Proceedings Article•
Revising hull and box consistency
29 Nov 1999-pp 230-244
TL;DR: HC4, an algorithm to enforce hull consistency without decomposing complex constraints into primitives is presented, and BC4, a new algorithm to efficiently enforce box consistency is described, which is shown to significantly outperform both HC3 and BC3.
Abstract: Most interval-based solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems. This paper first presents HC4, an algorithm to enforce hull consistency without decomposing complex constraints into primitives. Next, an extended definition for box consistency is given and the resulting consistency is shown to subsume hull consistency. Finally, BC4, a new algorithm to efficiently enforce box consistency is described, that replaces BC3—the “original” solely Newton-based algorithm to achieve box consistency—by an algorithm based on HC4 and BC3 taking care of the number of occurrences of each variable in a constraint. BC4 is then shown to significantly outperform both HC3 (the original algorithm enforcing hull consistency by decomposing constraints) and BC3.
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Book•
01 Jan 2006
TL;DR: Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.
Abstract: Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics.
The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area.
The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.
The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming.
- Covers the whole field of constraint programming
- Survey-style chapters
- Five chapters on applications
Table of Contents
Foreword (Ugo Montanari)
Part I : Foundations
Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh)
Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth)
Chapter 3. Constraint Propagation (Christian Bessiere)
Chapter 4. Backtracking Search Algorithms (Peter van Beek)
Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang)
Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel)
Chapter 7. Tractable Structures for CSPs (Rina Dechter)
Chapter 8. The Complexity of Constraint Languages
(David Cohen, Peter Jeavons)
Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex)
Chapter 10. Symmetry in Constraint Programming
(Ian P. Gent, Karen E. Petrie, Jean-Francois Puget)
Chapter 11. Modelling (Barbara M. Smith)
Part II : Extensions, Languages, and Applications
Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace)
Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte)
Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson)
Chapter 15. Operations Research Methods in Constraint Programming (John Hooker)
Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers)
Chapter 17. Constraints over Structured Domains
(Carmen Gervet)
Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh)
Chapter 19. Temporal CSPs (Manolis Koubarakis)
Chapter 20. Distributed Constraint Programming
(Boi Faltings)
Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel)
Chapter 22. Constraint-Based Scheduling and Planning
(Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten)
Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw)
Chapter 24. Configuration (Ulrich Junker)
Chapter 25. Constraint Applications in Networks
(Helmut Simonis)
Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)
1,527 citations
TL;DR: RealPaver is an interval software for modeling and solving nonlinear systems which efficiently combine interval methods and constraint satisfaction techniques.
Abstract: RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreover, they may have different natures, being square or nonsquare, sparse or dense, linear, polynomial, or involving transcendental functions.The modeling language permits stating constraint models and tuning parameters of solving algorithms which efficiently combine interval methods and constraint satisfaction techniques. Several consistency techniques (box, hull, and 3B) are implemented. The distribution includes C sources, executables for different machine architectures, documentation, and benchmarks. The portability is ensured by the GNU C compiler.
264 citations
TL;DR: A way to deal harmoniously with a larger set of problems while giving a fine control on the solving mechanisms is given, to give more freedom in solver design by introducing programming concepts where only configuration parameters were previously available.
222 citations
TL;DR: A procedure based on interval analysis is proposed to build a guaranteed qLPV (quasi-Linear Parameter-Varying) approximation of the nonlinear model.
170 citations
Cites background or methods from "Revising hull and box consistency"
...It is based on the methodology presented in Bernard and Gouzé (2004) and can be considered as a generalisation for any Lipschitzian nonlinear system....
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...As the generalisation of the results of Bernard and Gouzé (2004) and Moisan et al. (2009) is not straightforward, the qLPV approximation is used in the following....
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...This observer has been extended in Bernard and Gouzé (2004) to a whole set of observers (called a bundle of observers)....
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01 Jan 2006
TL;DR: This chapter reviews that continuous constraint solving has been widely studied in several fields of applied mathematics and computer science and contrasts that continuous and interval constraints are generally contrasted with non negative integer or more generally discrete constraints.
Abstract: Publisher Summary This chapter reviews that continuous constraint solving has been widely studied in several fields of applied mathematics and computer science. In computer algebra, continuous constraints are viewed as formulas from first-order logic interpreted over the real numbers. The symbolic algorithms transform the constraint systems within the same equivalence class in the interpretation domain according to some simplification ordering. The chapter also discusses the interval analysis, which is a set extension of numerical analysis such that the floating-point numbers are replaced with the intervals. The interval approximations are defined so as to enclose the computed real quantities and the algorithms are said to be complete. In constraint programming, continuous constraints are viewed as relations. The complete solving of nonlinear systems is implemented by exhaustive search techniques that compute solution space coverings by means of multi-dimensional boxes. The search is commonly accelerated through propagation-based algorithms. It reviews that continuous and interval constraints are generally contrasted with non negative integer or more generally discrete constraints. These last constraints, sometimes also called finite domain constraints, are studied in the constraint satisfaction problems (CSP) framework and are basic components of most current constraint-based languages.
161 citations
References
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TL;DR: The primary aim is to provide an accessible, unified framework, within which to present the algorithms including a new path consistency algorithm, to discuss their relationships and the may applications, both realized and potential of network consistency algorithms.
2,750 citations
"Revising hull and box consistency" refers methods in this paper
...Domains are associated to every variable occurring in the problem, and solving a particular constraint then lies in eliminating some of the values of these domains for which the constraint does not hold (inconsistency), using local consistency techniques and filtering [9]....
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TL;DR: A unified processing for real, integer, and Boolean constraints based on a general narrowing algorithm which applies to any n-ary relation on R is presented and a new Constraint Logic Programming language called CLP(BNR), where BNR stands for Booleans, Naturals, and Reals is proposed.
Abstract: We present in this paper a unified processing for real, integer, and Boolean constraints based on a general narrowing algorithm which applies to any n-ary relation on R. The basic idea is to define, for every such relation ρ, a narrowing function ρ based on the approximation of ρ by a Cartesian product of intervals whose bounds are floating-point numbers. We then focus on nonconvex relations and establish several properties. The more important of these properties is applied to justify the computation of usual relations defined in terms of intersections of simpler relations. We extend the scope of the narrowing algorithm used in the language BNR-Prolog to integer and disequality constraints, to Boolean constraints, and to relations mixing numerical and Boolean values. As a result, we propose a new Constraint Logic Programming language called CLP(BNR), where BNR stands for Booleans, Naturals, and Reals. In this language, constraints are expressed in a unique structure, allowing the mixing of real numbers, integers, and Booleans. We end with the presentation of several examples showing the advantages of such an approach from the point of view of the expressiveness, and give some preliminary computational results from a prototype.
354 citations
Book•
18 Apr 1997TL;DR: The meaning and implementation of Numerica: overview of the algorithm domain-specific and monotonic interval extensions constraint solving unconstrained optimization constrained optimization advanced techniques an implementation of box consistency.
Abstract: Part 1 Introduction: nonlinear programming local methods global methods Numerica outline. Part 2 A tour of Numerica: getting started generic constraints constants ranges input parameters aggregation operators functions sets unconstrained optimization constrained optimization local constraint solving local unconstrained optimization soft constraints real constraints and uncertain data display accuracy. Part 3 The meaning of Numerica: interval analysis constraint solving unconstrained optimization interpretation of the results. Part 4 Modelling in Numerica: what can go wrong in Numerica improving Numerica statements. Part 5 The syntax of Numerica: overall structure expressions the constant section the input section the set section the variable section the function section the body section the display section the pragma section scoping rules. Part 6 The semantics of Numerica: interval arithmetic semantics of constraint solving semantics of unconstrained minimization semantics of constrained minimization non-canonical boxes. Part 7 An implementation of Numerica: overview of the algorithm domain-specific and monotonic interval extensions constraint solving unconstrained optimization constrained optimization advanced techniques an implementation of box consistency. Part 8 Experimental results: constraint solving unconstrained optimization constrained optimization appendices.
339 citations
"Revising hull and box consistency" refers background in this paper
...Most interval-based solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems....
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Proceedings Article•
01 Nov 1994
TL;DR: Experimental results indicate that Newton outperforms existing languages by an order of magnitude and is competitive with some state-of-the-art tools on some standard benchmarks.
Abstract: The design and implementation of constraint logic programming (CLP) languages over intervals is revisited. Instead of decomposing complex constraints in terms of simple primitive constraints as in CLP(BNR), complex constraints are manipulated as a whole, enabling more sophisticated narrowing procedures to be applied in the solver. This idea is embodied in a new CLP language Newton whose operational semantics is based on the notion of box-consistency, an approximation of arc-consistency, and whose implementation uses Newton interval method. Experimental results indicate that Newton outperforms existing languages by an order of magnitude and is competitive with some state-of-the-art tools on some standard benchmarks. Limitations of our current implementation and directions for further work are also identified.
316 citations
"Revising hull and box consistency" refers background or methods in this paper
...Two worth mentioning approximate consistencies are hull consistency [1] and box consistency [2]....
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...Next, a slightly extended definition of box consistency is given, that no longer solely relies on the natural interval extension of constraints and captures both the original definition of box consistency [2] and the one by Collavizza et al....
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...Box consistency [2] has been introduced to avoid decomposing constraints, thus tackling the dependency problem for variables with many occurrences....
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...Algorithm HC32 [2, 4] partly overcomes this problem by enforcing hull consistency over a decomposition cdec of simple—primitive—constraints rather than considering the user constraint c....
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...,C} consistency is equivalent to the original definition [2]....
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01 Jan 1997
TL;DR: A C++ library that embodies Constraint Logic Programming (CLP) concepts such as logical variables, incremental constraint satisfaction and backtracking, and which combines Object Oriented Programming (OOP) with CLP.
Abstract: We have implemented a C++ library, called ILOG SOLVER, that embodies Constraint Logic Programming (CLP) concepts such as logical variables, incremental constraint satisfaction and backtracking. This library combines Object Oriented Programming (OOP) with CLP. This has two advantages. First of all, everything is an object in SOLVER: variables, constraints and search algorithms (goals). Thus, SOLVER is easily extendable by de ning new classes. Second, objects can be used for modeling the real problem that has to be solved, which is a great software engineering advantage. In particular, SOLVER provides for the de nition of class constraints, that are inherited by all the objects of that class.
195 citations
"Revising hull and box consistency" refers background in this paper
...Most interval-based solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems....
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