A Multi-Start Very Large Neighbourhood Search Approach with Local Search Methods for Examination Timetabling

This paper investigates a hybridisation of the very large neighbourhood search approach with local search methods to address examination timetabling problems. In this paper, we describe a 2 phase approach. The first phase employs “multi start” to carry out search upon a very large neighbourhood of solutions using graph theoretical algorithms implemented on an improvement graph. The second phase makes further improvements by utilising a local search method. We present experimental results which show that this combined approach compares favourably with other algorithms on the standard benchmark problems. Introduction: Formalising the Examination Timetabling Problem Examination timetabling is concerned with an assignment of exams into a limited number of timeslots so that no student is assigned two or more exams at the same time. Overviews of the scientific literature on university timetabling can be seen in, for example, [9,13,22]. The objective, in the problems we tackle, is to try to spread the exams as evenly as possible throughout the schedule. We can represent the examination timetabling problem using a formal model which was adapted from the version presented in [11]. We are given the input for the examination timetabling problem as follows: • N is the number of exams • P is the given number of available timeslots • M is the number of students • C = (cij)NxN is the conflict matrix where each element, denoted by cij (i,j ∈ {1,...,N}), represents the number of students taking exams i and j. • tk (1 tk ≤P) specifies the assigned timeslot for exam k (k ∈ {1,...,N}) The objective is to minimise the proximity cost which can be formulated as a minimisation of Expression (1):