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Practical Applications of Constraint Programming
 CONSTRAINTS
, 1996
"... Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples, ..."
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Cited by 111 (1 self)
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Constraint programming is newly flowering in industry. Several companies have recently started up to exploit the technology, and the number of industrial applications is now growing very quickly. This survey will seek, by examples,
Universally Quantified Interval Constraints
 PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2000
"... Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decompo ..."
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Cited by 54 (0 self)
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Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decomposition (CAD). However, CAD restricts its input to be conjunctions and disjunctions of polynomial constraints with rational coefficients, while some applications such as camera control involve systems with arbitrary forms where time is the only universally quantified variable. In this paper, the handling of universally quantified variables is first related to the computation of innerapproximation of real relations.
Heterogeneous Constraint Solving
 PROCEEDINGS OF ALP'96, VOLUME 1139 OF LNCS
, 1996
"... Most CLP languages designed in the past few years feature at least some combination of constraint solving capabilities. These combinations can take multiple forms since they achieve either the mixing of di erent domains or the use of di erent algorithms over the same domain. These solvers are also v ..."
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Cited by 51 (10 self)
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Most CLP languages designed in the past few years feature at least some combination of constraint solving capabilities. These combinations can take multiple forms since they achieve either the mixing of di erent domains or the use of di erent algorithms over the same domain. These solvers are also very di erent in nature. Some of them perform complete constraint solving while others are based on propagation methods. This paper is an attempt to design a uni ed framework describing the cooperation of constraint solving methods. Most techniques used in constraintbased systems are shown to be implementations of operators called constraint narrowing operators. A generalized notion of arcconsistency, called weak arcconsistency is proposed and is used to model heterogeneous constraint solving. We provide conditions on the constraint solving algorithms which guarantee termination, correctness and con uence of the resulting combined solver. This framework is shown to be general enough to describe the operational semantics of the basic constraint solving mechanisms in a number of current CLP systems. 1
Interval Computations: Introduction, Uses, and Resources
 Euromath Bulletin
, 1996
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Contractor Programming
 Artificial Intelligence
"... Abstract. 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 restr ..."
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Cited by 39 (18 self)
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Abstract. 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. 1
Continuous and interval constraints
 Handbook of Constraint Programming, chapter 16
, 2006
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Efficient solving of quantified inequality constraints over the real numbers
 ACM Transactions on Computational Logic
"... Let a quantified inequality constraint over the reals be a formula in the firstorder predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. Solving such constraints is an undecidable problem when allowing function symbols such sin or cos. In t ..."
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Cited by 31 (9 self)
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Let a quantified inequality constraint over the reals be a formula in the firstorder predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. Solving such constraints is an undecidable problem when allowing function symbols such sin or cos. In the paper we give an algorithm that terminates with a solution for all, except for very special, pathological inputs. We ensure the practical efficiency of this algorithm by employing constraint programming techniques. 1
Comparing Partial Consistencies
, 1999
"... Global search algorithms have been widely used in the constraint programming framework to solve constraint systems over continuous domains. This paper precisely states the relations among the different partial consistencies which are main emphasis of these algorithms. The ..."
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Cited by 30 (5 self)
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Global search algorithms have been widely used in the constraint programming framework to solve constraint systems over continuous domains. This paper precisely states the relations among the different partial consistencies which are main emphasis of these algorithms. The
Dynamic domain splitting for numeric CSPs
, 1998
"... In this paper, a new search technique over numeric csps is presented: dynamic domain splitting. The usual search technique over numeric csps is a dichotomic search interleaved with a consistency filtering, which is called domain splitting. This paper proposes to replace chronological backtracking ..."
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Cited by 28 (12 self)
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In this paper, a new search technique over numeric csps is presented: dynamic domain splitting. The usual search technique over numeric csps is a dichotomic search interleaved with a consistency filtering, which is called domain splitting. This paper proposes to replace chronological backtracking at the core of domain splitting by a non destructive backtracking technique.