A Multiobjective Optimisation Technique for Exam Timetabling Based on Trajectories

The most common approach to multiobjective examination timetabling is the weighted sum aggregation of all criteria into one cost function and application of some single-objective metaheuristic. However, the translation of user preferences into the weights of criteria is a sophisticated task, which requires experience on the part of the user, especially for problems with a high number of criteria. Moreover, the results produced by this technique are usually substantially scattered. Thus, the outcome of weighted sum algorithms is often far from user expectation. In this paper we suggest a more transparent method, which enables easier expression of user preferences. This method requires the user to specify a reference solution, which can be either produced manually or chosen among the set of solutions, generated by any automated method. Our aim is to improve the values of the reference objectives, i.e. to produce a solution which dominates the reference one. In order to achieve this, a trajectory is drawn from the origin to the reference point and a “Great Deluge” local search is conducted through the specified trajectory. During the search the weights of the criteria are dynamically changed. The proposed technique was experimentally tested on real-world exam timetabling problems on both bi-criteria and nine-criteria cases. All results obtained by the variable weights Great Deluge algorithm outperformed the ones published in the literature by all criteria.