Examination Timetabling Problem Research Articles

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.

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

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

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

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

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.

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.

Solving examination timetabling problem within a hyper-heuristic framework

Scheduling exams in colleges are a complicated job that is difficult to solve conventionally. Exam timetabling is one of the combinatorial optimization problems where there is no exact algorithm that can answer the problem with the optimum solution and minimum time possible. This study investigated the University of Toronto benchmark dataset, which provides 13 real instances regarding the scheduling of course exams from various institutions. The hard constraints for not violate the number of time slots must be fulfilled while paying attention to fitness and running time. Algorithm of largest degree, hill climbing, and tabu search within a hyper-heuristic framework is investigated with regards to each performance. This study shows that the Tabu search algorithm produces much lower penalty value for all datasets by reducing 18-58% from the initial solution.

Two-stage multi-neighborhood simulated annealing for uncapacitated examination timetabling

We propose a Simulated Annealing approach for the Examination Timetabling problem, in the classical uncapacitated formulation of Carter et al. (1996). Our solver is based on a novel combination of many neighborhoods and a principled tuning procedure performed on artificial training instances. The experimental results on real-world benchmarks show that our solver is able to improve upon all state-of-the-art search methods from the literature on most instances, running time being equal. In addition, we performed an ablation analysis, so as to identify the most important neighborhoods. Finally, we propose a novel dataset obtained by translating real-world instances for other examination timetabling formulations. Instances and solutions, along with our source code, are available on the web for inspection and future comparison.

Conflict Management in University Examination Timetabling Problem: A case study of summer school mid-terms


 
 
 
 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
 
 
 

Application of Heuristic Combinations in Hyper-Heuristic Framework for Exam Scheduling Problems

Examination Timetabling Problem is one of the optimization and combinatorial problems. It is proved to be a non-deterministic polynomial (NP)-hard problem. On a large scale of data, the examination timetabling problem becomes a complex problem and takes time if it solved manually. Therefore, heuristics exist to provide reasonable enough solutions and meet the constraints of the problem. In this study, a real-world dataset of Examination Timetabling (Toronto dataset) is solved using a Hill-Climbing and Tabu Search algorithm. Different from the approach in the literature, Tabu Search is a meta-heuristic method, but we implemented a Tabu Search within the hyper-heuristic framework. The main objective of this study is to provide a better understanding of the application of Hill-Climbing and Tabu Search in hyper-heuristics to solve timetabling problems. The results of the experiments show that Hill-Climbing and Tabu Search succeeded in automating the timetabling process by reducing the penalty 18-65% from the initial solution. Besides, we tested the algorithms within 10,000-100,000 iterations, and the results were compared with a previous study. Most of the solutions generated from this experiment are better compared to the previous study that also used Tabu Search algorithm.

Evaluation of Hyper-Heuristic Method Using Random-Hill Climbing Algorithm in the Examination Timetabling Problem

Examination timetabling is included in the category of Nondeterministic Polynomial-Hard (NP-Hard) problems, namely problems that cannot be solved by conventional methods in finding optimal solutions. One solution to this problem is to use the Simple Random - Hill Climbing - Hyper Heuristic (SR-HC-HH) approach. But this approach still cannot produce an optimum solution. The researcher presents a critical analysis of the performance evaluation of the solution method used. The stages of this research include: (1) problem identification; (2) literature study; (3) data retrieval and understanding; (4) translation of mathematical models into data structures; (5) evaluation of the SR-HC-HH algorithm; (6) trial implementation; (7) algorithmic experiment parameters; and (8) analysis of results and conclusions. SR-HC-HH algorithm used in Hyper-Heuristics-based applications is able to solve timetabling problems in the Examination Timetabling Problem domain in the ITC-2007 dataset, but it is still not optimal. Parameters that can be changed in this study are the number of iterations (time limit) and algorithms for selection of Low Level Heuristics. Changing parameters in the trial scenario can also affect the results of a more optimum solution. The parameters to be explored in this study include LLH selection strategies and move acceptance in hyper-heuristics.

A $$\beta $$-hill climbing optimizer for examination timetabling problem

Examination timetable is a non-trivial task for administrators of the academic institutions repeated every semester. In terms of optimization, examination timetabling is a combinatorial optimization problem concerned with assigning a set of exams to a predefined number of timeslots and rooms with accordance to a given constraints. In this paper, the extended version of hill climbing algorithm called $$\beta $$ -hill climbing is utilized to tackle the examination timetabling problem. $$\beta $$ -hill climbing is a new local search-based method that has two operators ( $$\beta $$ -operator and $${\mathcal {N}}$$ -operator) to iterate towards the optimal solution. The saturation degree heuristic method is utilized in the improvement loop of $$\beta $$ -hill climbing to ensure the solution feasibility. For experimental evaluation, Carter dataset is used comprising 12 instances selected from several real-world universities. Eight convergence scenarios are designed to sensitively analyze the behavior of the proposed algorithm. For comparative evaluations, the results produced by $$\beta $$ -hill climbing are comparatively comparable with previous methods that utilized the same Carter instances.

Addressing Examination Timetabling Problem Using a Partial Exams Approach in Constructive and Improvement

The paper investigates a partial exam assignment approach for solving the examination timetabling problem. Current approaches involve scheduling all of the exams into time slots and rooms (i.e., produce an initial solution) and then continuing by improving the initial solution in a predetermined number of iterations. We propose a modification of this process that schedules partially selected exams into time slots and rooms followed by improving the solution vector of partial exams. The process then continues with the next batch of exams until all exams are scheduled. The partial exam assignment approach utilises partial graph heuristic orderings with a modified great deluge algorithm (PGH-mGD). The PGH-mGD approach is tested on two benchmark datasets, a capacitated examination dataset from the 2nd international timetable competition (ITC2007) and an un-capacitated Toronto examination dataset. Experimental results show that PGH-mGD is able to produce quality solutions that are competitive with those of the previous approaches reported in the scientific literature.

A spreadsheet-based decision support system for examination timetabling

Examination timetabling is an inevitable problem of educational institutions. Each institution has its own particular limitations; however, the main structure is the same: assigning exams to time slots and classrooms. Several institutions solve the problem manually, but it becomes more difficult every year with increasing numbers of students and limited resources. There are many studies in the literature addressing the examination timetabling problem ETP and providing high quality solutions within reasonable amounts of time. Nevertheless, almost none of them can be used in practice since they are not converted into a decision support system DSS . Commercial DSSs, on the other hand, are generally transactionally based and do not have optimization capabilities, i.e. they prevent conflicts via functional user interfaces. In this study, we propose a mixed integer programming MIP model that addresses the ETP of the Industrial Engineering Department of Yildiz Technical University. The model, which is capable of solving a wide range of similar ETP instances, is embedded into a DSS in the form of a spreadsheet. Given the enrollment lists of the courses, it generates schedules with minimum conflicts and consecutive exams while addressing requests of the lecturers and students. It does not require any technical knowledge and can be used by an average spreadsheet user. Moreover, it is flexible in terms of use for scheduling problems of other educational institutions. Currently, the DSS is in use by the department and real-life instances can be solved within a few seconds, saving significant amount of man-hours.

Performance Analyses of Graph Heuristics and Selected Trajectory Metaheuristics on Examination Timetable Problem

Examination timetabling problem is hard to solve due to its NP-hard nature, with a large number of constraints having to be accommodated. To deal with the problem effectually, frequently heuristics are used for constructing feasible examination timetable while meta-heuristics are applied for improving the solution quality. This paper presents the performances of graph heuristics and major trajectory metaheuristics or S-metaheuristics for addressing both capacitated and un-capacitated examination timetabling problem. For constructing the feasible solution, six graph heuristics are used. They are largest degree (LD), largest weighted degree (LWD), largest enrolment degree (LE), and three hybrid heuristic with saturation degree (SD) such as SD-LD, SD-LE, and SD-LWD. Five trajectory algorithms comprising of tabu search (TS), simulated annealing (SA), late acceptance hill climbing (LAHC), great deluge algorithm (GDA), and variable neighborhood search (VNS) are employed for improving the solution quality. Experiments have been tested on several instances of un-capacitated and capacitated benchmark datasets, which are Toronto and ITC2007 dataset respectively. Experimental results indicate that, in terms of construction of solution of datasets, hybridizing of SD produces the best initial solutions. The study also reveals that, during improvement, GDA, SA, and LAHC can produce better quality solutions compared to TS and VNS for solving both benchmark examination timetabling datasets.

Performance Analyses of Graph Heuristics and Selected Trajectory Metaheuristics on Examination Timetable Problem

Examination timetabling problem is hard to solve due to its NP-hard nature, with a large number of constraints having to be accommodated. To deal with the problem effectually, frequently heuristics are used for constructing feasible examination timetable while meta-heuristics are applied for improving the solution quality. This paper presents the performances of graph heuristics and major trajectory metaheuristics or S-metaheuristics for addressing both capacitated and un-capacitated examination timetabling problem. For constructing the feasible solution, six graph heuristics are used. They are largest degree (LD), largest weighted degree (LWD), largest enrolment degree (LE), and three hybrid heuristic with saturation degree (SD) such as SD-LD, SD-LE, and SD-LWD. Five trajectory algorithms comprising of tabu search (TS), simulated annealing (SA), late acceptance hill climbing (LAHC), great deluge algorithm (GDA), and variable neighborhood search (VNS) are employed for improving the solution quality. Experiments have been tested on several instances of un-capacitated and capacitated benchmark datasets, which are Toronto and ITC2007 dataset respectively. Experimental results indicate that, in terms of construction of solution of datasets, hybridizing of SD produces the best initial solutions. The study also reveals that, during improvement, GDA, SA, and LAHC can produce better quality solutions compared to TS and VNS for solving both benchmark examination timetabling datasets.

Development of an Interactive Tool based on Combining Graph Heuristic with Local Search for Examination Timetable Problem

Every university faces a lot of challenges to solve the examination timetabling problem because the problem is NP-hard and contains numerous institutional constraints. Although several attempts have been taken to address the issue, there are scarcities of interactive and automated tools in this domain that can schedule exams effectively by considering institutional resources, different constraints, and student enrolment in courses. This paper presents the development of a system as a graphical and interactive tool for examination timetabling problem. To develop the system, combining graph coloring heuristic and local search meta-heuristic algorithms are employed. The graph heuris-tic ordering is incorporated for constructing initial solution(s), whereas the local search meta-heuristic algorithms are used to produce quality exam timetables. Different constraints and objective functions from ITC2007 exam competition rules are adopted, as it is a complex real word exam timetabling problem. Finally, the system is tested on the ITC2007 exam benchmark dataset, and test results are presented. The main aspect of the system is to deliver an easy-to-handle tool that can generate quality timetables based on institutional demands and smoothly manage several key components. These components are collecting data associated with the enrolment of students in exams, defining hard and soft constraints, and allocating times and resources. Overall, this software can be used as a commercial scheduler in order to provide institutions with automated, accurate, and quick exam timetable.