Integrating matheuristics and metaheuristics for timetabling

The High School Timetabling Problem requires the assignment of times and resources to events, while sets of required and desirable constraints must be considered. The most common approach for this problem is to employ metaheuristic methods. This work presents a matheuristic approach that combines a Variable Neighbourhood Search algorithm with mathematical programming-based neighbourhoods for high school timetabling. Computational experiments on well-known benchmark instances demonstrate the success of the proposed hybrid approach, which outperforms the standalone Variable Neighbourhood Search algorithm by far. Additionally, the proposed algorithm was able to improve 15 out of 17 current best known solutions in a very famous benchmark set.