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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.

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The work presented in this thesis concerns the problem of timetabling at universitiesparticularly course-timetabling, and examines the various ways in which metaheuristic techniques might be applied to these sorts of problems. Using a popular benchmark version of a university course timetabling problem, we examine the implications of using a "twostaged" algorithmic approach, whereby in stage-one only the mandatory constraints are considered for satisfaction, with stage-two then being concerned with satisfying the remaining constraints but without re-breaking any of the mandatory constraints in the process.Consequently, algorithms for each stage of this approach are proposed and analysed in detail.For the first stage we examine the applicability of the so-called Grouping Genetic Algorithm (GGA). In our analysis of this algorithm we discover a number of scaling-up issues surrounding the general GGA approach and discuss various reasons as to why this is so. Two separate ways of enhancing general performance are also explored. Secondly, an Iterated Heuristic Search algorithm is also proposed for the same problem, and in experiments it is shown to outperform the GGA in almost all cases. Similar observations to these are also witnessed in a second set of experiments, where the analogous problem of colouring equipartite graphs is also considered.Two new metaheuristic algorithms are also proposed for the second stage of the twostaged approach: an evolutionary algorithm (with a number of new specialised evolutionary operators), and a simulated annealing-based approach. Detailed analyses of both algorithms are presented and reasons for their relative benefits and drawbacks are discussed.Finally, suggestions are also made as to how our best performing algorithms might be modified in order to deal with further "real-world" constraints. In our analyses of these modified algorithms, as well as witnessing promising behaviour in some cases, we are also able to highlight some of the limitations of the two-stage approach in certain cases.ii Table of Fig. 3.2:A demonstration of the matrix representation for timetables used throughout this thesis. Here, event 11 has been assigned to room 2 and timeslot 2, event 8 has been assigned to room 2, timeslot 11, and so on. Also indicated in this diagram is the presence of the end-of-day timeslots (which will occur in timeslots 9, 18, 27, 36 and 45). These might be considered slightly different to the remaining forty timeslots, because events that are assigned to these will automatically cause soft constraint SC to have a higher distance-to-feasibility than the best candidate solution in the initial population of the GGA, and will thus generally start at a higher point on the y-axis. 84 1: IntroductionTimetables are ubiquitous in many areas of daily life such as work, education, transport, and entertainment. Indeed, it is quite difficult to imagine an organized and modern society coping without them. Yet in many real-world cases, particularly where resources (such as peopl...