Pattern-based models and a cooperative parallel metaheuristic for high school timetabling problems

• We propose two mixed-integer formulations for a timetabling problem. • We strengthen one of the models with a Fenchel enumeration cutting planes technique. • We propose a column generation procedure for the second model. • We implement a parallel metaheuristic that uses the proposed column generation. High school timetabling problems consist in building periodic timetables for class-teacher meetings considering compulsory and non-compulsory requirements. This family of problems has been widely studied since the 1950s, mostly via mixed-integer programming and metaheuristic techniques. However, the efficient search of optimal or near-optimal solutions is still a challenge for many problems of practical size. In this paper, we investigate mixed-integer programming formulations and a parallel metaheuristic based algorithm for solving high school timetabling problems with compactness and balancing requirements. We propose two pattern-based formulations and a solution algorithm that simultaneously exploits column generation and a team of metaheuristics to build and improve solutions. Extensive computational experiments conducted with real-world instances demonstrate that our formulations are competitive with the best existing high school timetabling formulations, while our parallel algorithm presents superior performance to alternative methods available in the literature.