A two-phase multiple objective approach to university timetabling utilising optimisation and evolutionary solution methodologies

Abstract

The timetabling problem is generally large, highly constrained and discrete in nature. This makes solution by exact optimisation methods difficult. Therefore, often a heuristic search is deemed acceptable providing a simple (non-optimal) solution. This paper discusses the timetabling problem for a university department, where a large-scale integer goal programming (IGP) formulation is implemented for its efficient optimal solution in two phases. The first phase allocates lectures to rooms and the second allocates start-times to lectures. Owing to the size and complicated nature of the model, an initial analysis procedure is employed to manipulate the data to produce a more manageable model, resulting in considerable reductions in problem size and increase of performance. Both phases are modelled as IGPs. Phase 1 is solved using a state-of-the-art IGP optimisation package. However, due to the scale of the model, phase 2 is solved to optimality using a genetic algorithm approach.

Keywords:

• goal programming
• timetabling
• integer goal programming
• multi-objective genetic algorithms

Acknowledgements

We thank Mr Tom Manns for his valuable advice during the course of this research regarding the structure of the data and of the general timetabling process in the department. We also thank the anonymous referees for their useful comments on an earlier draft of this paper.