A Fast Threshold Acceptance Algorithm for the Examination Timetabling Problem

In this chapter, an accelerated variant of the threshold acceptance (TA) metaheuristic, named FastTA, is proposed for solving the examination timetabling problem. FastTA executes a lower number of evaluations compared to TA while not worsening the solution cost in a significant way. Each exam selected for scheduling is only moved if that exam had any accepted moves in the immediately preceding threshold bin; otherwise, the exam is fixed and is not evaluated anymore. If an exam had zero accepted movements in the preceding threshold bin, it is likely to have few or zero accepted movements in the future, as it is becoming crystallised. The FastTA and TA were tested on the Toronto and Second International Timetabling Competition benchmark (ITC 2007) sets. Compared to TA, the FastTA uses 38% and 22% less evaluations, on average, on the Toronto and ITC 2007 sets, respectively. On the ITC 2007 set, the FastTA is competitive with TA attaining the best average solution cost value in four out of twelve instances while requiring less time to execute. Compared with the state-of-the-art approaches, the FastTA is able to achieve competitive results. The main contribution/value of this chapter is the proposal of a new acceptance criterion for the TA metaheuristic, which leads to a significantly faster variant (FastTA), and its application to solve public examination timetabling benchmark sets.