On the Reification of Global Constraints

We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on the observation that most global constraints can be reformulated as a conjunction of pure functional dependency constraints together with a constraint that can be easily reified. We first show how the core constraints of the Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at least 82% of the constraints in the Global Constraint Catalogue

Optimal binning: mathematical programming formulation

The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation to solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not previously addressed. For all three target types, we introduce a convex mixed-integer programming formulation. Several algorithmic enhancements such as automatic determination of the most suitable monotonic trend via a Machine-Learning-based classifier and implementation aspects are thoughtfully discussed. The new mathematical programming formulations are carefully implemented in the open-source python library OptBinning

On the Reification of Global Constraints

We introduce a simple idea for deriving reified global constraints in a systematic way. It is based on the observation that most global constraints can be reformulated as a conjunction of pure functional dependency constraints together with a constraint that can be easily reified. We first show how the core constraints of the Global Constraint Catalogue can be reified and we then identify several reification categories that apply to at least 82% of the constraints in the Global Constraint Catalogue