Exploiting Common Subexpressions in Numerical CSPs

Araya, Ignacio; Neveu, Bertrand; Trombettoni, Gilles

doi:10.1007/978-3-540-85958-1_23

Cited by 18 publications

(18 citation statements)

References 13 publications

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“…Each row has a sum constraint such as: m [5,1] + m [5,2] + · · · + m [5,14] + m [5,15] + · · · + m [5,28] …”

Section: + · · · + M[5 28] =mentioning

confidence: 99%

“…The common subset m [5,15] + · · · + m [5,28] is represented by a new variable a, resulting in the following three constraints. m [5,1] + m [5,2] + · · · + m [5,14] + a = 14 a = 6 a = m [5,15] + · · · + m [5,28] Variable unification replaces a with 6 throughout, leading to the following: Meseguer and Torras's model was improved by Frisch et al [23] by the addition of a set of implied constraints (i.e. redundant constraints that are entailed by the original set of constraints), creating the best published model (to our knowledge).…”

Section: = 14mentioning

confidence: 99%

“…We evaluate a range of reformulations for use in automated modelling. Common Sub-expression Elimination (CSE) is a particular focus of this paper [60,59,2]. CSE is a type of constraint reformulation that has proved to be useful on a range of problems, including both finite-domain and numerical constraint problems.…”

Section: Contributionsmentioning

confidence: 99%

“…Araya, Neveu and Trombettoni [2] exploited common subexpressions among + and × expressions in the context of numerical CSP. They proposed two algorithms named I-CSE and I-CSE-NC.…”

Section: Associative-commutative Csementioning

confidence: 99%

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Automatically improving constraint models in Savile Row

Nightingale

Akgün

Gent

et al. 2017

Artificial Intelligence

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When solving a combinatorial problem using Constraint Programming (CP) or Satisfiability (SAT), modelling and formulation are vital and difficult tasks. Even an expert human may explore many alternatives in modelling a single problem. We make a number of contributions in the automated modelling and reformulation of constraint models. We study a range of automated reformulation techniques, finding combinations of techniques which perform particularly well together. We introduce and describe in detail a new algorithm, X-CSE, to perform Associative-Commutative Common Subexpression Elimination (AC-CSE) in constraint problems, significantly improving existing CSE techniques for associative and commutative operators such as +. We demonstrate that these reformulation techniques can be integrated in a single automated constraint modelling tool, called Savile Row, whose architecture we describe. We use Savile Row as an experimental testbed to evaluate each reformulation on a set of 50 problem classes, with 596 instances in total. Our recommended reformulations are well worthwhile even including overheads, especially on harder instances where solver time dominates. With a SAT solver we observed a geometric mean of 2.15 times speedup compared to a straightforward tailored model without recommended reformulations. Using a CP solver, we obtained a geometric mean of 5.96 times speedup for instances taking over 10 seconds to solve.

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“…Each row has a sum constraint such as: m [5,1] + m [5,2] + · · · + m [5,14] + m [5,15] + · · · + m [5,28] …”

Section: + · · · + M[5 28] =mentioning

confidence: 99%

Section: = 14mentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

“…Araya, Neveu and Trombettoni [2] exploited common subexpressions among + and × expressions in the context of numerical CSP. They proposed two algorithms named I-CSE and I-CSE-NC.…”

Section: Associative-commutative Csementioning

confidence: 99%

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Automatically improving constraint models in Savile Row

Nightingale

Akgün

Gent

et al. 2017

Artificial Intelligence

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“…Other algorithms exploit the monotonicity properties of the constraints [9] and show that hull-consistency can be enforced in polynomial time if the constraint functions are all monotonic [29]. Algorithm I − CSE [7] exploits common sub-expressions obtaining a DAG that is rewritten into a new optimized system of constraints that can be processed by the tree-based algorithms.…”

Section: Definition 224 (Consistent Ccsp)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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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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Exploiting Common Subexpressions in Numerical CSPs

Cited by 18 publications

References 13 publications

Automatically improving constraint models in Savile Row

Automatically improving constraint models in Savile Row

Probabilistic constraint reasoning

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

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