Hybrid variable neighbourhood approaches to university exam timetabling

Abstract

Abstract. In this paper, we investigate variable neighbourhood search (VNS) approaches for the university examination timetabling problem. In addition to a basic VNS method, we introduce variants of the technique with different initialisation methods including a biased VNS and its hybridisation with a Genetic Algorithm. A number of different neighbourhood structures are analysed. It is demonstrated that the proposed technique is able to produce high quality solutions across a wide range of benchmark problem instances. In particular, we demonstrate that the Genetic Algorithm, which intelligently selects approporiate neighbourhoods to use within the biased VNS produces the best known results in the literature, in terms of solution quality, on some of the the benchmark instances, although it requires relatively large amount of computational time. Possible extensions to this overall approach are also discussed.

Adaptive selection of heuristics for improving exam timetables

“…These include the of hybridisation of an electromagnetic-like mechanism (EM) and the Great Deluge algorithm employed by Abdullah et al [1], the hill-climbing with a late acceptance strategy implemented by Burke et al [6], the variable neighbourhood search incorporating the use of genetic algorithms used by Burke et al [7] and the sequential construction method developed by Caramia et al [11]. These algorithms are described in section 2.4.…”

“…Kempe Chain Move (KCM): This is similar to the SE heuristic but is more complex as it involves swapping a subset of conflicting exams in two distinct timeslots. This neighbourhood operator proved success in some previous research [7,27]. 4.…”

“…The process starts by constructing an initial feasible solution. Since the initial solution constructed affects the improvement process, a random largest degree graph colouring heuristic which orders exams according to the number of conflicts each exam has with others is used [7]. This allows us to compare our approach to other approaches in the literature which use a similar method in construction.…”

“…We use the Kempe chain move heuristic as the basic heuristic in the sequences as it has proved to be successful in previous work [7,27]. The Kempe chain move involves swapping a subset of exams in two distinct timeslots making sure that a hard constraint violation does not occur.…”

“…A penalty decreaser and trader are then applied to improve the quality of the constructed solution. Burke et al [7] introduced an approach which combines a variable neighbourhood search with a genetic algorithm which produced the best quality solution for one of the Toronto instances. In addition Burke et.…”