Interval propagation and search on directed acyclic graphs for numerical constraint solving

Vu, Xuan-Ha; Schichl, Hermann; Sam-Haroud, Djamila

doi:10.1007/s10898-008-9386-7

Cited by 20 publications

(28 citation statements)

References 19 publications

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“…The FBBT was employed as a range reduction technique for Mixed Integer Linear Programs (MILP) in [9,10] and then for MINLPs in [11]. Within the context of GO, the FBBT was discussed in [12] and recently improved in [13] by considering its effect on common subexpressions of g(x).…”

Section: Introductionmentioning

confidence: 99%

Feasibility-Based Bounds Tightening via Fixed Points

Belotti¹,

Cafieri²,

Lee³

et al. 2010

Combinatorial Optimization and Applications

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Abstract. The search tree size of the spatial Branch-and-Bound algorithm for Mixed-Integer Nonlinear Programming depends on many factors, one of which is the width of the variable ranges at every tree node. A range reduction technique often employed is called Feasibility Based Bounds Tightening, which is known to be practically fast, and is thus deployed at every node of the search tree. From time to time, however, this technique fails to converge to its limit point in finite time, thereby slowing the whole Branch-and-Bound search considerably. In this paper we propose a polynomial time method, based on solving a linear program, for computing the limit point of the Feasibility Based Bounds Tightening algorithm applied to linear equality and inequality constraints.

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Section: Introductionmentioning

confidence: 99%

Feasibility-Based Bounds Tightening via Fixed Points

Belotti¹,

Cafieri²,

Lee³

et al. 2010

Combinatorial Optimization and Applications

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“…More recent algorithms [115] replace the tree by a representation of constraints with direct acyclic graphs (DAGs), thus allowing common sub-expressions to be shared and enhancing the constraint propagation process.…”

Section: Is In the Box Face With Largest X Value)mentioning

confidence: 99%

Probabilistic constraint reasoning

Carvalho¹

2015

Constraints

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perpétuo e sem limites geográficos, de arquivar e publicar esta dissertação através de exemplares impressos reproduzidos em papel ou de forma digital, ou por qualquer outro meio conhecido ou que venha a ser inventado, e de a divulgar através de repositórios científicos e de admitir a sua cópia e distribuição com objectivos educacionais ou de investigação, não comerciais, desde que seja dado crédito ao autor e editor.For Laura with love.My endless source of inspiration with her tender heart and ingenious mind. AcknowledgementsFor me, writing this thesis was like a long, long journey, with many ups and downs. In every step of the way I faced challenges that made me grow as a researcher and as a person. But the journey is coming to an end and is now time to remember and be grateful to those who crossed my path and helped me to achieve my goal in many different ways. Neste trabalho desenvolvemos um paradigma de restrições em domínios contínuos que associa um espaço probabilísticoàs variáveis do problema, permitindo efectuar raciocínio probabilístico. Tal raciocínio baseia-se na avaliação de informação probabilística que requer a computação de integrais multidimensionais em regiões possivelmente não lineares. São desenvolvidos algoritmos capazes de avaliar essa informação, usando técnicas de integração seguras ou aproximadas e dependendo de métodos de programação por restrições em domínios contínuos para obter coberturas da região de integração.A plataforma probabilística de restrições em domínios contínuosé adequada para suporteà decisão em problemas não lineares em domínios contínuos, com incerteza. A sua aplicabilidadeé ilustrada em problemas inversos e problemas de fiabilidade, que são duas classes distintas de problemas de engenharia, representativas do tipo de raciocínio com incerteza requerido pelos decisores.

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“…As a consequence, their application has raised interest in fields as diverse as neurophysiology and economics [2], biochemistry, crystallography, robotics [3] and, more generally, in those related to global optimization [4]. Symmetries naturally occur in many of these applications, and it is advisable to exploit them in order to reduce the search space and, thus, to increase the efficiency of the solvers.…”

Section: Introductionmentioning

confidence: 99%

Variable symmetry breaking in numerical constraint problems

Goldsztejn¹,

Jermann

Angulo

et al. 2015

Artificial Intelligence

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Symmetry breaking has been a hot topic of research in the past years, leading to many theoretical developments as well as strong scaling strategies for dealing with hard applications. Most of the research has however focused on discrete, combinatorial, problems, and only few considered also continuous, numerical, problems. While part of the theory applies in both contexts, numerical problems have specificities that make most of the technical developments inadequate.In this paper, we present the rlex constraints, partial symmetry-breaking inequalities corresponding to a relaxation of the famous lex constraints extensively studied in the discrete case. They allow (partially) breaking any variable symmetry and can be generated in polynomial time. Contrarily to lex constraints that are impractical in general (due to their overwhelming number) and inappropriate in the continuous context (due to their form), rlex constraints can be efficiently handled natively by numerical constraint solvers. Moreover, we demonstrate their pruning power on continuous domains is almost as strong as that of lex constraints, and they subsume several previous work on breaking specific symmetry classes for continuous problems. Their experimental behavior is assessed on a collection of standard numerical problems and the factors influencing their impact are studied. The results confirm rlex constraints are a dependable counterpart to lex constraints for numerical problems.

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Interval propagation and search on directed acyclic graphs for numerical constraint solving

Cited by 20 publications

References 19 publications

Feasibility-Based Bounds Tightening via Fixed Points

Feasibility-Based Bounds Tightening via Fixed Points

Probabilistic constraint reasoning

Variable symmetry breaking in numerical constraint problems

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