Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Constraint reasoning based on interval arithmetic: the tolerance propagation approach
Artificial Intelligence - Special volume on constraint-based reasoning
Arc-consistency for continuous variables
Artificial Intelligence
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Efficient interval partitioning-Local search collaboration for constraint satisfaction
Computers and Operations Research
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As opposed to finite domain CSPs, arc consistency cannot be enforced, in general, on CSPs over the reals, including very simple instances. In contrast, a stronger property, the so-called box-set consistency, that requires a no-split condition in addition to arc consistency, can be obtained on a much larger number of problems.To obtain this property, we devise a lazy algorithm that combines hull consistency filtering, interval union projection, and intelligent domain splitting. It can be applied to any numerical CSP, and achieves box-set consistency if constraints are redundancy-free in terms of variables. This holds even if the problem is not intervalconvex. The main contribution of our approach lies in the way we bypass the non-convexity issue, which so far was a synonym for either a loss of accuracy or an unbounded growth of label size.We prove the correctness of our algorithm and through experimental results, we show that, as compared to a strategy based on a standard bisection, it may lead to gains while never producing an overhead.