This work 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. 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 constraint propagation, interval arithmetic, affine arithmetic and linear programming illustrate the flexibility and efficiency of the approach.

The paper of H. Schichl & A. Neumaier has given the fundamentals of interval analysis on DAGs for global optimization and constraint propagation. We show in This work how constraint propagation on DAGs can be made efficient and practical by: (i) working on partial DAG representations; and (ii) enabling the flexible choice of the interval inclusion functions during propagation. We then propose a new simple algorithm, which coordinates constraint propagation and exhaustive search for solving numerical constraint satisfaction problems. The experiments carried out on different problems show that the new approach outperforms previously available propagation techniques by an order of magnitude or more in speed, while being roughly the same quality w.r.t. enclosure properties.

The paper presents SpaceSolver, a constraint satisfaction toolbox, providing access to constraint satisfaction techniques on continuous variables through an intuitive, Web based user interface. Moreover, we describe possible applications of such a platform to collaborative design and conclude that Internet based use of constraint satisfaction techniques has the potential of increasing productivity in several fields in engineering.