Paul McMullan

Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition

The Second International Timetabling Competition (TTC2007) opened in August 2007. Building on the success of the first competition in 2002, this sequel aimed to further develop research activity in the area of educational timetabling. The broad aim of the competition was to create better understanding between researchers and practitioners by allowing emerging techniques to be developed and tested on real-world models of timetabling problems. To support this, a primary goal was to provide researchers with models of problems faced by practitioners through incorporating a significant number of real-world constraints. Another objective of the competition was to stimulate debate within the widening timetabling research community. The competition was divided into three tracks to reflect the important variations that exist in educational timetabling within higher education. Because these formulations incorporate an increased number of “real-world” issues, it is anticipated that the competition will now set the research agenda within the field. After finishing in January 2008, final results were made available in May 2008. Along with background to the competition, the competition tracks are described here along with a brief overview of the techniques used by the competition winners.

An Extended Implementation of the Great Deluge Algorithm for Course Timetabling

Course Scheduling consists of assigning lecture events to a limited set of specific timeslots and rooms. The objective is to satisfy as many soft constraints as possible, while maintaining a feasible solution timetable. The most successful techniques to date require a compute-intensive examination of the solution neighbourhood to direct searches to an optimum solution. Although they may require fewer neighbourhood moves than more exhaustive techniques to gain comparable results, they can take considerably longer to achieve success. This paper introduces an extended version of the Great Deluge Algorithm for the Course Timetabling problem which, while avoiding the problem of getting trapped in local optima, uses simple Neighbourhood search heuristics to obtain solutions in a relatively short amount of time. The paper presents results based on a standard set of benchmark datasets, beating over half of the currently published best results with in some cases up to 60% of an improvement.

A hybrid metaheuristic approach to the university course timetabling problem

This paper describes the development of a novel metaheuristic that combines an electromagnetic-like mechanism (EM) and the great deluge algorithm (GD) for the University course timetabling problem. This well-known timetabling problem assigns lectures to specific numbers of timeslots and rooms maximizing the overall quality of the timetable while taking various constraints into account. EM is a population-based stochastic global optimization algorithm that is based on the theory of physics, simulating attraction and repulsion of sample points in moving toward optimality. GD is a local search procedure that allows worse solutions to be accepted based on some given upper boundary or ‘level’. In this paper, the dynamic force calculated from the attraction-repulsion mechanism is used as a decreasing rate to update the ‘level’ within the search process. The proposed method has been applied to a range of benchmark university course timetabling test problems from the literature. Moreover, the viability of the method has been tested by comparing its results with other reported results from the literature, demonstrating that the method is able to produce improved solutions to those currently published. We believe this is due to the combination of both approaches and the ability of the resultant algorithm to converge all solutions at every search process.

Towards improving the utilization of university teaching space

There is a perception that teaching space in universities is a rather scarce resource. However, some studies have revealed that in many institutions it is actually chronically under-used. Often, rooms are occupied only half the time, and even when in use they are often only half full. This is usually measured by the ‘utilization’ which is defined as the percentage of available ‘seat-hours’ that are employed. Within real institutions, studies have shown that this utilization can often take values as low as 20–40%. One consequence of such a low level of utilization is that space managers are under pressure to make more efficient use of the available teaching space. However, better management is hampered because there does not appear to be a good understanding within space management (near-term planning) of why this happens. This is accompanied, within space planning (long-term planning) by a lack of experise on how best to accommodate the expected low utilizations. This motivates our two main goals: (i) To understand the factors that drive down utilizations, (ii) To set up methods to provide better space planning. Here, we provide quantitative evidence that constraints arising from timetabling and location requirements easily have the potential to explain the low utilizations seen in reality. Furthermore, on considering the decision question ‘Can this given set of courses all be allocated in the available teaching space?’ we find that the answer depends on the associated utilization in a way that exhibits threshold behaviour: There is a sharp division between regions in which the answer is ‘almost always yes’ and those of ‘almost always no’. Through analysis and understanding of the space of potential solutions, our work suggests that better use of space within universities will come about through an understanding of the effects of timetabling constraints and when it is statistically likely that it will be possible for a set of courses to be allocated to a particular space. The results presented here provide a firm foundation for university managers to take decisions on how space should be managed and planned for more effectively. Our multi-criteria approach and new methodology together provide new insight into the interaction between the course timetabling problem and the crucial issue of space planning.

Adaptive linear combination of heuristic orderings in constructing examination timetables

In this paper, we investigate adaptive linear combinations of graph coloring heuristics with a heuristic modifier to address the examination timetabling problem. We invoke a normalisation strategy for each parameter in order to generalise the specific problem data. Two graph coloring heuristics were used in this study (largest degree and saturation degree). A score for the difficulty of assigning each examination was obtained from an adaptive linear combination of these two heuristics and examinations in the list were ordered based on this value. The examinations with the score value representing the higher difficulty were chosen for scheduling based on two strategies. We tested for single and multiple heuristics with and without a heuristic modifier with different combinations of weight values for each parameter on the Toronto and ITC2007 benchmark data sets. We observed that the combination of multiple heuristics with a heuristic modifier offers an effective way to obtain good solution quality. Experimental results demonstrate that our approach delivers promising results. We conclude that this adaptive linear combination of heuristics is a highly effective method and simple to implement.

A new neural network based construction heuristic for the examination timetabling problem

This paper examines the application of neural networks as a construction heuristic for the examination timetabling problem. Building on the heuristic ordering technique, where events are ordered by decreasing scheduling difficulty, the neural network allows a novel dynamic, multi-criteria approach to be developed. The difficulty of each event to be scheduled is assessed on several characteristics, removing the dependence of an ordering based on a single heuristic. Furthermore, this technique allows the ordering to be reviewed and modified as each event is scheduled; a necessary step since the timetable and constraints are altered as events are placed. Our approach uses a Kohonen self organising neural network and is shown to have wide applicability. Results are presented for a range of examination timetabling problems using standard benchmark datasets.

Dual sequence simulated annealing with round-robin approach for university course timetabling

The university course timetabling problem involves assigning a given number of events into a limited number of timeslots and rooms under a given set of constraints; the objective is to satisfy the hard constraints (essential requirements) and minimize the violation of soft constraints (desirable requirements). In this study we employed a Dual-sequence Simulated Annealing (DSA) algorithm as an improvement algorithm. The Round Robin (RR) algorithm is used to control the selection of neighbourhood structures within DSA. The performance of our approach is tested over eleven benchmark datasets. Experimental results show that our approach is able to generate competitive results when compared with other state-of-the-art techniques.

A new hybrid imperialist swarm-based optimization algorithm for university timetabling problems

Generating timetables for an institution is a challenging and time consuming task due to different demands on the overall structure of the timetable. In this paper, a new hybrid method which is a combination of a great deluge and artificial bee colony algorithm (INMGD-ABC) is proposed to address the university timetabling problem. Artificial bee colony algorithm (ABC) is a population based method that has been introduced in recent years and has proven successful in solving various optimization problems effectively. However, as with many search based approaches, there exist weaknesses in the exploration and exploitation abilities which tend to induce slow convergence of the overall search process. Therefore, hybridization is proposed to compensate for the identified weaknesses of the ABC. Also, inspired from imperialist competitive algorithms, an assimilation policy is implemented in order to improve the global exploration ability of the ABC algorithm. In addition, Nelder-Mead simplex search method is incorporated within the great deluge algorithm (NMGD) with the aim of enhancing the exploitation ability of the hybrid method in fine-tuning the problem search region. The proposed method is tested on two differing benchmark datasets i.e. examination and course timetabling datasets. A statistical analysis t-test has been conducted and shows the performance of the proposed approach as significantly better than basic ABC algorithm. Finally, the experimental results are compared against state-of-the art methods in the literature, with results obtained that are competitive and in certain cases achieving some of the current best results to those in the literature.

A tabu-based memetic approach for examination timetabling problems

Constructing examination timetable for higher educational institutions is a very complex task due to the complexity of the issues involved. The objective of examination timetabling problem is to satisfy the hard constraints and minimize the violations of soft constraints. In this work, a tabu-based memetic approach has been applied and evaluated against the latest methodologies in the literature on standard benchmark problems. The approach hybridizes the concepts of tabu search and memetic algorithms. A tabu list is used to penalise neighbourhood structures that are unable to generate better solutions after the crossover and mutation operators have been applied to the selected solutions from the population pool. We demonstrate that our approach is able to enhance the quality of the solutions by carefully selecting the effective neighbourhood structures. Hence, some best known results have been obtained.

Dynamic job scheduling on the grid environment using the great deluge algorithm

The utilization of the computational Grid processor network has become a common method for researchers and scientists without access to local processor clusters to avail of the benefits of parallel processing for computeintensive applications. As a result, this demand requires effective and efficient dynamic allocation of available resources. Although static scheduling and allocation techniques have proved effective, the dynamic nature of the Grid requires innovative techniques for reacting to change and maintaining stability for users. The dynamic scheduling process requires quite powerful optimization techniques, which can themselves lack the performance required in reaction time for achieving an effective schedule solution. Often there is a trade-off between solution quality and speed in achieving a solution. This paper presents an extension of a technique used in optimization and scheduling which can provide the means of achieving this balance and improves on similar approaches currently published.