ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Interval arithmetic: From principles to implementation
Journal of the ACM (JACM)
Search Techniques for Non-linear Constraint Satisfaction Problems with Inequalities
AI '01 Proceedings of the 14th Biennial Conference of the Canadian Society on Computational Studies of Intelligence: Advances in Artificial Intelligence
Generating Semantic Descriptions From Drawings of Scenes With Shadows
Generating Semantic Descriptions From Drawings of Scenes With Shadows
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Combining Multiple Inclusion Representations in Numerical Constraint Propagation
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Interval Analysis on Directed Acyclic Graphs for Global Optimization
Journal of Global Optimization
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
Mathematical Modeling And Global Optimization
Mathematical Modeling And Global Optimization
Numerica: a modeling language for global optimization
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Enhancing numerical constraint propagation using multiple inclusion representations
Annals of Mathematics and Artificial Intelligence
Constraint propagation on quadratic constraints
Constraints
Feasibility-based bounds tightening via fixed points
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Symmetry breaking in numeric constraint problems
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
First order rejection tests for multiple-objective optimization
Journal of Global Optimization
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The fundamentals of interval analysis on directed acyclic graphs (DAGs) for global optimization and constraint propagation have recently been proposed in Schichl and Neumaier (J. Global Optim. 33, 541---562, 2005). For representing numerical problems, the authors use DAGs whose nodes are subexpressions and whose directed edges are computational flows. Compared to tree-based representations [Benhamou et al. Proceedings of the International Conference on Logic Programming (ICLP'99), pp. 230---244. Las Cruces, USA (1999)], DAGs offer the essential advantage of more accurately handling the influence of subexpressions shared by several constraints on the overall system during propagation. In this paper we show how interval constraint propagation and search on DAGs can be made practical and efficient by: (1) flexibly choosing the nodes on which propagations must be performed, and (2) working with partial subgraphs of the initial DAG rather than with the entire graph. We propose a new interval constraint propagation technique which exploits the influence of subexpressions on all the constraints together rather than on individual constraints. We then show how the new propagation technique can be integrated into branch-and-prune search to solve numerical constraint satisfaction problems. This algorithm is able to outperform its obvious contenders, as shown by the experiments.