Curriculum-based Course Timetabling Research Articles

A New Greedy Algorithm for the Curriculum-based Course Timetabling Problem

This study describes a novel greedy algorithm for optimizing the well-known Curriculum-Based Course Timetabling (CB-CTT) problem. Greedy algorithms are a good alternative to brute-force and evolutionary algorithms, which take a long time to execute in order to find the best solution. Rather than employing a single heuristic, as many greedy algorithms do, we define and apply 120 new heuristics to the same problem instance. To assign courses to available rooms, our proposed greedy algorithm employs the Largest-First, Smallest-First, Best-Fit, Average-weight first, and Highest Unavailable course-first heuristics. Extensive experiments are carried out on 21 problem instances from the benchmark set of the Second International Timetabling Competition (ITC-2007). For 18 problems with significantly reduced soft-constraint values, the proposed greedy algorithm can report zero hard constraint violations (feasible solutions). The proposed algorithm outperforms state-of-the-art greedy heuristics in terms of performance.

Algorithm selection for solving educational timetabling problems

In this paper, we present the construction process of a per-instance algorithm selection model to improve the initial solutions of Curriculum-Based Course Timetabling (CB-CTT) instances. Following the meta-learning framework, we apply a hybrid approach that integrates the predictions of a classifier and linear regression models to estimate and compare the performance of four meta-heuristics across different problem sub-spaces described by seven types of features. Rather than reporting the average accuracy, we evaluate the model using the closed SBS-VBS gap, a performance measure used at international algorithm selection competitions. The experimental results show that our model obtains a performance of 0.386, within the range obtained by per-instance algorithm selection models in other combinatorial problems. As a result of the process, we conclude that the performance variation between the meta-heuristics has a significant role in the effectiveness of the model. Therefore, we introduce statistical analyses to evaluate this factor within per-instance algorithm portfolios.

$${\varvec{teaspoon}}$$: solving the curriculum-based course timetabling problems with answer set programming

Answer Set Programming (ASP) is an approach to declarative problem solving, combining a rich yet simple modeling language with high performance solving capacities. We here develop an ASP-based approach to curriculum-based course timetabling (CB-CTT), one of the most widely studied course timetabling problems. The resulting teaspoon system reads a CB-CTT instance of a standard input format and converts it into a set of ASP facts. In turn, these facts are combined with a first-order encoding for CB-CTT solving, which can subsequently be solved by any off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting it to the best known bounds obtained so far via dedicated implementations. Furthermore, we extend the teaspoon system to multi-objective course timetabling and consider minimal perturbation problems.

Benders’ decomposition for curriculum-based course timetabling

In this paper we applied Benders’ decomposition to the Curriculum-Based Course Timetabling (CBCT) problem. The objective of the CBCT problem is to assign a set of lectures to time slots and rooms. Our approach was based on segmenting the problem into time scheduling and room allocation problems. The Benders’ algorithm was then employed to generate cuts that connected the time schedule and room allocation. We generated only feasibility cuts, meaning that most of the solutions we obtained from a mixed integer programming solver were infeasible, therefore, we also provided a heuristic in order to regain feasibility.We compared our algorithm with other approaches from the literature for a total of 32 data instances. We obtained a lower bound on 23 of the instances, which were at least as good as the lower bounds obtained by the state-of-the-art, and on eight of these, our lower bounds were higher. On two of the instances, our lower bound was an improvement of the currently best-known. Lastly, we compared our decomposition to the model without the decomposition on an additional six instances, which are much larger than the other 32. To our knowledge, this was the first time that lower bounds were calculated for these six instances.

An overview of curriculum-based course timetabling

In 2007, the Second International Timetabling Competition (ITC-2007) has been organized and a formal definition of the Curriculum-Based Course Timetabling (CB-CTT) problem has been given, by taking into account several real-world constraints and objectives while keeping the problem general. CB-CTT consists of finding the best weekly assignment of university course lectures to rooms and time periods. A feasible schedule must satisfy a set of hard constraints and must also take into account a set of soft constraints, whose violation produces penalty terms to be minimized in the objective function. From ITC-2007, many researchers have developed advanced models and methods to solve CB-CTT. This survey is devoted to review the main works on the topic, with focus on mathematical models, lower bounds, and exact and heuristic algorithms. Besides giving an overview of these approaches, we highlight interesting extensions that could make the study of CB-CTT even more challenging and closer to reality.

Comments on: An overview of curriculum-based course timetabling

I think that the paper provides a very good and well organized overview of the research on the Curriculum-Based Course Timetabling (CB-CTT) problem. Up to my knowledge, all the relevant literature on the specific problem has been discussed. The literature on educational timetabling in general has not been considered, but I believe that it would broaden the scope of the paper too much; therefore I agree with the selection of references made by the authors.

Practical relaxation of a special case of the Curriculum-Based Course Timetabling problem

The Curriculum-Based Course Timetabling (CB-CTT) problem involves the task of scheduling lectures of courses to classrooms, considering teacher availability, a specified curricula, and a set of constraints. In the Polytechnic University of Victoria (PUV), Mexico, the CB-CTT problem occurs with the additional constraints that the courses must be assigned to teachers and that a teacher cannot teach more than one course in the same curriculum. This document proposes a methodology to solve this special case CB-CTT problem. The main contributions derived from the research are: (a) the solution of the special case of the CB-CTT problem; (b) the use of a Simulated Annealing based methodology, which relaxes the problem into three simpler subproblems (the assignment, distribution, and scheduling of courses), to reduce the search space and speed up the construction of a solution; and (c) the solution of a real world instance using the proposed methodology. The results show that the approach can construct solutions for the problem in the PUV in a few minutes, and of a similar quality to those manually constructed in a couple of weeks.

Fairness in academic course timetabling

We consider the problem of creating fair course timetables in the setting of a university. The central idea is that undesirable arrangements in the course timetable, i.e., violations of soft constraints, should be distributed in a fair way among the stakeholders. We propose and discuss in detail two fair versions of the popular curriculum-based course timetabling (CB-CTT) problem, the MMF-CB-CTT problem and the JFI-CB-CTT problem, which are based on max–min fairness (MMF) and Jain’s fairness index (JFI), respectively. For solving the MMF-CB-CTT problem, we present and experimentally evaluate an optimization algorithm based on simulated annealing. We introduce three different energy difference measures and evaluate their impact on the overall algorithm performance. The proposed algorithm improves the fairness on 20 out of 32 standard instances compared to the known best timetables. The JFI-CB-CTT problem formulation focuses on the trade-off between fairness and the aggregated soft constraint violations. Here, our experimental evaluation shows that the known best solutions to 32 CB-CTT standard instances are quite fair with respect to JFI. Our experiments show that the fairness can often be improved at the cost of only a small increase in the overall amount of penalty.

SAT Model for the Curriculum-Based Course Timetabling Problem

Two widely used problems are the Satisability problem (SAT) and the Curriculum-Based Course Timetabling (CB-CTT) prob- lem. The SAT problem searches for an assignment that make true a cer- tain boolean formula. On the other side, the CB-CTT involves the task of scheduling lectures of courses to rooms, considering teacher availability, a specied curricula, and a set of constraints. Given the advances achieved in the solution of the SAT Problem, this research proposes a SAT Model of the CB-CTT problem, to aid in the construction of timetables. To demonstrate that the model can aid in the solution of real instances of the CB-CTT problem, a case of study derived from a university in Mex- ico was considered. This special case of CB-CTT involves the constraint where each teacher cannot teach more than one course in the same cur- riculum, which is included in the set of 3 hard constraints and 2 soft constraints analyzed in this research. According to the results obtained, the considered complete SAT solver required a few minutes to nd a solution for the instance.

A new lower bound for curriculum-based course timetabling

In this paper, we propose a new method to compute lower bounds for curriculum-based course timetabling (CTT), which calls for the best weekly assignment of university course lectures to rooms and time slots. The lower bound is obtained by splitting the objective function into two parts, considering one separate problem for each part of the objective function, and summing up the corresponding optimal values (or, in some cases, lower bounds on these values), found by formulating the two parts as Integer Linear Programs (ILPs). The solution of one ILP is obtained by using a column generation procedure. Experimental results show that the proposed lower bound is often better than the ones found by the previous methods in the literature, and also much better than those found by other new ILP formulations illustrated in this paper. The proposed approach is able to obtain improved lower bounds on real-world benchmark instances from the literature, used in the international timetabling competitions ITC2002 and ITC2007, proving for the first time that some of the best-known heuristic solutions are indeed optimal (or close to the optimal ones).

Artificial Bee Colony Algorithm for Solving Educational Timetabling Problems

This paper presents an artificial bee colony algorithm (ABC) for Education Timetabling Problem (ETP). It is aimed at developing a good-quality solution for the problem. The initial population of solutions was generated using Saturation Degree (SD) and Backtracking Algorithm (BA) to ensure the feasibility of the solutions. At the improvement stage in the solution method, ABC uses neighbourhood structures iteratively within the employed and onlooker bee operators, in order to rigorously navigate the UTP search space. The technique was evaluated using curriculum-based course timetabling (CB-CTT) and Uncapacitated Examination Timetabling Problem (UETP) problem instances. The experimental results on UETP showed that the technique is comparable with other state-of-the-art techniques and provides encouraging results on CB-CTT.