Abstract: We study the complexity of two-person constraint satisfaction games. An instance of such a game is given by a collection of constraints on overlapping sets of variables, and the two players alternately make moves assigning values from a finite domain to the variables, in a specified order. The first player tries to satisfy all constraints, while the other tries to break at least one constraint; the goal is to decide whether the first player has a winning strategy. We show that such games can be conveniently represented by a logical form of quantified constraint satisfaction, where an instance is given by a first-order sentence in which quantifiers alternate and the quantifier-free part is a conjunction of (positive) atomic formulas; the goal is to decide whether the sentence is true. While the problem of deciding such a game is PSPACE-complete in general, by restricting the set of allowed constraint predicates, one can obtain infinite classes of constraint satisfaction games of lower complexity. We use the quantified constraint satisfaction framework to study how the complexity of deciding such a game depends on the parameter set of allowed predicates. With every predicate, one can associate certain predicate-preserving operations, called polymorphisms. We show that the complexity of our games is determined by the surjective polymorphisms of the constraint predicates. We illustrate how this result can be used by identifying the complexity of a wide variety of constraint satisfaction games.

Abstract: We propose a new extended format to represent constraint networks using XML. This format allows us to represent constraints defined either in extension or in intension. It also allows us to reference global constraints. Any instance of the problems CSP (Constraint Satisfaction Problem), QCSP (Quantified CSP) and WCSP (Weighted CSP) can be represented using this format.

Abstract: This paper introduces a global constraint encapsulating a regular constraint together with several cumulative costs. It is motivated in the context of personnel scheduling problems, where a schedule meets patterns and occurrence requirements which are intricately bound. The optimization problem underlying the multicost-regular constraint is NP-hard but it admits an efficient Lagrangian relaxation. Hence, we propose a filtering based on this relaxation. The expressiveness and the efficiency of this new constraint is experimented on personnel scheduling benchmark instances with standard work regulations. The comparative empirical results show how multicost-regular can significantly outperform a decomposed model with regular and global-cardinality constraints.

Abstract: We study the CardPath constraint. This ensures a given constraint holds a number of times down a sequence of variables. We show that SLIDE, a special case of CardPath where the slid constraint must hold always, can be used to encode a wide range of sliding sequence constraints including CardPath itself. We consider how to propagate SLIDE and provide a complete propagator for CardPath. Since propagation is NP-hard in general, we identify special cases where propagation takes polynomial time. Our experiments demonstrate that using SLIDE to encode global constraints can be as efficient and effective as specialised propagators.

Abstract: Embodiment design (ED) is an early phase of product development. ED problems consist of finding solution principles that satisfy product requirements such as physics behaviors and interactions between components. Constraint satisfaction techniques are useful to solve constraint-based models that are often partial, heterogeneous, and uncertain in ED. This paper proposes new constraint satisfaction techniques to tackle piecewise-defined physics phenomena or skill-based rules and multiple categories of variables arising in design applications. New search heuristics and a global piecewise constraint are introduced in the branch and prune framework. The capabilities of these techniques are illustrated with both academic and real-world problems. Complete models of the latter are presented.

Abstract: Many practical optimization problems are constrained black boxes. Covariance Matrix Adaptation Evolution Strategies (CMA-ES) belong to the most successful black box optimization methods. Up to now no sophisticated constraint handling method for Covariance Matrix Adaptation optimizers has been proposed. In our novel approach we learn a meta-model of the constraint function and use this surrogate model to adapt the covariance matrix during the search at the vicinity of the constraint boundary. The meta-model can be used for various purposes, i.e. rotation of the mutation ellipsoid, checking the feasibility of candidate solutions or repairing infeasible mutations by projecting them onto the constraint surrogate function. Experimental results show the potentials of the proposed approach.

Abstract: To model combinatorial decision problems involving uncertainty and probability, we extend the stochastic constraint programming framework proposed in [Walsh, 2002] along a number of important dimensions (e.g. to multiple chance constraints and to a range of new objectives). We also provide a new (but equivalent) semantics based on scenarios. Using this semantics, we can compile stochastic constraint programs down into conventional (nonstochastic) constraint programs. This allows us to exploit the full power of existing constraint solvers. We have implemented this framework for decision making under uncertainty in stochastic OPL, a language which is based on the OPL constraint modelling language [Hentenryck et al., 1999]. To illustrate the potential of this framework, we model a wide range of problems in areas as diverse as finance, agriculture and production.

Abstract: Today's models for propagation-based constraint solvers require propagators as implementations of constraints to be at least contracting and monotonic. These models do not comply with reality: today's constraint programming systems actually use nonmonotonic propagators. This paper introduces the first realistic model of constraint propagation by assuming a propagator to be weakly monotonic (complying with the constraint it implements). Weak monotonicity is shown to be the minimal property that guarantees constraint propagation to be sound and complete. The important insight is that weak monotonicity makes propagation in combination with search well behaved. A case study suggests that non-monotonicity can be seen as an opportunity for more efficient propagation.

Abstract: GloptLab is an easy-to-use testing and development platform for solving quadratic constraint satisfaction problems, written in Matlab. The algorithms implemented in GloptLab are used to reduce the search space: scaling, constraint propagation, linear relaxations, strictly convex enclosures, conic methods, and branch and bound. All these methods are rigorous; hence, it is guaranteed that no feasible point is lost. Finding and verifying feasible points complement the reduction methods. From the method repertoire custom-made strategies can be built, with a user-friendly graphical interface. GloptLab was tested on a large test set of constraint satisfaction problems, and the results show the importance of composing a clever strategy.

Abstract: Building adaptive constraint solvers is a major challenge in constraint programming. An important line of research towards this goal is concerned with ways to dynamically adapt the propagation method applied on the constraints of the problem during search. In this paper we present a heuristic approach to this problem based on the monitoring of propagation events like value deletions and domain wipeouts. We develop a number of heuristics that allow the constraint solver to dynamically switch between a weaker and cheap local consistency and a stronger, but more expensive one, when certain conditions are met. The success of this approach is based on the observation that propagation events for individual constraints in structured problems mostly occur in clusters of nearby revisions. Hence, parts of the search space where certain constraints are highly active can be identified and exploited paving the way for the informed use of constraint propagation techniques. In this paper we first give some experimental results displaying the clustering of propagation events in structured binary CSPs. Then we present simple heuristics that exploit this clustering to efficiently switch between different local consistencies on individual constraints during search. Finally, we make an experimental study on various binary CSPs demonstrating the effectiveness of the proposed heuristics.

Abstract: We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary constraint satisfaction problems with domain size three.

Abstract: This paper introduces a generalization of the nvalue constraint that bounds the number of distinct values taken by a set of variables. The generalized constraint (called nvector) bounds the number of distinct (multi-dimensional) vectors. The first contribution of this paper is to show that this global constraint has a significant role to play with continuous domains, by taking the example of simultaneous localization and map building (SLAM). This type of problem arises in the context of mobile robotics. The second contribution is to prove that enforcing bound consistency on this constraint is NP-complete. A simple contractor (or propagator) is proposed and applied on a real application.

Abstract: A recent line of research concerns the integration of ant colony optimization and constraint programming Hereby, constraint programming is used for eliminating parts of the search tree during the solution construction of ant colony optimization In the context of a single machine scheduling problem, for example, it has been shown that the integration of constraint programming can significantly improve the ability of ant colony optimization to find feasible solutions One of the remaining problems, however, concerns the elevated computation time requirements of the hybrid algorithm, which are due to constraint propagation In this work we propose a possible solution to this problem by integrating constraint programming with a specific version of ant colony optimization known as Beam-ACO The idea is to reduce the time spent for constraint propagation by parallelizing the solution construction process as done in Beam-ACO The results of the proposed algorithm show indeed that it is currently the best performing algorithm for the above mentioned single machine job scheduling problem

Abstract: Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved. We introduce a new model of open global constraint where the length of the sequence of variables can be constrained but there is no a priori restriction on the variables that might be added. In general, propagation that is sound for a global constraint can be unsound when the constraint is open. We identify properties of constraints that simplify the design of algorithms for propagation by identifying when no propagation can be done, and use them to design propagation algorithms for several open global constraints.

Abstract: Building tight and conservative enclosures of the solution set is of crucial importance in the design of efficient complete solvers for numerical constraint satisfaction problems (NCSPs). This paper proposes a novel generic algorithm enabling the cooperative use, during constraint propagation, of multiple enclosure techniques. The new algorithm brings into the constraint propagation framework the strength of techniques coming from different areas such as interval arithmetic, affine arithmetic, and mathematical programming. It is based on the directed acyclic graph (DAG) representation of NCSPs whose flexibility and expressiveness facilitates the design of fine-grained combination strategies for general factorable systems. The paper presents several possible combination strategies for creating practical instances of the generic algorithm. The experiments reported on a particular instance using interval constraint propagation, interval arithmetic, affine arithmetic, and linear programming illustrate the flexibility and efficiency of the approach.

Abstract: We present a new method for generating a concise and representative approximation of the (weakly) efficient set of a nonlinear multi-objective optimization problem For the parameter dependent e-constraint scalarization an algorithm is given which allows an adaptive controlling of the parameters—the upper bounds—based on sensitivity results such that equidistant approximation points are generated The proposed method is applied to a variety of test-problems

Abstract: Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved. However, in general, filtering that is sound for a global constraint can be unsound when the constraint is open. This paper provides a simple characterization, called contractibility, of the constraints where filtering remains sound when the constraint is open. With this characterization we can easily determine whether a constraint is contractible or not. In the latter case, we can use it to derive the strongest contractible approximation to the constraint. We demonstrate how specific algorithms for some closed contractible constraints are easily adapted to open constraints.

Abstract: This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond–Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al. (2007), which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

Abstract: We study nonsmooth mathematical programs with equilibrium constraints. First we consider a general disjunctive program which embeds a large class of problems with equilibrium constraints. Then, we establish several constraint qualifications for these optimization problems. In particular, we generalize the Abadie and Guignard-type constraint qualifications. Subsequently, we specialize these results to mathematical program with equilibrium constraints. In our investigation, we show that a local minimum results in a so-called M-stationary point under a very weak constraint qualification.

Abstract: In constraint programming there are often many choices regarding the propagation method to be used on the constraints of a problem However, simple constraint solvers usually only apply a standard method, typically (generalized) arc consistency, on all constraints throughout search Advanced solvers additionally allow for the modeler to choose among an array of propagators for certain (global) constraints Since complex interactions exist among constraints, deciding in the modelling phase which propagation method to use on given constraints can be a hard task that ideally we would like to free the user from In this paper we propose a simple technique towards the automation of this task Our approach exploits information gathered from a random probing preprocessing phase to automatically decide on the propagation method to be used on each constraint As we demonstrate, data gathered though probing allows for the solver to accurately differentiate between constraints that offer little pruning as opposed to ones that achieve many domain reductions, and also to detect constraints and variables that are amenable to certain propagation methods Experimental results from an initial evaluation of the proposed method on binary CSPs demonstrate the benefits of our approach

Abstract: This paper investigates the potential of constraint programming for solving set partitioning problems occurring in crew scheduling, where constraint programming is restricted to not employ external solvers, as for instance integer linear programming solvers. We evaluate preprocessing steps known from the OR literature on moderately sized set partitioning problems. Further, we propose a new preprocessing technique which allows to reduce problem size more effectively than standard preprocessing techniques but with similar computational effort. Additionally, we propose a propagation algorithm for a global set partitioning constraint which, compared with other constraint programming approaches, finds and proves optimal solutions significantly faster resp. produces better solutions in a given time period.

Abstract: This paper presents the first experimental evaluation of the length-lex domain for set variables. The implementation is based on bound-consistency algorithms proposed in earlier work and two novel technical contributions: a generic filtering algorithm which automatically pushes ordering constraints into symmetric binary constraints with only a logarithmic overhead and an adaptation of symmetry-breaking constraints from 0/1 matrices to the length-lex ordering. The experimental results indicate that the length-lex representation for set variables is very effective and robust on traditional set-CSPs benchmarks.

Abstract: The constraint satisfaction problem (CSP) is a convenient framework for modelling search problems; the CSP involves deciding, given a set of constraints on variables, whether or not there is an assignment to the variables satisfying all of the constraints. This paper is concerned with the more general framework of quantified constraint satisfaction, in which variables can be quantified both universally and existentially. We study the relatively quantified constraint satisfaction problem (RQCSP), in which the values for each individual variable can be arbitrarily restricted. We give a complete complexity classification of the cases of the RQCSP where the types of constraints that may appear are specified by a constraint language.

Abstract: The combinatorial problem of decomposing an integer matrix into a small positive linear combination of binary matrices that have the consecutive-ones property arises in cancer radiotherapy delivery planning. A fast constraint programming approach for this problem exists. I present a propagation algorithm for a constraint in this approach that can speed up solving by an order of magnitude.

Abstract: The standard model of distributed constraints optimization problems (DCOPs), assumes that the cost of a constraint is checked by one of the agents involved in the constraint. For DCOPs this is equivalent to the assumption that each constraint has a global cost which applies to each of the participating agents and in other words that all constraints are symmetric. Many multi agent system (MAS) problems involve asymmetric constraints. For example, the gain from a scheduled meeting of two agents is naturally different for each of the participants. In order to solve Asymmetric DCOPs (ADCOPs), one needs to design algorithms in which all agents participating in a constraint independently check the gain for each of them. This naturally brings up the question of privacy, enabling agents to keep their cost (or gain) of constraints private, at least partially. The present paper presents search algorithms for ADCOPs which handle asymmetric constraints in a privacy preserving manner. New versions of Asynchronous Forward Bounding and of Synchronous Branch & Bound are proposed. In addition, two local search algorithms are presented in which agents negotiate moves prior to assigning values. All algorithms are empirically evaluated, and their performance in terms of run-time, network load and solution quality is presented.

Abstract: A key problem when interpolating a network of curves occurs at vertices: an algebraic condition called the vertex enclosure constraint must hold wherever an even number of curves meet. This paper recasts the constraint in terms of the local geometry of the curve network. This allows formulating a new geometric constraint, related to Euler's Theorem on local curvature, that implies the vertex enclosure constraint and is equivalent to it where four curve segments meet without forming an X.

Abstract: Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many clusters. In this paper we argue that this ergodicity-breaking transition is preceded by a homogeneity-breaking transition. For random K-SAT and K-XORSAT, we show that many solution communities start to form in the solution space as the constraint density reaches a critical value alpha_cm, with each community containing a set of solutions that are more similar with each other than with the outsider solutions. At alpha_cm the solution space is in a critical state. The connection of these results to the onset of dynamical heterogeneity in lattice glass models is discussed.

Abstract: This paper introduces six ways for handling a chain of lexicographic ordering (lex-chain) constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a lex-chain constraint within a generic geometric constraint kernel, the four latter ways deal with the conjunction of a lex-chain constraint and a non-overlapping or a cumulative constraint. Experiments on academic two and three dimensional placement problems as well as on industrial problems show the benefit of such a strong integration of symmetry breaking constraints and non-overlapping ones.