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.

The scheduling of exams in institutions of higher education is known to be a highly constrained problem. The advent of modularity in many institutions in the UK has resulted in a significant increase in its complexity, imposing even more difficulties on university administrators who must find a solution, often without any computer aid. Of the many methods that have been applied to solving the problem automatically, evolutionary techniques have shown much promise due to their general purpose optimisation capabilities. However, it has also been found that hybrid evolutionary methods can yield even better results. In this paper we present such a hybrid approach in the form of an evolutionary algorithm that incorporates local search methods (known as a memetic algorithm) . 1.

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.

In this paper we use a recently proposed metaheuristic, the Ant System, to solve the Vehicle Routing Problem (VRP) in its basic form, i.e. with capacity and distance restrictions, one central depot and identical vehicles. A "hybrid" Ant System algorithm is first presented and then improved using problem specific information (savings, capacity utilization). Experiments on various aspects of the algorithm and computational results for fourteen benchmark problems are reported and compared to those of other metaheuristic approaches such as Tabu Search, Simulated Annealing and Neural Networks. 1 Introduction The Ant System, introduced by Colorni, Dorigo and Maniezzo [6], [10], [12] is a new distributed metaheuristic for hard combinatorial optimization problems and was first used on the well known Traveling Salesman Problem (TSP). It has further been applied to the Job Shop Scheduling Problem in [7], to the Graph Colouring Problem in [8] and to the Quadratic Assignment Problem in [18]. Obse...

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.

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We summarize selected recent developments and promising directions for improving the quality of models of human performance in synthetic environments. The potential uses and goals for behavioral models in synthetic environments are first summarized. Within that context, we examine relevant, current work related to modeling more complete performance, for example, on cognitive modeling of emotion, advanced techniques for testing and building models of behavior, new cognitive architectures, and agent and Belief, Desires and Intentions (BDI) technology. The report also considers the usability of these systems as an important but neglected aspect of their performance. A list of projects with high payoff for modeling human performance in synthetic environments is noted.

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 discusses a series of recombination operators for the timetabling problem. These operators act upon a direct representation of the timetable and maintain the property of feasibility. That is that there are no conflicts and no overfilled rooms. Various approaches to solving the timetabling problem using evolutionary computing methods are first compared. The recombination operators are then presented and various alternatives for incorporating heuristic knowledge in the search are described. Finally, results are presented comparing the operators on a real timetabling problem. 1 Introduction Recently, there has been a lot of attention paid to the problem of automating the construction of university course and examination timetables. Many different techniques have and are being applied, including Simulated Annealing [14][20], Constraint Logic Programming [2][17], Linear Programming [21] and Graph Colouring Heuristics [5]. A growing number of researchers are now turning to Evo...