Curriculum based course timetabling: new solutions to Udine benchmark instances

Abstract

We present an integer programming approach to the university course timetabling problem, in which weekly lectures have to be scheduled and assigned to rooms. Students' curricula impose restrictions as to which courses may not be scheduled in parallel. Besides some hard constraints (no two courses in the same room at the same time, etc.), there are several soft constraints in practice which give a convenient structure to timetables; these should be met as well as possible.We report on solving benchmark instances from the literature and the 2nd International Timetabling Competition which are based on real data from the university of Udine. The first set is solved to proven optimality; for the second set we give solutions which on average compete well with or beat the previously best known solutions. Our algorithm is not an overall winner, but it is very robust in the sense that it deterministically gives satisfactory lower and upper bounds in reasonable computation time without particular tuning. For slightly larger instances from the literature our approach shows significant potential as it considerably beats previous benchmarks. We further present solutions of proven quality to a few much larger instances with more elaborate hard constraints.

Lower bounds for the ITC-2007 curriculum-based course timetabling problem

“…To the best of our knowledge, only two recently published studies are devoted to the calculation of lower bounds for the CBCT problem ( [4], [12]). These studies are based on different integer programming formulations.…”

“…Soft constraints are used to define the objective function to be minimized. Examples of recent studies on university timetabling can be found in [1,2,4,5,6,10,12,14,16,18].…”

“…In [12], Lach and Lübbecke proposed an integer programming formulation that gives satisfactory lower and upper bounds in reasonable computational time without particular tuning. Solving their model using CPLEX11 on a 3.4GHz Linux PC with 1GB memory within a time limit of about 4 hours, they obtain lower bounds with an average gap to the best existing upper bounds of 32.63% over the first 14 benchmark instances.…”

“…The sum of lower bounds of the subproblems corresponds then to a lower bound of the initial problem. For each sub-problem, we adopt the Lach and Lübbecke's IP formulation [12]. To be effective, this partition-based approach needs to optimize the way the initial problem is divided.…”

“…The CBCT problem description is introduced in Section 2, together with the ITC-2007 benchmark instances and the best known bounds. In Section 3, we briefly introduce the IP model presented in [12], which we used in our partition-based approach. The partition-based approach is described in Section 4.…”