Search algorithms for improving the pareto front in a timetabling problem with a solution network-based robustness measure

Abstract

We develop search algorithms based on local search, and a matheuristic that solves a set of mixed integer programming models to improve the robustness of a set of solutions for an academic timetabling problem. The matheuristic uses the solution pool feature of CPLEX while solving two related MIP models iteratively. The solutions form a network (Akkan et al. in Eur J Oper Res 249(2):560–576, 2016. doi: 10.1016/j.ejor.2015.08.047 ), in which edges are defined by the Hamming distance between pairs of solutions. This network is used to calculate a robustness measure, where disruption of a solution is assumed to occur when the time slot to which a team had been assigned is no longer feasible for that team and the heuristic response to this disruption is choosing one of the neighbors of the disrupted solution. Considering the objective function of the timetabling problem and this robustness measure results in a bi-criteria optimization problem where the goal is to improve the Pareto front by enlarging the network. We compare the performance of the heuristics on a set of random instances and seven semesters’ actual data. These results show that some of the proposed local search algorithms and the matheuristic find high quality approximate Pareto fronts. Besides being one of the few timetabling algorithms in the literature addressing robustness, a key contribution of this research is the demonstration of the effectiveness of the matheuristic approach. By using this matheuristic approach, for any discrete optimization model that can be solved optimally or near-optimally in an acceptable time, researchers can develop a robustness improvement algorithm.