Robust University Course Timetabling Problem Subject to Single and Multiple Disruptions

Abstract

University course timetables are often finalized in stages, in between which, changes in the data make the earlier version infeasible. As each version is announced to the community, it is desirable to have a robust initial timetable, i.e. one that can be repaired with limited number of changes and yielding a new solution whose quality is degraded as little as possible. We define two versions of the robust timetabling problem, first one assuming that only one lecture is disrupted (its scheduled period ceasing to be fea- sible) and the second one assuming multiple lectures are disrupted. The objective of the algorithms is to identify a good Pareto front defined by the solution quality (penalty associated with soft-constraint violations) and the robustness measure. Two versions of a multi-objective simulated annealing (MOSA) algorithm is developed (MOSA-SD and MOSA-SAA, for single and multiple disruptions, respectively), with the difference being in the way robustness of a solution is estimated within the MOSA algorithm. Exten- sive computational experiments done using the International Timetabling Competition ITC-2007 data set confirm that MOSA-SD outperforms a genetic algorithm from the literature, and MOSA-SAA outperforms MOSA-SD when there are multiple disruptions. For MOSA-SAA an innovative solution network to struc- ture feasible solutions for a set of disruption scenarios has been developed to efficiently perform sample average approximation (SAA) calculations, which can be adopted for other stochastic combinatorial opti- mization problems.