Managing the tabu list length using a fuzzy inference system: an application to exams timetabling

In this paper we present an application of Tabu Search (TS) to the exams timetabling problem. One of the drawback of this meta-heuristic is related with some parameter that can affect the performance of the algorithm and must be tuned. One of such is tabu tenure which is much problem dependent. Our goal is to have a automatic process of managing the memory which is important for practical applications. We can in general consider that the degree of expertise of the users ( university staff for instance) is low. To automatically manage the tabu tenure we employ techniques used in fuzzy decision expert systems. We developed a fuzzy inference rule based system (FIRBS) to handle the tabu tenure based on two concepts ”frequency” and ”inactivity”. These concepts are related to the number of times a move was attempt and the last time it was called. We have implemented the simplest form of a tabu search in order to evaluate this new feature. Computational results show that using a FIRBS improves the performance of Tabu Search. Key word: Exams timetabling; Tabu Search; Fuzzy Inference System. 1 The examination timetabling problem Problems related to timetabling are present in daily life. Solving timetabling problems is a crucial task and affect many institutions and services like hospital, transportation enterprizes, educational establishments, among many others. This problems have been an object of increasingly interest since the 1960s. Mainly in the field of Operations Research and Artificial Intelligence many interesting proposals have been presented. A general definition of timetabling was given by Burke, Kingston and Werra [3]. ” A timetabling problem is a problem with four parameters, T a finite set of times, R a finite ser of recourses, M, a finite set of meetings: and C, a finite set of constraints. The problem is to assign times and recourses to the meetings so as to satisfy the constraints as far as possible.” If in particular we consider exams as meetings then we are dealing with exams timetabling problems. This problems have attracted a considerable interests absolutely justified by ∗CA3 UNINOVA, Quinta da Torre Campus FCT-UNL 2829 516 Caparica Portugal, [email protected] †Dep. Mathematics, Universidade Nova de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal