A Study on the Short-Term Prohibition Mechanisms in Tabu Search for Examination Timetabling

Tabu Search (TS) is a well known local search method [11] which has been widely used for solving timetabling problems. Different versions of TS have been proposed in the literature, and many features of TS have been considered and tested experimentally. They range from long-term tabu, to dynamic cost functions, to strategic oscillation, to elite candidate lists, to complex aspiration criteria, just to mention some (see [10] for an overview). The feature that is included in virtually all TS variants is the so called (shortterm) tabu list. The tabu list is indeed recognized as the basic ingredient for the effectiveness of a TS-based solution, and its behaviour is a crucial issue of TS. Unfortunately, despite the fact that the importance of a correct empirical analysis has been recognised in the general context of heuristic methods [1,12] and even in the specific case of TS [15], the definition of the parameters associated with the tabu list remains in most research work still a handcrafted activity. Often, the experimental work behind the parameter setting remains hidden or is condensed in a few lines of text reporting only the final best configuration. Even the recently introduced racing methodology for the tuning of algorithms [3] only allows to determine the best possible configuration. This procedures are certainly justified from a practical point of view, but a description of the behavior of the algorithm with respect to its different factors and parameters is surely of great interest in the research field. In this work, we aim at determining which factors of basic TS are important and responsible for the good behaviour of the algorithm. Instead of the onefactor-at-a-time approach used in [15], our approach uses experimental design techniques [14] combining the racing methodology for the definition of quantitative factors and the analysis of variance for the study of qualitative factors. We focus our analysis on the Examination Timetabling problem, for which there is a consistent literature and many benchmark instances. In particular, we consider the formulation proposed by Burke et al [5], which considers first