Simon Kristiansen

Integer programming for the generalized high school timetabling problem

Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby, the XHSTT format serves as a common ground for researchers within this area. This paper describes the first exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a mixed-integer linear programming (MIP) model, which is solved in two steps with a commercial general-purpose MIP solver. Computational results show that our approach is able to find previously unknown optimal solutions for 2 instances of XHSTT and proves optimality of 4 known solutions. For the instances not solved to optimality, new non-trivial lower bounds were found in 11 cases, and new best known solutions were found in 9 cases. Furthermore, the approach is compared with the finalists of Round 2 of the International Timetabling Competition 2011 and is shown to be competitive with one of the finalists.

Elective course student sectioning at Danish high schools

The Elective Course Student Sectioning (ECSS) problem is a yearly recurrent planning problem at the Danish high schools. The problem is of assigning students to elective classes given their requests such that as many requests are fulfilled and the violations of the soft constraints are minimized. This paper presents an Adaptive Large Neighborhood Search heuristic for the ESCC. The algorithm is applied to 80 real-life instances from Danish high schools and compared with solutions found by using the state-of-the-art MIP solver Gurobi. The algorithm has been implemented in the commercial product Lectio, and is thereby available for approximately 200 high schools in Denmark.