An Iterative Re-start Variable Neighbourhood Search for the Examination Timetabling Problem

Producing good quality examination timetables is a difficult task which is faced by many academic institutions. Due to the complexity and the large size of the realworld university examination timetabling problems, it is difficult to obtain an optimal solution. Indeed, due to the complex nature of the problem, it is questionable if an end user would recognise a truly optimal solution. Carter and Laporte [1] defined the exam timetabling as: “the assigning of examinations to a limited number of available time periods in such a way that there are no conflicts or clashes.” In principle, the exam timetabling problem involves, assigning exams to timeslots subject to a set of hard and soft constraints. Hard constraints are rigidly enforced whilst soft constraints should be satisfied as far as possible. For example, exams which have common students have to be assigned to different timeslots (hard constraint). Wherever possible, examinations should be spread out over timeslots so that students have large gaps in between exams (soft constraint). Constraints vary among institutions and further discussion of exam timetabling constraints can be found in Burke et al. [2] and Carter and Laporte [1]. Timetables that satisfy all the hard constraints are called feasible solutions. Due to the complexity of the problem, it is not usually possible to have solutions that do not violate some of the soft constraints. Indeed, the evaluation of the cost function (how good the solutions are) is a function of violated soft constraints. A weighted penalty value is associated with each violation of the soft constraint and the objective is to minimise the total penalty value. The exam timetabling problem can be modelled as a graph colouring problem (see Burke et al. [3, 4]). Usually, graph colouring heuristics, which order the events/exams based on an estimation of their difficulties, are used to construct the timetable. These include: Largest degree first. This first schedules the exam that has the largest number of conflicts with other exams.