Constraint Satisfaction Problems

In this paper, we develop a formalism called a distributed c onstraint satisfaction problem (distributed CSP) and algorithms for solving distributed CSPs. A distributed CSP is a constraint satisfaction problem in which variables and constraints are distributed among multiple agents. Various application problems in Distributed Articial Intelligence can be formalized as distributed CSPs.

In order to deal with over-constrained Constraint Satisfaction Problems, various extensions of the CSP framework have been considered by taking into account costs, uncertainties, preferences, priorities...Each extension uses a specific mathematical operator (+, max...) to aggregate constraint violations. In this paper, we consider a simple algebraic framework, related to Partial Constraint Satisfaction, which subsumes most of these proposals and use it to characterize existing proposals in terms of rationality and computational complexity. We exhibit simple relationships between these proposals, try to extend some traditional CSP algorithms and prove that some of these extensions may be computationally expensive.

Swarm . Optimizer which deals with permutation problems. Particles are defined as permutations of a group of unique values. Velocity updates are redefined based on the similarity of two particles. Particles change their permutations with a random rate defined by their velocities. A mutation factor is introduced to prevent the current pBest from becoming stuck at local minima. Preliminary study on the n-queens problem shows that the modified PSO is promising in solving constraint sstisfication problems.

The problem of radio frequency assignment is to provide communication channels from limited spectral resources whilst keeping to a minimum the interference suffered by those whishing to communicate in a given radio communication network. This problem is a combinatorial (NP-hard) optimization problem. In 1993, the CELAR (the French "Centre d'Electronique de l'Armement") built a suite of simplified versions of Radio Link Frequency Assignment Problems (RLFAP) starting from data on a real network . Initially designed for assessing the performances of several Constraint Logic Programming languages, these benchmarks have been made available to the public in the framework of the European EUCLID project CALMA (Combinatorial Algorithms for Military Applications).

A key issue for Cloud Computing data-centers is to maximize their profits by minimizing power consumption and SLA violations of hosted applications. In this paper, we propose a resource management framework combining a utility-based dynamic Virtual Machine provisioning manager and a dynamic VM placement manager. Both problems are modeled as constraint satisfaction problems. The VM provisioning process aims at maximizing a global utility capturing both the performance of the hosted applications with regard to their SLAs and the energy-related operational cost of the cloud computing infrastructure. We show several experiments how our system can be controlled through high level handles to make different trade-off between application performance and energy consumption or to arbitrate resource allocations in case of contention.

The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limited-width multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths. MDD propagation algorithms can be developed to exploit the structure of particular constraints, much as is done for domain filtering algorithms. We propose specialized propagation algorithms for alldiff and inequality constraints. Preliminary experiments show that MDD propagation solves multiple alldiff problems an order of magnitude more rapidly than traditional domain propagation. It also significantly reduces the search tree for inequality problems, but additional research is needed to reduce the computation time.

View-based query processing requires to answer a query posed to a database only on the basis of the information on a set of views, which are again queries over the same database. This problem is relevant in many aspects of database management, and has been addressed by means of two basic approaches, namely, query rewriting and query answering. In the former approach, one tries to compute a rewriting of the query in terms of the views, whereas in the latter, one aims at directly answering the query based on the view extensions. We study view-based query processing for the case of regular-path queries, which are the basic querying mechanisms for the emergent field of semistructured data. Based on recent results, we first show that a rewriting is in general a co-NP function wrt to the size of view extensions. Hence, the problem arises of characterizing which instances of the problem admit a rewriting that is PTIME. A second contribution of the work is to establish a tight connection between view-based query answering and constraint-satisfaction problems, which allows us to show that the above characterization is going to be difficult. As a third contribution of our work, we present two methods for computing PTIME rewritings of specific forms. The first method, which is based on the established connection with constraint-satisfaction problems, gives us rewritings expressed in Datalog with a fixed number of variables. The second method, based on automata-theoretic techniques, gives us rewritings that are formulated as unions of conjunctive regular-path queries with a fixed number of variables.

Feature models are widely used to model software product-line (SPL) variability. SPL variants are configured by selecting feature sets that satisfy feature model constraints. Configuration of large feature models involve multiple stages and participants, which makes it hard to avoid conflicts and errors. New techniques are therefore needed to debug invalid configurations and derive the minimal set of changes to fix flawed configurations. This paper provides three contributions to debugging feature model configurations: (1) we present a technique for transforming a flawed feature model configuration into a Constraint Satisfaction Problem (CSP) and show how a constraint solver can derive the minimal set of feature selection changes to fix an invalid configuration, (2) we show how this diagnosis CSP can automatically resolve conflicts between configuration participant decisions, and (3) we present experiment results that evaluate our technique. These results show how our technique scales to models with over 5,000 features, which is beyond the size used to validate other automated techniques.

A large number of interesting combinatorial optimization problems like M C, M k-S, and U G fall under the class of constraint satisfaction problems (CSPs). Recent work [32] by one of the authors identifies a semidefinite programming (SDP) relaxation that yields the optimal approximation ratio for every CSP, under the Unique Games Conjecture (UGC). Very recently , the authors also showed unconditionally that the integrality gap of this basic SDP relaxation cannot be reduced by adding large classes of valid inequalities (e.g., in the fashion of Sherali-Adams LP hierarchies).

We propose ConArg, a tool based on Constraint Programming, to model and solve various problems related to the Argumentation research field. Constraint Satisfaction Problems (CSPs) offer a wide number of efficient techniques (as inference and search algorithms) that can tackle the complexity in finding all the possible Dung's conflict-free, admissible, complete, stable, preferred and grounded extensions in Argumentation Frameworks. Moreover, we can use the tool to solve some computationally hard problems presented in [1]. To implement ConArg, we have used JaCoP, a Java library which provides the user with a Finite Domain Constraint Programming paradigm, to model and solve these two problems. ConArg is able to randomly generate two different kinds of smallworld networks in order to find Dung's extensions on such interaction graphs. We present the main features of ConArg and the reported performance in time.

Traditionally, interactive natural language systems assume a semantic model in which the entities referred to are in some abstract representation of a real or imagined world. In a system where graphical objects such as diagrams may be on the screen during the language interaction, there is possibility that the user may want to allude to these visual entities. Since graphical objects have their own properties (colour, shape, position on the screen, etc.) but may also represent items in a knowledge base which have other associated properties (price, geographical location, technical specifications, etc.), some systematic way is needed to enable such objects to be referred to in terms of either their screen properties or their associated attributes from the domain under discussion. In this paper, we present a formalisation for these arrangements, and show how our logical definitions can be used to generate constraints suitable for reference resolution within a natural language interpreter.

A constraint satisfaction problem (CSP) is a combinatorial optimisation problem with many real world applications. One of the key aspects to consider when solving a CSP is the order in which the variables are selected to be instantiated. In this study, we describe a genetic programming hyper-heuristic approach to automatically produce heuristics for CSPs. Humandesigned 'standard' heuristics are used as components enabling construction of new variable ordering heuristics which is achieved through the proposed approach. We present empirical evidence that the heuristics produced by our approach are competitive considering the cost of the search when compared to the standard heuristics used to obtain the components for the new heuristics. The proposed approach is able to produce specialised heuristics for specific classes of instances that outperform the best standard heuristics for the same instances.

A novel approach aiding in the prediction of RNA secondary structures is presented. Although phylogenetic methods are the most successful at Borde Rouge, BP 27, 31326 deriving RNA secondary structures, the are not applicable when the Castanet Tolosan, Cedex number of sequences or the sequence variability is too low. Methods based France on energy minimization are therefore of great interest. However, some of 2 IBMC/CNRS, 15 rue the suboptimal RNA secondary structures computed with classic methods Descartes, Strasbourg, 67084 are unsaturated structures, i.e. some structures are included into others. France

Feder and Vardi have conjectured that all constraint satisfaction problems to a fixed structure (constraint language) are polynomial or NP-complete. This so-called Dichotomy Conjecture remains open, although it has been proved in a number of special cases. Most recently, Bulatov has verified the conjecture for conservative structures, i.e., structures which contain all possible unary relations.

Hyper-heuristics are high level search methodologies that operate over a set of heuristics which operate directly on the problem domain. In one of the hyper-heuristic frameworks, the goal is automating the process of selecting a human-designed low level heuristic at each step to construct a solution for a given problem. Constraint Satisfaction Problems (CSP) are well know NP complete problems. In this study, behaviours of two variable ordering heuristics Max-Conflicts (MXC) and Saturation Degree (SD) with respect to various combinations of constraint density and tightness values are investigated in depth over a set of random CSP instances. The empirical results show that the performance of these two heuristics are somewhat complementary and they vary for changing constraint density and tightness value pairs. The outcome is used to design three hyper-heuristics using MXC and SD as low level heuristics to construct a solution for unseen CSP instances. It has been observed that these hyper-heuristics improve the performance of individual low level heuristics even further in terms of mean consistency checks for some CSP instances.

Project-driven manufacturing, based on the make-to-order or the build-to-order principle and predominant in small and medium-size enterprises (SMEs), calls for an efficient solution of large combinatorial problems, especially in such areas as task scheduling or resource management. This paper addresses the problem of finding a computationally effective approach to scheduling a new project subject to constraints imposed by a multi-project environment. A constraint programming (CP) modeling framework is discussed in the context of an efficient decomposition of the constraint satisfaction problem (CSP) and the evaluation of strategies for pruning the search tree. The proposed approach is illustrated through examples of its application to the evaluation of a new production order.

We present a new framework, managing Constraint Satisfaction Problems (CSPs) with preferences in a dynamic environment. Unlike the existing CSP models managing one form of preferences, ours supports four types, namely: unary and binary constraint preferences, composite preferences and conditional preferences. This offers more expressive power in representing a wide variety of dynamic constraint applications under preferences and where the possible changes are known and available a priori. Conditional preferences allow some preference functions to be added dynamically to the problem, during the resolution process, if a given condition on some variables is true. A composite preference is a higher level of preference among the choices of a composite variable. Composite variables are variables whose possible values are CSP variables. In other words, this allows us to represent disjunctive CSP variables. The preferences are viewed as a set of soft constraints using the fuzzy CSP framework. Solving constraint problems with preferences consists in finding a solution satisfying all the constraints while optimizing the global preference value. This is handled by four variants of the branch and bound algorithm, we propose in this paper, and where constraint propagation is used to improve the time efficiency in practice. In order to evaluate and compare the performance of these four strategies, we conducted an experimental study on randomly generated dynamic CSPs with quantitative preferences. The results are reported and discussed in the paper.

The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such combination should outperform the single heuristics. This paper presents a GAbased method that produces general hyper-heuristics for the dynamic variable ordering within Constraint Satisfaction Problems. The GA uses a variable-length representation, which evolves combinations of condition-action rules producing hyper-heuristics after going through a learning process which includes training and testing phases. Such hyper-heuristics, when tested with a large set of benchmark problems, produce encouraging results for most of the cases. The testebed is composed of problems randomly generated using an algorithm proposed by Prosser .

Constraint Programming constitutes a prominent paradigm for solving time-consuming Constraint Satisfaction Problems (CSPs). In this work, at first we model a generic course scheduling problem as a CSP, that complies with the International Timetabling Competition (ITC) standards. Constraint Programming allowed us to search for a solution via several state-of-the-art methodologies and compare them. For the stochastic search methods, we propose new hybrid semi-random heuristics. Second, we chose to maintain bounds consistency during search to prune 'no-good' branches of the search tree. We theoretically define new lightweight consistency types, namely k-bounds-consistency, in order to speed up the overall search procedure. Eventually, we process real world data and show the efficiency of our proposal: While plain backtracking produces poor results, constraint propagation dramatically boosts the solutions quality, and can be 'finetuned' in our adjustable schema to make it even faster.

Following a line outage, the fast corrective operations of transmission line switching might be used to regain N -1 security of the system without generation re-dispatch or load shedding. The problem to find feasible switching operations can be formulated as a constraint satisfaction problem (CSP). Feasibility checking, however, is difficult since changes in load flows caused by line switching operations are discontinuous, and many contingency cases need to be examined. In this paper, DC flow is considered for simplicity, and variables include binary line statuses and continuous phase angles. Security constraints for the base case, N -1, and selected N -2 cases are formulated in a unified way by using a separate set of phase angles for each case. The problem is solved by using constraint programming (CP), and a tree search procedure is developed. Since it is time consuming to handle continuous variables in the tree search, only binary variables are branched on. Once reaching a leaf node where the topology is fixed, the constraints become linear DC flow feasibility conditions and are examined by solving a linear programming problem. Effectiveness of the method is demonstrated on IEEE 30-bus and US-bus systems.

The universal-algebraic approach has proved a powerful tool in the study of the computational complexity of constraint satisfaction problems (CSPs). This approach has previously been applied to the study of CSPs with finite or (infinite) ω-categorical templates. Our first result is an exact characterization of those CSPs that can be formulated with (a finite or) an ω-categorical template.

A predictive control strategy is developed for set-point tracking of LTI plants in the presence of joint positional and incremental (rate) input saturation constraints. The resulting control algorithm is built so as to provide an integral action capable to asymptotically reject arbitrary constant disturbances. This task is achieved by possibly modifying on-line the set-point in the case this becomes incompatible with constraints and disturbances. When applied to asymptotically null controllable with bounded inputs (ANCBI) plants, viz. all stabilizable linear systems with eigenvalues in the closed unit circle, the control law is shown to globally provide set-point tracking in the presence of arbitrary constant disturbances and initial state. For non-ANCBI plants, viz. systems with exponentially unstable modes, the control law features the mentioned properties locally, viz. in bounded regions of initial states and disturbances.

This paper presents a new pattern recognition approach to the identification and characterization of multiple signal patterns in the domain of Sleep Apnoea Syndrome. This approach has been employed to identify apnoeas (cessations in the sleeping patient's respiratory airflow) and to relate them with the drops in blood oxyhaemoglobin saturation they give rise to. As a starting point, our algorithms take a projection over a computational representation of the morphological criteria which characterize apnoeas and desaturations. These criteria are obtained directly from a physician. The fuzzy set theory allows us to represent and handle the vagueness of the medical knowledge on which this proposal is based, and the constraint satisfaction problem formalism supplies a computable representation for this knowledge.

Hyper-heuristics are methodologies used to choose from a set of heuristics and decide which one to apply given some properties of the current instance. When solving a Constraint Satisfaction Problem, the order in which the variables are selected to be instantiated has implications in the complexity of the search. We propose a neural network hyper-heuristic approach for variable ordering within Constraint Satisfaction Problems. The first step in our approach requires to generate a pattern that maps any given instance, expressed in terms of constraint density and tightness, to one adequate heuristic. That pattern is later used to train various neural networks which represent hyper-heuristics. The results suggest that neural networks generated through this methodology represent a feasible alternative to code hyper-heuristic which exploit the strengths of the heuristics to minimise the cost of finding a solution.

We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited connection between the two phenomena indeed exists. Specifically, we extend the definition of the spine order parameter of Bollobás et al.

During the last two decades we have witnessed considerable activity in building bridges between the fields of information theory/communications, computer science, and statistical physics. This is due to the realization that many fundamental concepts and notions in these fields are in fact related and that each field can benefit from the insight and techniques developed in the others.

Conventional techniques for the constraint satisfaction problem (CSP) have had considerable success in their applications. However, there are many areas in which the performance of the basic approaches may be improved. These include heuristic ordering of certain tasks performed by the CSP solver, hybrids which combine compatible solution techniques and graph based methods which exploit the structure of the constraint graph representation of a CSP. Also, conventional constraint satisfaction techniques only address problems with hard constraints (i.e. each of which are completely satisfied or completely violated, and all of which must be satisfied by a valid solution). Many real applications require a more flexible approach which relaxes somewhat these rigid requirements. To address these issues various approaches have been developed. This paper attempts a systematic review of them.

In this paper we formalise CSP solving as an inference process. Based on the notion of Computational Systems we associate actions with rewriting rules and control with strategies that establish the order of application of the inferences. The main contribution of this work is to lead the way to the design of a formalism allowing to better understand constraint solving and to apply in the domain of CSP the knowledge already developed in Automated Deduction.

A novel combination of genetic algorithms and constraint satisfaction modelling for the solution of two and multi-layer over-thecell channel routing problems is presented. The two major objectives of the optimization task are to find an optimal assignment of nets to over-the-cell and within the channel tracks, and to minimize the channel widths through a simple but effective iterative routing methodology. Two genetic algorithms cooperate in a nested manner to perform the optimization task. The results obtained using the benchmark problems published in literature indicate that, without any predefined fixed upper/lower channel widths, the implemented algorithm outperforms wellknown channel routers.

Network design models allow to define an optimal network configuration by means of objective functions subject to a series of constraints. The starting data and/or the constraints of the problem can be affected by uncertainty. These uncertain values are better managed through the use of fuzzy values/constraints. In this paper we present a fuzzy non-linear programming to solve the equilibrium Network Design problem for urban areas. This problem is formulated as a fixed point optimization subject to fuzzy constraints. The proposed method has been applied to a test network. The obtained results show that the proposed approach is very interesting.

We investigate the variable performance of a genetic algorithm (GA) on randomly generated binary constraint satisfaction problem instances which occur near the phase transition from soluble to non-soluble. We ÿrst carry out a conventional landscape analysis and observe, next to a number of common features related to the interaction structure, important di erences between the instances, such as the number of solutions, the quality of the paths to the solutions, and the lengths and extent of the neutral paths for mutation. We then split the dynamics of the GA into two phases: the ascent towards the high ÿtness region, and from this high ÿtness region to a solution. To gain further information about the GA's behavior in the ÿrst phase, we construct two models based on the much simpler fully separable functions, and try to match instances which show a similar performance distribution. Although far from exact, this technique of comparing with analog search problems gives a hint about the landscape elements that are responsible for the GA's slow ascent.

Constraint Satisfaction Problems (CSP) have been widely studied in several research areas like Artificial Intelligence or Operational Research due their complexity and industrial interest. From previous research areas, heuristic (informed) search methods have been particularly active looking for feasible approaches. One of the critical problems to work with CSP is related to the exponential growth of computational resources needed to solve even the simplest problems. This paper presents a new efficient CSP graph-based representation to solve CSP by using Ant Colony Optimization (ACO) algorithms. This paper presents also a new heuristic (called Oblivion Rate), that have been designed to improve the current state-of-the-art in the application of ACO algorithms on these domains. The presented graph construction provides a strong reduction in both, the number of connections and the number of nodes needed to model the CSP. Also, the new heuristic is used to reduce the number of pheromones in the system (allowing to solve problems with an increasing complexity). This new approach has been tested, as case study, using the classical N-Queens Problem. Experimental results show how the new approach works in both, reducing the complexity of the resulting CSP graph and solving problems with increasing complexity through the utilization of the Oblivion Rate.

Constraint satisfaction problem is considered as an important area of research in artificial intelligence, so that many problems in artificial intelligence and other fields of computer science can be defined as constraint satisfaction problems (CSPs). On the other hand, there are situations where a problem needs to be solved in a distributed mode, such that it is impossible to use a central controller. In these conditions, the importance of multiagent systems is specified.

We investigate the complexity of the satisfiability problem of constraints over finite totally ordered domains. In our context, a clausal constraint is a disjunction of inequalities of the form x ≥ d and x ≤ d. We classify the complexity of constraints based on clausal patterns. A pattern abstracts away from variables and contains only information about the domain elements and the type of inequalities occurring in a constraint. Every finite set of patterns gives rise to a (clausal) constraint satisfaction problem in which all constraints in instances must have an allowed pattern. We prove that every such problem is either polynomially decidable or NPcomplete, and give a polynomial-time algorithm for recognizing the tractable cases. Some of these tractable cases are new and have not been previously identified in the literature. * The work has been supported byÉGIDE 06606ZF andÖAD Amadeus 18/2004. †

The active safety systems available on the passenger cars market today, automatically deploy automated safety interventions in situations where the driver is in need of assistance. In this paper, we consider the process of determining whether such interventions are needed. In particular, we design a threat assessment method which evaluates the risk that the vehicle will either leave the road or its maneuverability will be significantly reduced within a finite time horizon. The proposed threat assessment method accounts for combined braking and steering maneuvers, which results in a nonlinear dynamical vehicle behavior. We formulate the threat assessment problem as a nonconvex constraint satisfaction problem and implement an algorithm that solves it through interval-based consistency techniques. Experimental validation of the proposed approach indicates that constraint violation can be predicted, while avoiding the detection of false threats.

PCS is a CSP solver that can produce a machine-checkable deductive proof in case it decides that the input problem is unsatisfiable. The roots of the proof may be nonclausal constraints, whereas the rest of the proof is based on resolution of signed clauses, ending with the empty clause. PCS uses parameterized, constraint-specific inference rules in order to bridge between the nonclausal and the clausal parts of the proof. The consequent of each such rule is a signed clause that is 1) logically implied by the nonclausal premise, and 2) strong enough to be the premise of the consecutive proof steps. The resolution process itself is integrated in the learning mechanism, and can be seen as a generalization to CSP of a similar solution that is adopted by competitive SAT solvers.