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Propagation via Lazy Clause Generation
"... Finite domain propagation solvers effectively represent the possible values of variables by a set of choices which can be naturally modelled as Boolean variables. In this paper we describe how to mimic a finite domain propagation engine, by mapping propagators into clauses in a SAT solver. This imm ..."
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Finite domain propagation solvers effectively represent the possible values of variables by a set of choices which can be naturally modelled as Boolean variables. In this paper we describe how to mimic a finite domain propagation engine, by mapping propagators into clauses in a SAT solver. This immediately results in strong nogoods for finite domain propagation. But a naive static translation is impractical except in limited cases. We show how to convert propagators to lazy clause generators for a SAT solver. The resulting system introduces flexibility in modelling since variables are modelled dually in the propagation engine and the SAT solver, and we explore various approaches to the dual modelling. We show that the resulting system solves many finite domain problems significantly faster than other techniques.
Symmetry Breaking Constraints for Value Symmetries in Constraint Satisfaction
 Constraints
, 2006
"... Constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and ..."
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Cited by 17 (2 self)
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Constraint satisfaction problems (CSPs) sometimes contain both variable symmetries and value symmetries, causing adverse effects on CSP solvers based on tree search. As a remedy, symmetry breaking constraints are commonly used. While variable symmetry breaking constraints can be expressed easily and propagated efficiently using lexicographic ordering, value symmetry breaking constraints are often difficult to formulate. In this paper, we propose two methods of using symmetry breaking constraints to tackle value symmetries. First, we show theoretically when value symmetries in one CSP correspond to variable symmetries in another CSP of the same problem. We also show when variable symmetry breaking constraints in the two CSPs, combined using channeling constraints, are consistent. Such results allow us to tackle value symmetries efficiently using additional CSP variables and channeling constraints. Second, we introduce value precedence, a notion which can be used to break a common class of value symmetries, namely symmetries of indistinguishable values. While value precedence can be expressed using inefficient ifthen constraints in existing CSP solvers, we propose efficient propagation algorithms for implementing global value precedence constraints. We also characterize several theoretical properties of the value precedence constraints. Extensive experiments are conducted to verify the feasibility and efficiency of the two proposals. 1.
Towards Solverindependent Propagators
, 2012
"... We present an extension to indexicals to describe propagators for global constraints. The resulting language is compiled into actual propagators for different solvers, and is solverindependent. In addition, we show how this highlevel description eases the proof of propagator properties, such as co ..."
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Cited by 4 (3 self)
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We present an extension to indexicals to describe propagators for global constraints. The resulting language is compiled into actual propagators for different solvers, and is solverindependent. In addition, we show how this highlevel description eases the proof of propagator properties, such as correctness and monotonicity. Experimental results show that propagators compiled from their indexical descriptions are sometimes not significantly slower than builtin propagators of Gecode. Therefore, our language can be used for the rapid prototyping of new global constraints.
The Systematic Generation Of Channelled Models In Constraint Satisfaction
"... Key words: constraint modelling, channelling constraints, channels, channelled models, representations, redundant representations, automatic modelling, refinement Solving a problem with finitedomain constraint programming requires generating a model from the informal description of the problem such ..."
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Cited by 2 (0 self)
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Key words: constraint modelling, channelling constraints, channels, channelled models, representations, redundant representations, automatic modelling, refinement Solving a problem with finitedomain constraint programming requires generating a model from the informal description of the problem such that this model can be accepted by a constraint solver. This generation process, called constraint modelling, is considered a hard task due to the number of choices and decisions it includes. Experience of skilled modellers in handcrafting many effective models has allowed identifying numerous patterns. One of these patterns is the addition of redundant information to a model. When this addition takes place, the consistency between all the redundant information needs to be maintained. The special constraints inserted to carry out this consistency maintenance are called channelling constraints (channels) and the models
Z.: On Redundant Topological Constraints
, 2014
"... The Region Connection Calculus (RCC) is a wellknown calculus for representing partwhole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC has been investigat ..."
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Cited by 2 (1 self)
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The Region Connection Calculus (RCC) is a wellknown calculus for representing partwhole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC has been investigated in depth in the literature. Most of these works focus on the consistency of RCC constraint networks. In this paper, we consider the important problem of redundant RCC constraints. For a set Γ of RCC constraints, we say a constraint (xRy) in Γ is redundant if it can be entailed by the rest of Γ. A prime network of Γ is a subset of Γ which contains no redundant constraints but has the same solution set as Γ. It is natural to ask how to compute a prime network, and when it is unique. In this paper, we show that this problem is in general coNP hard, but becomes tractable if Γ is over a tractable subclass of RCC. If S is a tractable subclass in which weak composition distributes over nonempty intersections, then we can show that Γ has a unique prime network, which is obtained by removing all redundant constraints from Γ. As a byproduct, we identify a sufficient condition for a pathconsistent network being minimal. 1
Automatic Generation of Redundant Models for Permutation Constraint Satisfaction Problems
"... If we have two representations of a problem as constraint satisfaction problem (CSP) models, it has been shown that combining the models using channeling constraints can increase constraint propagation in tree search CSP solvers. Handcrafting two CSP models for a problem, however, is often timecons ..."
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If we have two representations of a problem as constraint satisfaction problem (CSP) models, it has been shown that combining the models using channeling constraints can increase constraint propagation in tree search CSP solvers. Handcrafting two CSP models for a problem, however, is often timeconsuming. In this paper, we propose model induction, a process which generates a second CSP model from an existing model using channeling constraints, and study its theoretical properties. The generated induced model is in a different viewpoint, i.e., set of variables. It is mutually redundant to and can be combined with the input model, so that the combined model contains more redundant information, which is useful to increase constraint propagation. We also propose two methods of combining CSP models, namely model intersection and model channeling. The two methods allow combining two mutually redundant models in the same and different viewpoints respectively. We exploit the applications of model induction, intersection, and channeling and identify three new classes of combined models, which contain different amounts of redundant information. We construct combined models of Permutation CSPs and show in extensive benchmark results that the combined models are more robust and efficient to solve than the single models. 1
Solving the Salinity Control Problem in a Potable Water System
"... Abstract. Salinity is the relative concentration of salts in water. In a city of southern China, the local water supply company pumps water from a nearby river for potable use. During the winter dry season, the intrusion of sea water raises the salinity of the river to a high level and affects appr ..."
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Abstract. Salinity is the relative concentration of salts in water. In a city of southern China, the local water supply company pumps water from a nearby river for potable use. During the winter dry season, the intrusion of sea water raises the salinity of the river to a high level and affects approximately the daily life of 450,000 residents of the city. This paper reports the application of constraint programming (CP) to optimize the logistical operations of the raw water system so as to satisfy the daily water consumption requirement of the city and to keep the potable salinity below a desirable level for as many days as possible. CP is the key to the success of the project for its separation of concerns and powerful constraint language that allows for rapid construction of a functional prototype and production system. Flexibility and adaptiveness allow us to deal with our clients' many changes in the requirements. Deriving good variable and value ordering heuristics, and generating useful implied constraints, we demonstrate that branchandbound search with constraint propagation can cope with an optimization problem of large size and great difficulty.
Manuscript Latex Source Click here to download Manuscript: article.tex 1 2 3 4 5 6 7 8
"... If we have two representations of a problem as constraint satisfaction problem (CSP) models, it has been shown that combining the models using channeling constraints can increase constraint propagation in tree search CSP solvers. Handcrafting two CSP models for a problem, however, is often timecons ..."
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If we have two representations of a problem as constraint satisfaction problem (CSP) models, it has been shown that combining the models using channeling constraints can increase constraint propagation in tree search CSP solvers. Handcrafting two CSP models for a problem, however, is often timeconsuming. In this paper, we propose model induction, a process which generates a second CSP model from an existing model using channeling constraints, and study its theoretical properties. The generated induced model is in a different viewpoint, i.e., set of variables. It is mutually redundant to and can be combined with the input model, so that the combined model contains more redundant information, which is useful to increase constraint propagation. We also propose two methods of combining CSP models, namely model intersection and model channeling. The two methods allow combining two mutually redundant models in the same and different viewpoints respectively. We exploit the applications of model induction, intersection, and channeling and identify three new classes of combined models, which contain different amounts of redundant information. We construct combined models of Permutation CSPs and show in extensive benchmark results that the combined models are more robust and efficient to solve than the single models. 1