Alexander Schnell’s research while affiliated with University of Vienna and other places

In curriculum-based course timetabling, lectures have to be assigned to periods and rooms, while avoiding overlaps between courses of the same curriculum. Taking into account the inherent complexity of the problem, a metaheuristic solution approach is proposed, more precisely an adaptive large neighborhood search, which is based on repetitively destroying and subsequently repairing relatively large parts of the solution. Several problem-specific operators are introduced. The proposed algorithm proves to be very effective for the curriculum-based course timetabling problem. In particular, it outperforms the best algorithms of the international timetabling competition in 2007 and finds five new best known solutions for benchmark instances of the competition.

In our paper, we analyze new exact approaches for the multi-mode resource-constrained project scheduling (MRCPSP) problem with the aim of makespan minimization. For the single-mode RCPSP (SRCPSP) recent exact algorithms combine a Branch and Bound algorithm with principles from Constraint Programming (CP) and Boolean Satisfiability Solving (SAT). We extend the above principles for the solution of MRCPSP instances. This generalization is on the one hand achieved on the modeling level. We propose three CP-based formulations of the MRCPSP for the G12 CP platform and the optimization framework SCIP which both provide solution techniques combining CP and SAT principles. For one of the latter we implemented a new global constraint for SCIP, which generalizes the domain propagation and explanation generation principles for renewable resources in the context of multi-mode jobs. Our constraint applies the above principles in a more general way than the existing global constraint in SCIP. We compare our approaches with the state-of-the-art exact algorithm from the literature on MRCPSP instances with 20 and 30 jobs. Our computational experiments show that we can outperform the latter approach on these instances. Furthermore, we are the first to close (find the optimal solution and prove its optimality for) 628 open instances with 50 and 100 jobs from the literature. In addition, we improve the best known lower bound of 2815 instances and the best known upper bound of 151 instances.

For variants of the single-mode resource-constrained project scheduling problem, state-of-the-art exact algorithms combine a Branch and Bound algorithm with principles from Constraint Programming and Boolean Satisfiability Solving. In our paper, we propose new exact approaches extending the above principles to the multi-mode RCPSP (MRCPSP) with generalized precedence relations (GPRs). More precisely, we implemented two constraint handlers cumulativemm and gprecedencemm for the optimization framework SCIP. With the latter, one can model renewable resource constraints and GPRs in the context of multi-mode activities, respectively. Moreover, they integrate domain propagation and explanation generation techniques for the above problem characteristics. We formulate three SCIP-models for the MRCPSP with GPRs, two without and one with our constraint handler gprecedencemm. Our computational results on instances from the literature with 30, 50 and 100 activities show that the addition of this constraint handler significantly strengthens the SCIP-model. Moreover, we outperform the state-of-the-art exact approach on instances with 50 activities when imposing time limits of 27 s. In addition, we close (find the optimal solution and prove its optimality for) 289 open instances and improve the best known makespan for 271 instances from the literature.