The timetabling problem consists in fixing a sequence of meetings between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of institution involved (university or high school) and the type of constraints. This problem, that has been traditionally considered in the operational research field, has recently been tackled with techniques belonging also to artificial intelligence (e.g. genetic algorithms, tabu search, simulated annealing, and constraint satisfaction). In this paper, we survey the various formulations of the problem, and the techniques and algorithms used for its solution.

The aim of this paper is to give a brief introduction to some recent approaches to timetabling problems that have been developed or are under development in the Automated Scheduling, Optimisation and Planning Research Group (ASAP) at the University of Nottingham. We have concentrated upon university timetabling but we believe that some of the methodologies that are described can be used for different timetabling problems such as employee timetabling, timetabling of sports fixtures, etc. The paper suggests a number of approaches and comprises three parts. Firstly, recent heuristic and evolutionary timetabling algorithms are discussed. In particular, two evolutionary algorithm developments are described: a method for decomposing large real-world timetabling problems and a method for heuristic initialisation of the population. Secondly, an approach that considers timetabling problems as multicriteria decision problems is presented. Thirdly, we discuss a case-based reasoning approach that employs previous experience to solve new timetabling problems. Finally, we outline some new research ideas and directions in the field of timetabling. The overall aim of these research directions is to explore approaches that can operate at a higher level of generality than is currently possible. Keywords: Combinatorial optimisation; Timetabling/Scheduling; Meta-heuristic approaches; Multiple criteria analysis; Case-based reasoning, Hyper-heuristics.

It is well known that timetabling problems can be particularly difficult to solve, especially when dealing with particularly large instances. Finding near optimal results can prove to be extremely difficult, even when using advanced search methods such as evolutionary algorithms (EAs). In this paper we present a method of decomposing larger problems into smaller components, each of which is of a size that the EA can effectively handle. We will show various experimental results using this method to prove that not only can the execution time be considerably reduced but also that the presented method can actually improve the quality of produced solutions.

In recent years the computational power of computers has increased dramatically. This in turn has allowed search algorithms to execute more iterations in a given amount of real time. Does this necessarily always lead to an improvement in the quality of final solutions? This paper is devoted to the investigation of that question. We present two variants of local search algorithms where the search time can be set as an input parameter. These two approaches are: a time-predefined variant of simulated annealing and an adaptation of the "Great Deluge" method. We present a comprehensive series of experiments, which show that these approaches significantly outperform the previous best results (in terms of solution quality) on the most popular benchmark exam timetabling problems. Of course, there is a price to pay for such better results: increased execution time. We discuss the impact of this trade-off between quality and execution time. In particular we discuss issues involving the proper estimation of the algorithm's execution time and the assessment of its importance.

Heuristic ordering based methods, very similar to those used for graph colouring problems, have long been applied successfully to the examination timetabling problem. Despite the success of these methods on real life problems, even with limited computing resources, the approach has the fundamental flaw that it is only as effective as the heuristic that is used. One of the motivations of this paper is to attempt to develop approaches that can operate at a higher level of generality and that can adapt heuristics to suit the particular problem instance in hand.

this paper we present an ongoing research on the development of a solution algorithm for Examination Timetabling based on tabu search (TS) [8]. The algorithm makes use of several features imported from the literature on the Graph Colouring problem. We perform preliminary experiments of the algorithm on the popular Carter's benchmarks [5], and we compared our results with Carter's ones.

In this paper, we present a powerful hybrid genetic algorithm based around a heuristic timetabling framework. This combines a direct representation of the timetable with heuristic crossover operators to ensure that the most fundamental constraints are never violated. We explain how the population is seeded so as to produce a solution which cannot be outperformed by the heuristic method alone. We also see how the algorithm is guaranteed to always produce a feasible solution by hard coding constraints which must not be broken. Hybrid crossover operators are used, which propagate the most desirable features of the timetable to produce good quality solutions, even for large and highly constrained problems. Finally, we present the results from applying the algorithm to a particularly difficult problem, and demonstrate the variety of possible timetables that can be generated, depending upon the requirements of the user. 1 INTRODUCTION Recently, there has been a lot of attention paid to the...

Abstract. It is well known that domain-specific heuristics can produce good-quality solutions for timetabling problems in a short amount of time. However, they often lack the ability to do any thorough optimisation. In this paper we will study the effects of applying local search techniques to improve good-quality initial solutions generated using a heuristic construction method. While the same rules should apply to any heuristic construction, we use here an adaptive approach to timetabling problems. The focus of the experiments is how parameters to the local search methods affect quality when started on already good solutions. We present experimental results which show that this combined approach produces the best published results on several benchmark problems and we briefly discuss the implications for future work in the area.

Ordering exams by simultaneously considering two ordering criteria using a fuzzy expert system is presented in this paper. Combinations of two of the three ordering criteria largest degree, saturation degree and largest enrollment are considered. 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 datasets 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 criteria.

This paper briefly looks at various popular techniques and recent work on both exam and course scheduling around the world, and should serve as an introduction to the field