A Generic Scheme for Combining Multiple Inclusion Representations in Numerical Constraint Propagation

This paper proposes a novel generic scheme enabling the combination of multiple inclusion representations to propagate numerical constraints. The scheme allows bringing into the constraint propagation framework the strength of inclusion techniques coming from different areas such as interval arithmetic, affine arithmetic or mathematical programming. The scheme is based on the DAG representation of the constraint system. This enables devising fine-grained combination strategies involving any factorable constraint system. The paper presents several possible combination strategies for creating practical instances of the generic scheme. The experiments reported on a particular instance using interval propagation, interval arithmetic, affine arithmetic and linear programming illustrate the flexibility and efficiency of the approach.