Global propagation of side constraints for solving over‐constrained problems

This article deals with the resolution of over‐constrained problems using constraint programming, which often imposes to add to the constraint network new side constraints. These side constraints control how the initial constraints of the model should be satisfied or violated, to obtain solutions that have a practical interest. They are specific to each application. In our experiments, we show the superiority of a framework where side constraints are encoded by global constraints on new domain variables, which are directly included into the model. The case‐study is a cumulative scheduling problem with over‐loads. The objective is to minimize the total amount of over‐loads. We augment the Cumulative global constraint of the constraint programming solver Choco with sweep and task interval violation‐based algorithms. We provide a theoretical and experimental comparison of the two main approaches for encoding over‐constrained problems with side constraints.