Solving Set Partitioning Problems with Global Constraint Propagation

We propose a constraint-based approach for solving set partitioning problems. We show that an efficient, open and easily modifying model is obtained by using a constraint propagator that is: global, in the sense that it enforces consistency between local knowledge (such as variable domains) and global knowledge (such as the optimisation goal); and dynamic, in the sense that it propagates the decisions taken during the search process. This propagator derives new constraints based on the existing ones by efficiently chaining a set of propagation rules that we present here and demonstrate. This propagator can be used not only to prune efficiently the search space, but also to prove in certain cases that a given solution is optimal. This approach was tested with five crew duty scheduling problems supplied by two operators from the railway and bus domains. Results were compared with the ones obtained with an approach that is a good representative of the industrial state-of-the-art.