Finite Domain Bounds Consistency Revisited

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency. In this paper we clarify the differences and similarities among the three commonly used notions of bounds consistency.Comment: 12 page

Global Optimization based on Contractor Programming: an Overview of the IBEX library

International audienceIBEX is an open-source C++ library for constraint processing over real numbers. It provides reliable algorithms for handling non-linear constraints. In particular, roundoff errors are also taken into account. It is based on interval arithmetic and affine arithmetic. The main feature of IBEX is its ability to build strategies declaratively through the contractor programming paradigm. It can also be used as a black-box solver or with an AMPL interface. Two emblematic problems that can be addressed are: (i) System solving: A guaranteed enclosure for each solution of a system of (nonlinear) equations is calculated; (ii) Global optimization: A global minimizer of some function under non-linear constraints is calculated with guaranteed and reliable bounds on the objective minimum

Structural Constraint-Based Modeling and Reasoning with Basic Configuration Cells

Configuration tasks are an important application area in engineering design. The proposed solving techniques use either a constraintbased framework or a logic-based approach. We propose a methodology to obtains desired configuration using basic configuration cells(BCC). They are built by means of the predefined components and connections of the given configuration problem. In practical applications of configuration tasks the BCCs and configuration goals are represented according to object-oriented programming paradigm. They are mapped into a numeric constraint satisfaction problem. The transformation of a basic configuration cell into a new one generates a sequence of numeric constraint satisfaction problems. We propose an algorithm that solves this sequence of problems in order to obtain a configuration solution according to the desired requirements or that detects inconsistencies in the requirements. The integration of objectoriented and constraint programming paradigms allows us to achieve a synergy that produces results that could not be obtained if each one were working individually

Configuring a machining operation as a Constraint Satisfaction Problem

International audienceThe problem of configuring a machining operation is complex (many parameters and many interactions between parameters) and is generally achieved thanks to expert heuristic knowledge. Indeed, the configuration of a machining operation is often carried out according to a specific procedure: choice of a kind of operation and of a kind of machine, then choice of a set of tools and at the end selection of cutting conditions. We propose in this paper a general framework for the configuration of a machining operation based on a constraint representation and manipulation. We first present a model of the decision variables (such as the machine, the tool, the insert or the feed rate), the non-decision variable and the constraints between variables. An overview of the 32 identified constraints is given in the paper. Even though it is not exhaustive, the basic constraints of the domain are represented. A typology of the constraints to be manipulated is then given leading order to a specification of algorithms for search and consistency checking that may allow to manage these kinds of constraints

Hull Consistency Under Monotonicity

International audienceWe prove that hull consistency for a system of equations or inequalities can be achieved in polynomial time providing that the underlying functions are monotone with respect to each variable. This result holds including when variables have multiple occurrences in the expressions of the functions, which is usually a pitfall for interval-based contractors. For a given constraint, an optimal contractor can thus be enforced quickly under monotonicity and the practical significance of this theoretical result is illustrated on a simple example

Consistency techniques for the localization of a satellite

International audienceThis paper recalls that the problem of estimating the state vector of a nonlinear dynamic system can be interpreted as a constraint satisfaction problem over continuous domains with a large number (several thousands) of variables and constraints. Consistency techniques are then shown to be particularly efficient to contract the domains for the variables involved. This is probably due to the large number of redundancies naturally involved in the constraints of the problem. The approach is illustrated on the estimation of the position of a satellite in orbit around the earth

A Proof Theoretic View of Constraint Programming

We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and illustrate their use by analyzing the constraint propagation process for the {\tt SEND + MORE = MONEY} puzzle. We also show how this approach allows one to build new constraint solvers.Comment: 25 page