Accelerating filtering techniques for numeric CSPs

Lebbah, Yahia; Lhomme, Olivier

doi:10.1016/s0004-3702(02)00194-7

Cited by 21 publications

(15 citation statements)

References 18 publications

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“…Using one priority queue S for all the projections, as done in bc3, is a suboptimal strategy here in that it may create propagation cycles leading to overall slow convergence phenomena [17]. As an illustration, consider two projections p 1 and p 2 such that when p 1 is applied, p 2 is inserted in S and conversely.…”

Section: Algorithm 3 Box Consistency With Reinforcement Learning (Bcrl)mentioning

confidence: 99%

“…We suspect that it is because this problem has only one solution that can be obtained without any splitting. Lastly, in a somewhat orthogonal approach, Lebbah and Lhomme [17] try to identify cycles in the propagation inside bc3 to avoid slow convergence phenomena. One direction for future research might indeed be to try taking advantage of their methods in bcrl.…”

Section: Related Workmentioning

confidence: 99%

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A Reinforcement Learning Approach to Interval Constraint Propagation

Goualard

Jermann

2008

Constraints

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International audienceWhen solving systems of nonlinear equations with interval constraint methods, it has often been observed that many calls to contracting operators do not participate actively to the reduction of the search space. Attempts to statically select a subset of efficient contracting operators fail to offer reliable performance speed-ups. By embedding the recency-weighted average Reinforcement Learning method into a constraint propagation algorithm to dynamically learn the best operators, we show that it is possible to obtain robust algorithms with reliable performances on a range of sparse problems. Using a simple heuristic to compute initial weights, we also achieve significant performance speed-ups for dense problems

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Section: Algorithm 3 Box Consistency With Reinforcement Learning (Bcrl)mentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

A Reinforcement Learning Approach to Interval Constraint Propagation

Goualard

Jermann

2008

Constraints

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“…Sophisticated splitting strategies have been developed for finite domains but few results [23] are available for continuous domains. [11,26]. Local consistencies are conditions that filtering algorithms must satisfy.…”

Section: The General Frameworkmentioning

confidence: 99%

Efficient and Safe Global Constraints for Handling Numerical Constraint Systems

Lebbah

Michel

Rueher

et al. 2005

SIAM J. Numer. Anal.

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Abstract. Numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques, local consistencies, and interval methods. This paper first recalls the principles of Quad, a global constraint that works on a tight and safe linear relaxation of quadratic subsystems of constraints. Then, it introduces a generalization of Quad to polynomial constraint systems. It also introduces a method to get safe linear relaxations and shows how to compute safe bounds of the variables of the linear constraint system. Different linearization techniques are investigated to limit the number of generated constraints. QuadSolver, a new branch and prune algorithm that combines Quad, local consistencies, and interval methods, is introduced. QuadSolver has been evaluated on a variety of benchmarks from kinematics, mechanics, and robotics. On these benchmarks, it outperforms classical interval methods as well as constraint satisfaction problem solvers and it compares well with state-of-the-art optimization solvers.Key words. systems of equations and inequalities, constraint programming, reformulation linearization technique, global constraint, interval arithmetic, safe rounding AMS subject classifications. 65H10, 65G40, 65H20, 93B18, 65G20 DOI. 10.1137/S00361429034361741. Introduction. Many applications in engineering sciences require finding all isolated solutions to systems of constraints over real numbers. These systems may be nonpolynomial and are difficult to solve: the inherent computational complexity is NP-hard and numerical issues are critical in practice (e.g., it is far from being obvious to guarantee correctness and completeness as well as to ensure termination). These systems, called numerical CSP (constraint satisfaction problem) in the rest of this paper, have been approached in the past by different interesting methods:

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“…Experimentations covering 2B-filtering, Box-filtering and 3B-filtering have been performed with the implementation of iCOs [20,21], one of the most efficient library for this kind of algorithms [7].…”

Section: Experimentationsmentioning

confidence: 99%

A Rigorous Global Filtering Algorithm for Quadratic Constraints*

2005

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This article 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 often unable to achieve a significant pruning of the domains of the variables occurring in quadratic constraint 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. The Simplex algorithm is then used to narrow the domains. Since most implementations of the Simplex work with floating point numbers and thus, are unsafe, we provide a procedure to generate safe linearizations. We also exploit a procedure provided by Neumaier and Shcherbina to get a safe objective value when calling the Simplex algorithm. With these two procedures, we prevent the Simplex algorithm from removing any solution while filtering linear constraint systems. Experimental results on classical benchmarks show that this new algorithm yields a much more effective pruning of the domains than local consistency filtering algorithms.

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Accelerating filtering techniques for numeric CSPs

Cited by 21 publications

References 18 publications

A Reinforcement Learning Approach to Interval Constraint Propagation

A Reinforcement Learning Approach to Interval Constraint Propagation

Efficient and Safe Global Constraints for Handling Numerical Constraint Systems

A Rigorous Global Filtering Algorithm for Quadratic Constraints*

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