Making Adaptive an Interval Constraint Propagation Algorithm Exploiting Monotonicity

Araya, Ignacio; Trombettoni, Gilles; Neveu, Bertrand

doi:10.1007/978-3-642-15396-9_8

Cited by 6 publications

(8 citation statements)

References 8 publications

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“…Incorporating consistency techniques43, 78–82 (Chapter 10 in Hansen, Walster43), state‐of‐the‐art propagation methods,83 and box consistency techniques84 into the solver is expected to significantly increase both efficiency and robustness. The cutting‐edge consistency techniques can exploit common subexpressions,85 monotonicity,86 and the structure of the problem 87. Numerical evidence confirm88 that symbolic preprocessing and automatic generation of redundant constraints for pruning can speed up the search procedure by several orders of magnitude in time.…”

Section: Limitations Of the Current Implementationmentioning

confidence: 91%

Computing multiple steady states in homogeneous azeotropic and ideal two‐product distillation

Baharev¹,

Kolev²,

Rév³

2011

AIChE Journal

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Multiple steady states are typically discovered by tracing a solution path, including turning points. A new technique is presented here that does not follow this approach. The original problem is solved directly, without tracing a solution path. The proposed branch-and-prune algorithm is guaranteed to find all solutions automatically. Core components of the framework are affine arithmetic, constraint propagation, and linear programming. The Cþþ implementation is available as an open-source solver and has an interface to the AMPL V R modeling environment. In certain difficult cases, only continuation methods have been reported to find the unstable solution automatically. The proposed method seems to be the first published alternative method in those cases. Although this article focuses mainly on distillation, the presented framework is fairly general and applicable to a wide variety of problems. Further, computational results are given to demonstrate this.

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Section: Limitations Of the Current Implementationmentioning

confidence: 91%

Computing multiple steady states in homogeneous azeotropic and ideal two‐product distillation

Baharev¹,

Kolev²,

Rév³

2011

AIChE Journal

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“…Our first results are promising, so that it should be worthwhile hybridizing PolyBox with other algorithms, especially those achieving the Box-consistency or a weaker form of it [1,5]. An idea would be to keep the rewritten forms only if they are of degrees 2 and 3, and add them as global and redundant constraints in the system for improving the constraint propagation.…”

Section: Methodsmentioning

confidence: 99%

A Box-Consistency Contractor Based on Extremal Functions

Trombettoni

Papegay

Chabert

et al. 2010

Principles and Practice of Constraint Programming – CP 2010

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Abstract. Interval-based methods can approximate all the real solutions of a system of equations and inequalities. The Box interval constraint propagation algorithm enforces Box consistency. Its main procedure BoxNarrow handles one function f corresponding to the revised constraint, and one variable x, replacing the other variables of f by their current intervals. This paper proposes an improved BoxNarrow procedure for narrowing the domain of x when f respects certain conditions. In particular, these conditions are fulfilled when f is polynomial. f is first symbolically rewritten into a new form g. A narrowing step is then run on the non-interval extremal functions that enclose the interval function g. The corresponding algorithm is described and validated on several numerical constraint systems.

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“…Given a constraint system and an initial box, it computes a box approximating hull consistency, using an equivalent system made of primitive constraints. Several methods have been proposed to improve the precision of 1 [3], safe relaxation of quadratic constraints [4], or use of the monotonicity of the constraints [5]). …”

Section: A Constraint Programmingmentioning

confidence: 99%

“…Real values are encoded into floating-points intervals, and the interval computations may generate overestimations of the solutions, depending on the constraints forms. Efficient computation of approximations of real constraints is still a research matter, with many recent contributions (for instance [3], [4], [5], [6]). …”

Section: Introductionmentioning

confidence: 99%

Abstract Domains for Constraint Programming, with the Example of Octagons

Truchet

Pelleau

Benhamou

2010

2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing

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International audienceIn Constraint Programming (CP), the central notion of consistency can be defined as a fix point of some contracting operators. These operators always deal with cartesian products of domains of the same nature (real intervals, integer sets, etc), due to the cartesian nature of the CSP format. However, textit{inside} the solving process, there is no particular reason why the domains should be cartesian. In another research field, Abstract Interpretation (AI) in semantics relies on a strong and elegant theory dealing with over-approximations of variables. It allows in particular to mix abstract domains of different kinds (integer, reals...). Several numerical abstract domains for continuous variables have recently been proposed, some of them cartesian, other relational. In this article, we adapt to CP the AI definition of abstract domains. We give an abstract consistency definition, and show it extends the usual CP consistencies. We also give a general solving algorithm for abstract domains. Finally, we propose the octagon abstract domain and study its practical feasibility

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Making Adaptive an Interval Constraint Propagation Algorithm Exploiting Monotonicity

Cited by 6 publications

References 8 publications

Computing multiple steady states in homogeneous azeotropic and ideal two‐product distillation

Computing multiple steady states in homogeneous azeotropic and ideal two‐product distillation

A Box-Consistency Contractor Based on Extremal Functions

Abstract Domains for Constraint Programming, with the Example of Octagons

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