Barry McCollum

A Graph-Based Hyper-Heuristic for Educational Timetabling Problems

This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyper-heuristic framework, a tabu search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the tabu search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-theart approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems. � 2005 Elsevier B.V. All rights reserved.

A survey of search methodologies and automated system development for examination timetabling

Examination timetabling is one of the most important administrative activities that takes place in all academic institutions. In this paper, we present a critical discussion of the research on exam timetabling which has taken place in the last decade or so. This last ten years has seen a significantly increased level of research attention for this important area. There has been a range of insightful contributions to the scientific literature both in terms of theoretical issues and practical aspects. The main aim of this survey is to highlight the new trends and key research achievements that have been carried out in the last decade. We also aim to outline a range of relevant important research issues and challenges that have been generated by this body of work.We first define the problem and discuss previous survey papers. Within our presentation of the state-of-the-art methodologies, we highlight recent research trends including hybridisations of search methodologies and the development of techniques which are motivated by raising the level of generality at which search methodologies can operate. Summarising tables are presented to provide an overall view of these techniques. We also present and discuss some important issues which have come to light concerning the public benchmark exam timetabling data. Different versions of problem datasets with the same name have been circulating in the scientific community for the last ten years and this has generated a significant amount of confusion. We clarify the situation and present a re-naming of the widely studied datasets to avoid future confusion. We also highlight which research papers have dealt with which dataset. Finally, we draw upon our discussion of the literature to present a (non-exhaustive) range of potential future research directions and open issues in exam timetabling research.

The practice and theory of automated timetabling

This special volumecomprises revisedversions of a selectionof the papers thatwere presented at the 9th International Conference on the Practice and Theory of Automated Timetabling (PATAT) in Belfast between 10th and 13th August 2010. The PATAT conferences are held biennially and this is the second time that the Annals of Operations Research has provided the venue for such a special collection of papers. The first PATAT special volume of this journal (Volume 194) contains papers associated with the 8th conference which was held in Montreal in 2008. PATAT acts as an international forum for all aspects of timetabling, including educational timetabling, personnel rostering, sports timetabling, and transport scheduling. The conference series is particularly concerned both with closing the gap between timetabling theory and practice and with supporting multidisciplinary interactions. The collection of papers in this special volume reflect these aims. The conference in Belfast brought together approximately 100 participants from around the world. There were five plenary presentations, 74 standard talks, and 16 practitioner presentations. All the delegates were invited to submit their revised papers to this special volume. The papers have been through a rigorous and thorough review process, and we are delighted to be able to present the community with such an interesting and diverse selection of articles that reflect the latest thinking in timetabling research. We would like to take this opportunity to thank all those who were responsible for the success of the conference. We would particularly like to thank Brian Fleming and all those within the School of Electronics, Electrical Engineering andComputer Science at theQueen’s University of Belfast who worked so hard before and during the conference.

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.

Hybrid variable neighbourhood approaches to university exam timetabling

In this paper, we investigate variable neighbourhood search (VNS) approaches for the university examination timetabling problem. In addition to a basic VNS method, we introduce variants of the technique with different initialisation methods including a biased VNS and its hybridisation with a Genetic Algorithm. A number of different neighbourhood structures are analysed. It is demonstrated that the proposed technique is able to produce high quality solutions across a wide range of benchmark problem instances. In particular, we demonstrate that the Genetic Algorithm, which intelligently selects appropriate neighbourhoods to use within the biased VNS, produces the best known results in the literature, in terms of solution quality, on some of the benchmark instances. However, it requires relatively large amount of computational time. Possible extensions to this overall approach are also discussed.

A hybrid evolutionary approach to the university course timetabling problem

Combinations of evolutionary based approaches with local search have provided very good results for a variety of scheduling problems. This paper describes the development of such an algorithm for university course timetabling. This problem is concerned with the assignment of lectures to specific timeslots and rooms. For a solution to be feasible, a number of hard constraints must be satisfied. The quality of the solution is measured in terms of a penalty value which represents the degree to which various soft constraints are satisfied. This hybrid evolutionary approach is tested over established datasets and compared against state-of-the-art techniques from the literature. The results obtained confirm that the approach is able to produce solutions to the course timetabling problem which exhibit some of the lowest penalty values in the literature on these benchmark problems. It is therefore concluded that the hybrid evolutionary approach represents a particularly effective methodology for producing high quality solutions to the university course timetabling problem.

Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems

In this paper, we present a random iterative graph based hyper-heuristic to produce a collection of heuristic sequences to construct solutions of different quality. These heuristic sequences can be seen as dynamic hybridisations of different graph colouring heuristics that construct solutions step by step. Based on these sequences, we statistically analyse the way in which graph colouring heuristics are automatically hybridised. This, to our knowledge, represents a new direction in hyper-heuristic research. It is observed that spending the search effort on hybridising Largest Weighted Degree with Saturation Degree at the early stage of solution construction tends to generate high quality solutions. Based on these observations, an iterative hybrid approach is developed to adaptively hybridise these two graph colouring heuristics at different stages of solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme on developing computer methods to design and adapt heuristics automatically. Experimental results on benchmark exam timetabling and graph colouring problems demonstrate the effectiveness and generality of this adaptive hybrid approach compared with previous methods on automatically generating and adapting heuristics. Indeed, we also show that the approach is competitive with the state of the art human produced methods.

Fuzzy multiple heuristic orderings for examination timetabling

In this paper, we address the issue of ordering exams by simultaneously considering two separate heuristics using fuzzy methods. Combinations of two of the following three heuristic orderings are employed: largest degree, saturation degree and largest enrolment. The fuzzy weight of an exam is used to represent how difficult it is to schedule. The decreasingly ordered exams are sequentially chosen to be assigned to the last slot with least penalty cost value while the feasibility of the timetable is maintained throughout the process. Unscheduling and rescheduling exams is performed until all exams are scheduled. The proposed algorithm has been tested on 12 benchmark examination timetabling data sets and the results show that this approach can produce good quality solutions. Moreover, there is significant potential to extend the approach by including a larger range of heuristics.

A Hybrid Evolutionary Approach to the Nurse Rostering Problem

Nurse rostering is an important search problem with many constraints. In the literature, a number of approaches have been investigated including penalty function methods to tackle these constraints within genetic algorithm frameworks. In this paper, we investigate an extension of a previously proposed stochastic ranking method, which has demonstrated superior performance to other constraint handling techniques when tested against a set of constrained optimization benchmark problems. An initial experiment on nurse rostering problems demonstrates that the stochastic ranking method is better at finding feasible solutions, but fails to obtain good results with regard to the objective function. To improve the performance of the algorithm, we hybridize it with a recently proposed simulated annealing hyper-heuristic (SAHH) within a local search and genetic algorithm framework. Computational results show that the hybrid algorithm performs better than both the genetic algorithm with stochastic ranking and the SAHH alone. The hybrid algorithm also outperforms the methods in the literature which have the previously best known results.

Using a Randomised Iterative Improvement Algorithm with Composite Neighbourhood Structures for the University Course Timetabling Problem

The course timetabling problem deals with the assignment of a set of courses to specific timeslots and rooms within a working week subject to a variety of hard and soft constraints. Solutions which satisfy the hard constraints are called feasible. The goal is to satisfy as many of the soft constraints as possible whilst constructing a feasible schedule. In this paper, we present a composite neighbourhood structure with a randomised iterative improvement algorithm. This algorithm always accepts an improved solution and a worse solution is accepted with a certain probability. The algorithm is tested over eleven benchmark datasets (representing one large, five medium and five small problems). The results demonstrate that our approach is able to produce solutions that have lower penalty on all the small problems and two of the medium problems when compared against other techniques from the literature. However, in the case of the medium problems, this is at the expense of significantly increased computational time.