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 high-school timetabling problem regards the weekly scheduling for all the lectures of a high school. The problem consists in assigning lectures to periods in such a way that no teacher (or class) is involved in more than one lecture at a time, and other side constraints are satisfied. The problem is NP-complete and is usually tackled using heuristic methods. This paper describes a solution algorithm (and its implementation) based on tabu search. The algorithm interleaves different types of moves and makes use of an adaptive relaxation of the hard constraints. The implementation of the algorithm has been successfully experimented in some large high schools with various kinds of side constraints.

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.

Abstract. In this study we have tackled the NP-hard problem of academic class scheduling (or timetabling) at the university level. We have investigated a variety of approaches based on simulated annealing, including mean-field annealing, simulated annealing with three different cooling schedules, and the use of a rule-based preprocessor to provide a good initial solution for annealing. The best results were obtained using simulated annealing with adaptive cooling and reheating as a function of cost, and a rule-based preprocessor. This approach enabled us to obtain valid schedules for the timetabling problem for a large university, using a complex cost function that includes student preferences. None of the other methods were able to provide a complete valid schedule. 1

In this paper a logic-based specification language, called NP-SPEC, is presented. The language is obtained by extending DATALOG through allowing a limited use of some second-order predicates of predefined form. NP-SPEC programs specify solutions to problems in a very abstract and concise way, and are executable. In the present prototype they are compiled to PROLOG code, which is run to construct outputs. Second-order predicates of suitable form allow to limit the size of search spaces in order to obtain reasonably efficient construction of problem solutions. NP-SPEC expressive power is precisely characterized as to express exactly the problems in the class NP. The specification of several combinatorial problems in NP-SPEC is shown, and the efficiency of the generated programs is evaluated.

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Abstract Automating the neighbourhood selection process in an iterative approach that uses multiple heuristics is not a trivial task. Hyper-heuristics are search methodologies that not only aim to provide a general framework for solving problem instances at different difficulty levels in a given domain, but a key goal is also to extend the level of generality so that different problems from different domains can also be solved. Indeed, a major challenge is to explore how the heuristic design process might be automated. Almost all existing iterative selection hyper-heuristics performing single point search contain two successive stages; heuristic selection and move acceptance. Different operators can be used in either of the stages. Recent studies explore ways of introducing learning mechanisms into the search process for improving the performance of hyper-heuristics. In this study, a broad empirical analysis is performed comparing Monte Carlo based hyper-heuristics for solving capacitated examination timetabling problems. One of these hyper-heuristics is an approach that overlaps two stages and presents them in a single algorithmic body. A learning heuristic selection method (L) operates in harmony with a simulated annealing move acceptance method using reheating (SA) based on some shared variables. Yet, the heuristic selection and move

The university course timetabling problem is an optimisation problem in which a set of events has to be scheduled in timeslots and located in suitable rooms. Recently, a set of benchmark instances was introduced and used for an ‘International Timetabling Competition’ to which 24 algorithms were submitted by various research groups active in the field of timetabling. We describe and analyse a hybrid metaheuristic algorithm which was developed under the very same rules and deadlines imposed by the competition and outperformed the official winner. It combines various construction heuristics, tabu search, variable neighbourhood descent and simulated annealing. Due to the complexity of developing hybrid metaheuristics, we strongly relied on an experimental methodology for configuring the algorithms as well as for choosing proper parameter settings. In particular, we used racing procedures that allow an automatic or semi-automatic configuration of algorithms with a good save in time. Our successful example shows that the systematic design of hybrid algorithms through an experimental methodology leads to high performing algorithms for hard combinatorial optimisation problems.

Timetabling the courses offered at the Computer Science Department of the University of Munich requires the processing of hard and soft constraints. Hard constraints are conditions that must be satisfied, soft constraints, however, may be violated, but should be satisfied as much as possible. This paper shows how to model our timetabling problem as a partial constraint satisfaction problem and gives a concise finite domain solver implemented with Constraint Handling Rules that, by performing soft constraint propagation, allows for making soft constraints an active part of the problem solving process. Furthermore, we improve efficiency by reusing parts of the timetable of the previous year. Our prototype needs only a few minutes to create a timetable while manual timetabling usually takes a few days. It was presented at the Systems’98 computer fair in Munich and several universities have enquired for it. 1