Constraint propagation with interval labels
Artificial Intelligence
Constraint reasoning based on interval arithmetic: the tolerance propagation approach
Artificial Intelligence - Special volume on constraint-based reasoning
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
A Comparison of some Methods for Solving Linear Interval Equations
SIAM Journal on Numerical Analysis
The OPL optimization programming language
The OPL optimization programming language
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Quantified constraints under perturbation
Journal of Symbolic Computation
Extending Consistent Domains of Numeric CSP
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Constraint Processing
Constraint-Based Local Search
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
A branch and prune algorithm for the approximation of non-linear AE-solution sets
Proceedings of the 2006 ACM symposium on Applied computing
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Generalized interval projection: a new technique for consistent domain extension
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Optimal and suboptimal singleton arc consistency algorithms
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Advisors for incremental propagation
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Localization of an underwater robot using interval constraint propagation
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
When interval analysis helps inter-block backtracking
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Efficient pruning technique based on linear relaxations
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
Brief Guaranteed parameter bounding for nonlinear models with uncertain experimental factors
Automatica (Journal of IFAC)
Filtering numerical CSPs using well-constrained subsystems
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
A constraint on the number of distinct vectors with application to localization
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Standardized interval arithmetic and interval arithmetic used in libraries
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Octagonal domains for continuous constraints
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
ICN-RE: redundancy elimination for information-centric networking
Proceedings of the second edition of the ICN workshop on Information-centric networking
Loop detection of mobile robots using interval analysis
Automatica (Journal of IFAC)
Hi-index | 0.00 |
This paper describes a solver programming method, called contractor programming, that copes with two issues related to constraint processing over the reals. First, continuous constraints involve an inevitable step of solver design. Existing softwares provide an insufficient answer by restricting users to choose among a list of fixed strategies. Our first contribution is to give more freedom in solver design by introducing programming concepts where only configuration parameters were previously available. Programming consists in applying operators (intersection, composition, etc.) on algorithms called contractors that are somehow similar to propagators. Second, many problems with real variables cannot be cast as the search for vectors simultaneously satisfying the set of constraints, but a large variety of different outputs may be demanded from a set of constraints (e.g., a paving with boxes inside and outside of the solution set). These outputs can actually be viewed as the result of different contractors working concurrently on the same search space, with a bisection procedure intervening in case of deadlock. Such algorithms (which are not strictly speaking solvers) will be made easy to build thanks to a new branch & prune system, called paver. Thus, this paper gives a way to deal harmoniously with a larger set of problems while giving a fine control on the solving mechanisms. The contractor formalism and the paver system are the two contributions. The approach is motivated and justified through different cases of study. An implementation of this framework named Quimper is also presented.