Educational Timetabling, in essence, consists in assigning teacher/student meetings to days, timeslots, and classrooms. Despite this apparent simplicity, experience teaches us that every single institution has its own rules, conventions, and fixations, thus making each specific problem almost unique. As a consequence, uncountably many different problem formulations have been proposed in the literature on Educational Timetabling, depending on the type of institution (high-school, university, or other), the type of meetings (lectures, exams,...), and the different settings, constraints, and objectives. Many papers in the literature tackle a specific problem using a selected search method. The authors normally claim the success of the application, though rarely dispelling the doubt over the readers that the method used was more the authors' "favorite" rather than the most suitable for the problem under consideration.

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.