Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numer... more Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numerical constraints. This algorithm is basedon the RLT (Reformulation-Linearization Technique) schema. In the reformulationphase, tight convex and concave approximations of nonlinearterms are generated, that's to say for bilinear terms, product of variables,power and univariate terms. New variables are introduced to linearizethe initial constraint system. A linear
Abstract: Numeric systems of constraints are widely used to model problems in numerousapplication... more Abstract: Numeric systems of constraints are widely used to model problems in numerousapplication areas ranging from robotics to chemistry. This paper introduces a new lteringalgorithm (GFLR) to prune the domains of the variables in such numeric applications. Roughlyspeaking, GFLR combines classical local consistencies and a new global ltering algorithmthat works on a linear relaxation of numeric constraints. We introduce a
Optimality-based reduction attempts to take advantage of the known bounds of the objective functi... more Optimality-based reduction attempts to take advantage of the known bounds of the objective function to reduce the domain of the variables, and thus to speed up the search of a global optimum. However, the basic algorithm is unsafe, and thus, the overall process may no longer be complete and may not reach the actual global optimum. Recently, Kearfott has proposed a safe implementation of optimality-based reduction. Unfortunately, his method suffers from some limitations and is rather slow. In this paper, we show how constraint programming filtering techniques can be used to implement optimality-based reduction in a safe and efficient way.
Solving constraints over the oating point numbers is a key issue in the process of software valid... more Solving constraints over the oating point numbers is a key issue in the process of software validation and verication. Techniques to solve such constraints on the basis of projection functions have been successfully developed. However, though correct, this approach can lead to slow convergence phenomena for very common constraints like addition and subtraction constraints. In this paper, we introduce new addition and subtraction constraints which, thanks to a new oating point subtraction property, directly compute optimal bounds for the domain of the variables at a low cost. Preliminary experiments have shown that these constraints can drastically speed up the ltering process.
ABSTRACT Static value analysis is a classical approach for verifying programs with floating-point... more ABSTRACT Static value analysis is a classical approach for verifying programs with floating-point computations. Value analysis mainly relies on abstract interpretation and over-approximates the possible values of program variables. State-of-the-art tools may however compute over-approximations that can be rather coarse for some very usual program expressions. In this paper, we show that constraint solvers can significantly refine approximations computed with abstract interpretation tools. More precisely, we introduce a hybrid approach combining abstract interpretation and constraint programming techniques in a single static and automatic analysis. This hybrid approach benefits from the strong points of abstract interpretation and constraint programming techniques, and thus, it is more effective than static analysers and constraint solvers, when used separately. We compared the efficiency of the system we developed—named rAiCp—with state-of-the-art static analyzers: rAiCp produces substantially more precise approximations and is able to check program properties on both academic and industrial benchmarks.
Abstract: Modern software systems, like GNU/Linux distributions or Eclipse-based development envi... more Abstract: Modern software systems, like GNU/Linux distributions or Eclipse-based development environment, are often deployed by selecting components out of large component repositories. Maintaining such software systems by performing component upgrades is a complex task, and the users need to have an expressive preferences language at their disposal to specify the kind of upgrades they are interested in. Recent research has shown that it is possible to develop solvers that handle preferences ...
Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numer... more Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numerical constraints. This algorithm is basedon the RLT (Reformulation-Linearization Technique) schema. In the reformulationphase, tight convex and concave approximations of nonlinearterms are generated, that's to say for bilinear terms, product of variables,power and univariate terms. New variables are introduced to linearizethe initial constraint system. A linear
This paper introduces a new filtering algorithm for handling systems of quadratic equations and i... more This paper introduces a new filtering algorithm for handling systems of quadratic equations and inequations. Such constraints are widely used to model distance relations in numerous application areas ranging from robotics to chemistry. Classical filtering algorithms are based upon local consistencies and thus, are unable to achieve a significant pruning of the domains of the variables occurring in quadratic constraints systems. The drawback of these approaches comes from the fact that the constraints are handled independently. We introduce here a global filtering algorithm that works on a tight linear relaxation of the quadratic constraints. First experimentations show that this new algorithm yields a much more effective pruning of the domains than local consistency filtering algorithms.
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound... more Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and inequalities. More precisely, it exploits the optimal solution of a linear relaxation of the problem to compute efficiently a promising upper bound. First experiments on the Coconuts benchmarks demonstrate that this approach is very effective.
Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numer... more Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numerical constraints. This algorithm is basedon the RLT (Reformulation-Linearization Technique) schema. In the reformulationphase, tight convex and concave approximations of nonlinearterms are generated, that's to say for bilinear terms, product of variables,power and univariate terms. New variables are introduced to linearizethe initial constraint system. A linear
Abstract: Numeric systems of constraints are widely used to model problems in numerousapplication... more Abstract: Numeric systems of constraints are widely used to model problems in numerousapplication areas ranging from robotics to chemistry. This paper introduces a new lteringalgorithm (GFLR) to prune the domains of the variables in such numeric applications. Roughlyspeaking, GFLR combines classical local consistencies and a new global ltering algorithmthat works on a linear relaxation of numeric constraints. We introduce a
Optimality-based reduction attempts to take advantage of the known bounds of the objective functi... more Optimality-based reduction attempts to take advantage of the known bounds of the objective function to reduce the domain of the variables, and thus to speed up the search of a global optimum. However, the basic algorithm is unsafe, and thus, the overall process may no longer be complete and may not reach the actual global optimum. Recently, Kearfott has proposed a safe implementation of optimality-based reduction. Unfortunately, his method suffers from some limitations and is rather slow. In this paper, we show how constraint programming filtering techniques can be used to implement optimality-based reduction in a safe and efficient way.
Solving constraints over the oating point numbers is a key issue in the process of software valid... more Solving constraints over the oating point numbers is a key issue in the process of software validation and verication. Techniques to solve such constraints on the basis of projection functions have been successfully developed. However, though correct, this approach can lead to slow convergence phenomena for very common constraints like addition and subtraction constraints. In this paper, we introduce new addition and subtraction constraints which, thanks to a new oating point subtraction property, directly compute optimal bounds for the domain of the variables at a low cost. Preliminary experiments have shown that these constraints can drastically speed up the ltering process.
ABSTRACT Static value analysis is a classical approach for verifying programs with floating-point... more ABSTRACT Static value analysis is a classical approach for verifying programs with floating-point computations. Value analysis mainly relies on abstract interpretation and over-approximates the possible values of program variables. State-of-the-art tools may however compute over-approximations that can be rather coarse for some very usual program expressions. In this paper, we show that constraint solvers can significantly refine approximations computed with abstract interpretation tools. More precisely, we introduce a hybrid approach combining abstract interpretation and constraint programming techniques in a single static and automatic analysis. This hybrid approach benefits from the strong points of abstract interpretation and constraint programming techniques, and thus, it is more effective than static analysers and constraint solvers, when used separately. We compared the efficiency of the system we developed—named rAiCp—with state-of-the-art static analyzers: rAiCp produces substantially more precise approximations and is able to check program properties on both academic and industrial benchmarks.
Abstract: Modern software systems, like GNU/Linux distributions or Eclipse-based development envi... more Abstract: Modern software systems, like GNU/Linux distributions or Eclipse-based development environment, are often deployed by selecting components out of large component repositories. Maintaining such software systems by performing component upgrades is a complex task, and the users need to have an expressive preferences language at their disposal to specify the kind of upgrades they are interested in. Recent research has shown that it is possible to develop solvers that handle preferences ...
Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numer... more Abstract: This paper introduces a ltering algorithm to prune the domainsof the variables in numerical constraints. This algorithm is basedon the RLT (Reformulation-Linearization Technique) schema. In the reformulationphase, tight convex and concave approximations of nonlinearterms are generated, that's to say for bilinear terms, product of variables,power and univariate terms. New variables are introduced to linearizethe initial constraint system. A linear
This paper introduces a new filtering algorithm for handling systems of quadratic equations and i... more This paper introduces a new filtering algorithm for handling systems of quadratic equations and inequations. Such constraints are widely used to model distance relations in numerous application areas ranging from robotics to chemistry. Classical filtering algorithms are based upon local consistencies and thus, are unable to achieve a significant pruning of the domains of the variables occurring in quadratic constraints systems. The drawback of these approaches comes from the fact that the constraints are handled independently. We introduce here a global filtering algorithm that works on a tight linear relaxation of the quadratic constraints. First experimentations show that this new algorithm yields a much more effective pruning of the domains than local consistency filtering algorithms.
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound... more Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible points. This strategy takes advantage of the Newton method for under-constrained systems of equations and inequalities. More precisely, it exploits the optimal solution of a linear relaxation of the problem to compute efficiently a promising upper bound. First experiments on the Coconuts benchmarks demonstrate that this approach is very effective.
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Papers by Claude Michel