University Examination Timetable Optimisation: Analysis, Initialisation, and Effective Heuristic Optimisation

Abstract

Abstract

In higher education institutions, particularly universities, the task of scheduling examinations is a heavily constrained problem involving the allocation of exams, and corresponding enrolled students, to examination rooms over a limited number of periods. This is commonly performed by heuristic optimisers, as the task is NP-complete. The research work presented in this thesis focuses on examination timetabling with the aim of investigating three main areas: (i) initialising efficient seeded solutions for starting examination timetabling heuristics, (ii) developing a novel genetic algorithm-based examination timetabling optimiser, and (iii) analysing and comparing published works from the literature.

The new iterative initialisation algorithm presented here attempts to generate legal and high-quality solutions, to feed into a heuristic optimiser. Subject to satisfying hard constraints, it schedules as many conflicting examinations as possible in the early and late periods of a timetable, whilst managing the soft constraints. The proposed initialisation strategy is empirically verified on problem instances from two different benchmark sets: ITC 2007 and Yeditepe, and compared to a number of popular initialisation approaches. The effectiveness of this approach is also evaluated via incorporation in an exemplar evolutionary algorithm.

This thesis also investigates a novel genetic algorithm that incorporates new operators to avoid various types of violations that occur in the exam timetable optimisation task. It utilises the initialisation approach developed earlier in the thesis, as well as specialised operators for search. It is validated on a range of problems and is seen to produce results that place its performance amongst the state-of-the-art.

The third area of investigation of this thesis is concerned with issues in the comparison between published works on examination timetabling in the literature. Such comparison is often difficult and can be misleading because results obtained differ significantly in run-times --- even when variations in computational power are accounted for. Consequently, a multi-objective comparison scheme based on (uncertain) Pareto dominance is presented and utilised with the aim of comparing published exam timetabling approaches on the Toronto benchmark sets to identify the (probabilistic) Pareto set of optimisers.