constraint programming method, the proposed approach is more effective and can provide more satisfactory solutions by considering educators’ availabilities, preferences, and expertise levels.

An Analysis Framework for Examination Timetabling

An examination timetabling problem taken from real world universities was proposed at the International Timetabling Competition (ITC2007). The aim was to establish a common base for comparing different solution approaches. This paper presents new preprocessing methods that disclose hidden constraints and significantly increase the number of new edges that can be added to the conflict graph. Results show that the size of the maximum clique of the obtained conflict graph has been more than doubled for two instances as a result of our preprocessing. These larger cliques mean that instances can be analyzed in advance of a solution and end users gain useful information for making decisions. In addition, we have looked at the different criteria that compose the objective function, in order to provide more useful insights into the difficulty of problems in practice. We propose new integer programming formulations using clique inequalities to compute optimal solutions for 4 criteria and to obtain lower bounds for the 3 others. Results are presented and discussed for all the benchmark instances.

Hybrid intelligent water Drops algorithm for examination timetabling problem

The current study investigates the Intelligent Water Drops (IWD) metaheuristic algorithm to construct and produce good quality solutions for the university examination timetabling problem (UETP). The IWD is a population-based metaheuristic that simulates the dynamic of the river systems. The main motivations for investigating IWD algorithm for examination timetabling problem is the ability to explore the search space effectively. The main drawback of IWD algorithm is like other population-based algorithm in exploitation process where it is very efficient scanning several search space niches, but it is unable to drilling down in each niche to which it navigates. In this paper we propose a hybrid approach based on IWD and locale search algorithm to improve the exploitation of IWD algorithm. The experimental results demonstrated that the proposed algorithm (i.e., Hybrid IWD) obtained best results in three datasets when comparing with the best-known results performed by the swarm intelligent approaches. Finally, the proposed algorithm achieved one best results in comparison with the other metaheuristic approaches.

A web-based decision support system for examination timetabling

We study exam timetabling problem (ETP) and supervisor assignment problem (SAP) of a vocational school offering associate level degrees in a university. The school has seven departments and plans almost 170 exams in each semester. We propose mixed integer programming (MIP) models for the ETP and the SAP. The optimal solution for ETP of the school is not attainable in two days with a commercial solver. We propose a decomposition method which is able to solve ETP using an open source solver in less than two minutes. The MIP models and the solution method are embedded into a web based decision support system (DSS). Using this DSS, a complete timetable can be prepared in less than two minutes by an average end-user.

Genetic Algorithm for Solving Multi-Objective Optimization in Examination Timetabling Problem

Examination timetabling is one of 3 critical timetabling jobs besides enrollment timetabling and teaching assignment. After a semester, scheduling examinations is not always an easy job in education management, especially for many data. The timetabling problem is an optimization and Np-hard problem. In this study, we build a multi-objective optimizer to create exam schedules for more than 2500 students. Our model aims to optimize the material costs while ensuring the dignity of the exam and students' convenience while considering the rooms' design, the time requirement of each exam, which involves rules and policy constraints. We propose a programmatic compromise to approach the maximum tar-get optimization model and solve it using the Genetic Algorithm. The results show the effectiveness of the introduced algorithm.