Decomposition and Recomposition Strategies to Solve Timetabling Problems

Timetabling is a crucial and often extremely time consuming task in many educational institutions. This task is generally performed periodically (each year, semester, quarter) for fulfilling the requirements imposed by the institution and people involved, such as students and teachers/lecturers making efficient and effective use of the available resources. The educational timetabling problem has been widely studied and different classifications have been proposed (see [1], [5]). The course timetabling problem (CTTP) is a combinatorial optimisation problem which involves assignment of a given set of meetings along with available resources to appropriate time slots subject to a set of constraints. In general, two types of constraints can be identified: hard and soft. The hard constraints are those that must be satisfied under any circumstances. Timetables that do not violate hard constraints are called feasible. On the other hand, soft constraints are those that need to be respected as many as possible, but can still be violated if necessary, i.e. they are desirable but not essential. These constraints are frequently used to evaluate how good the solutions (timetables) are. Two classes of well known solution methods in timetabling are construction and decomposition methods (e.g. [2], [3], [6]). In this study, we investigate an approach which decomposes a given problem into smaller subsets and then sequentially constructs a partial solution using the subsets recomposing them into a complete solution. The proposed approach is tested on the Post Enrolment based Course Timetabling problem instances of the Track 2 from the second International Timetabling Competition (ITC2007) for solving the hard constraints. The