Examination Timetabling Research Articles

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.

A Survey of Computational Intelligence in Educational Timetabling

Timetabling problems have been widely studied, of which Educational Timetabling Problem (ETP) is the biggest section. Generally, ETP can be divided into three modules, namely, course timetabling, school timetabling, and examination timetabling. For solving ETP, many techniques have been developed including conventional algorithms and computational intelligence approaches. Several surveys have been conducted focusing on those methods. Some surveys target on particular categories; some tend to cover all types of approaches. However, there are lack of reviews specifically focusing on computational intelligence in ETP. Therefore, this paper aims at providing a reference of selecting a method for the applications of ETP by reviewing popular computational intelligent algorithms, such as meta-heuristics, hyper-heuristics, hybrid methods, fuzzy logic, and multi-agent systems. The application would be categorised and described into the three types of ETP respectively.

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.

An improved grammatical evolution approach for generating perturbative heuristics to solve combinatorial optimization problems

Search methodologies such as hyper-heuristics have been successfully used to automate the generation of perturbative heuristics to solve combinatorial optimization problems. However, the domain of automated generation of perturbative heuristics has generally not been well researched and very few works have actually been conducted in the area. In addition, most of the proposed hyper-heuristic methods in the literature simply recombine already existing and human-derived low-level perturbative heuristics (or primitive heuristic components) with various move acceptance criteria to generate the new perturbative heuristics instead of producing the heuristics from scratch. As a result, these methods cannot be applied to problem domains where the human-derived low-level heuristics are not available. The study presented in this paper addresses this issue by proposing an improved approach, based on our previous work, that generates good quality reusable perturbative heuristics from scratch. While this new approach also uses grammatical evolution to generate the heuristics from a set of basic actions and components of the solution (as in our previous work), the grammar has been substantially extended and includes new methods for selecting solution components, conditional constructs, utilizes some information from the solution space as well as extends the syntax of the basic actions in order to cover a wider range of heuristics. Furthermore, the new approach has been applied to a new problem domain, i.e. the boolean satisfiability problem, in addition to the examination timetabling and vehicle routing problems investigated in the earlier work. The experimental results show that the new approach not only generates better perturbative heuristics than those produced in our earlier work, it also produces results that are competitive with those obtained by currently existing generation perturbative hyper-heuristics that have been applied to the benchmark sets in the three domains.

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.

A Convex LASSO Framework for Linear Timetabling

A new convex optimization framework for approximately solving timetabling problems that can be described as integer linear programs is proposed. The method is based on converting the timetabling problem into a cardinality constrained problem while viewing the operational constraints of the timetable as noisy measurements with an unknown average slack. The problem is then iteratively solved using weighted Lasso with weights that are updated using a simple linear program to satisfy the cardinality constraint while respecting the operational constraints in the least squares sense. Compared with previous convex relaxations for solving timetabling problems, our solution technique will converge to a binary solution without the need for subsequent randomized rounding. Moreover, the number of Lasso iterations required are in the order of the number of events to be scheduled and hence the method can handle very large timetabling problems using efficient Lasso solvers. We provide the assumptions required on the linear timetabling model and establish the associated error bound of the technique upon convergence assuming restricted strong convexity and uniqueness. We also study the effect of the Lasso regularization parameter and the effect of relaxing the objective on the extent of constraint satisfaction through several simulation experiments. Our experiment on one of the benchmark datasets for university examination timetabling improved the best documented result by more than 30% with 99.9% of all constraints satisfied.

Prey-predator algorithm for discrete problems: a case for examinationtimetabling problem

The prey-predator algorithm is a metaheuristic algorithm inspired by the interaction between a predator and its prey. Initial solutions are put into three categories: the better performing solution as the best prey, the worst performing solution as a predator, and the rest as ordinary prey. The best prey totally focuses on exploiting its neighborhood while the predator explores the search space searching for a promising region in the search space. The ordinary prey will be affected by these two extreme search behaviors of exploration and exploitation. The algorithm has been tested and found to be effective in solving different problems arising from different disciplines including engineering, tourism, and management. Originally, the algorithm was designed to deal with continuous problems. However, many problems arising from real aspects are not continuous. Hence, in this paper the prey-predator algorithm will be extended to suit discrete problems. Examination timetabling is used to test the approach. The simulation results with appropriate statistical analysis show that the approach is as good as the cumulative best performance of results recorded in the literature for the selected benchmark problems.

Lower bounds and compact mathematical formulations for spacing soft constraints for university examination timetabling problems

The examination timetabling problem (ETT) can be described as a set of exams to be scheduled over an examination session while respecting numerous hard and soft constraints. In this paper we consider the spacing soft constraints that seek to prevent students sitting more than one exam per day. Out of consideration for candidates, these soft constraints often feature in real ETT problems that academic institutions seek to solve. Work on ETT has tended to focus on heuristic approaches, and little effort has gone into developing lower bounds, although both are of practical and theoretical interest. For this study we consider formulations of these soft constraints as defined in the ITC2007 examination timetabling track. In existing mathematical formulations of these spacing soft constraints the number of equations is of the order of the square of the number of exams, and current solvers may face problems at runtime because of their large memory requirement. In this study we present a generic model for computing lower bounds, together with more compact formulations where the number of equations is of the order of the number of exams. Computational results on spacing soft constraints that seek to prevent students sitting more than one exam per day are an improvement on results obtained so far on lower bounds, and our new formulations yield a more compact model that gives better results than those given by existing formulations.

An ant colony algorithm for universiti sultan zainal abidin examination timetabling problem

The real-life construction of examination timetabling problem is considered as a common problem that always encountered and experienced in educational institution whether in school, college, and university. This problem is usually experienced by the academic management department where they have trouble to handle complexity for assign examination into a suitable timeslot manually. In this paper, an algorithm approach of ant colony optimisation (ACO) is presented to find an effective solution for dealing with Universiti Sultan Zainal Abidin (UniSZA) examination timetabling problems. A combination of heuristic with ACO algorithm contributes the development solution in order to simplify and optimize the pheromone occurrence of matrix updates which include the constraints problem. The implementation of real dataset instances from academic management is applied to the approach for generating the result of examination timetable. The result and performance that obtained will be used for further use to evaluate the quality and observe the solution whether our examination timetabling system is reliable and efficient than the manual management that can deal the constraints problem.

Genetic Algorithm and Tabu Search Memory with Course Sandwiching (GATS_CS) for University Examination Timetabling

Genetic Algorithm and Tabu Search Memory with Course Sandwiching (GATS_CS) for University Examination Timetabling

Genetic Algorithm and Tabu Search Memory with Course Sandwiching (GATS_CS) for University Examination Timetabling

Genetic Algorithm and Tabu Search Memory with Course Sandwiching (GATS_CS) for University Examination Timetabling

Great Deluge Based Hyper-heuristics for Solving Real-world University Examination Timetabling Problem: New Data set and Approach

The university examination timetabling problem is one of challenging optimization problems. Its NP-hard nature makes this problem attractive to be studied, especially in the field of operation research and artificial intelligence. In the literature, the state-of-the-art approach for solving examination timetabling problem is meta-heuristics. However, this approach has limitation, i.e. the need for intensive problem-specific parameter tuning. To cope with this problem, a relatively new approach namely hyper-heuristics was proposed. Different from meta-heuristics that search upon solution space, hyper-heuristics search upon low-level space. This strategy makes hyper-heuristics more generic that works over cross-domain, compared to meta-heuristics that usually designed for specific problem domain. This paper reports the success of solving real-world university examination timetabling problem in Institut Teknologi Sepuluh Nopember using hyper-heuristics based on great deluge algorithm. The main contributions of this study are two folds: a new dataset and new approach for solving examination timetabling problem. The computational results show that the proposed algorithm could produce much better solutions compared to the solutions generated manually. In addition, the proposed algorithm also outperforms two benchmarking algorithms, namely hill climbing and simulated annealing algorithms.