Haut PDF Algorithms and ordering Heuristics for distributed constraint satisfaction problems

Algorithms and ordering Heuristics for distributed constraint satisfaction problems

Algorithms and ordering Heuristics for distributed constraint satisfaction problems

DisChoco offers a library of generators for distributed constraint satisfaction/optimization problems e.g., random binary DisCSPs using model B, random binary DisCSPs with complex local [r]

160 En savoir plus

Weight-based heuristics for constraint satisfaction and combinatorial optimization problems

Weight-based heuristics for constraint satisfaction and combinatorial optimization problems

More particularly, the purpose of this paper is to propose improving techniques for tree search. The method that we privileged here is discrepancy search, an alternative to depth first search (the principles and references are given in the next section on the scientific background). We then propose to analyze the causes of failures in the search tree and derive variables weighting for ordering heuristics. In the first part of the paper, we use these techniques for constraint satisfaction problems, in particular randomly generated CSPs and car-sequencing instances. A variant, named as YIELDS, of the seminal limited discrepancy search (LDS) method serves as a support for developing the search tree. In the second part, the techniques are adapted for handling combinatorial optimization problems. A climbing discrepancy search (CDS) variant with weighted factors is proposed for jobshop scheduling with time-lags. We selected this particular scheduling problem for its intrinsic genericity, as well as its practical relevance in the process industry.
En savoir plus

30 En savoir plus

Algorithms and Ordering Heuristics for Distributed Constraint Satisfaction Problems

Algorithms and Ordering Heuristics for Distributed Constraint Satisfaction Problems

DisChoco offers a library of generators for distributed constraint satisfaction/optimization problems e.g., random binary DisCSPs using model B, random binary DisCSPs with complex local [r]

161 En savoir plus

Using Constraint Satisfaction Techniques and Variational Methods for Probabilistic Reasoning

Using Constraint Satisfaction Techniques and Variational Methods for Probabilistic Reasoning

In GEM-MP, we first re-parameterized the factor graph in such a way that the infer- ence task (that could be performed by LBP inference on the original factor graph) is equivalent to a variational EM procedure. Then, we take advantage of the fact that LBP and variational EM can be viewed in terms of different types of free energy mini- mization equations. We formulate our Message-Passing structure as the E and M steps of a variational EM procedure (Beal and Ghahramani, 2003; Neal and Hinton, 1999). This variational formulation leads to the synthesis of new rules that update marginals by maximizing a lower bound of the model evidence such that we never overshoot the model evidence (Answering research question RQ1 ). In addition, in the corresponding Expectation step of GEM-MP, the constructed expected log marginal-likelihood has been defined according to the posterior distribution over local entries of the logical clauses that define factors. This enables us to exploit their logical structures by ap- plying a generalized arc-consistency concept (Rossi et al., 2006), and to use that to perform a variational mean-field approximation when updating the marginals. This significantly amends smoothing out the marginals to converge correctly to a stable con- vergent fixed point in the presence of determinism (Answering research question RQ2 ). Our experiments on real-world problems demonstrate the increased accuracy and con- vergence of GEM-MP compared to existing state-of-the-art inference algorithms such as MC-SAT, LBP, and Gibbs sampling, and convergent message passing algorithms such as the Concave-Convex Procedure (CCCP), Residual BP, and the L2-Convex method. • Preference Relaxation (PR), a new two-stage strategy that uses the deter- minism (i.e., hard constraints) present in the underlying model to improve the scalability of relational inference.
En savoir plus

191 En savoir plus

Strong consistencies for weighted constraint satisfaction problems

Strong consistencies for weighted constraint satisfaction problems

AC2001 & AC3.1 Both AC4 and AC6 are fine-grained algorithms. The disadvantage of these algorithms is that the value-oriented propagation queue is expensive to maintain. Therefore, Bessière and Régin [ 2001 ] proposed a coarse-grain algorithm AC-2001 which keeps the optimal time complexity of AC6, by memorizing only the current support for each value in order to avoid redundant constraint checks. This idea is also used in [ Zhang , 2001 ] in an algorithm named AC3.1. AC2001 uses a pointer to store the first support for every value on each constraint. On the one hand, this data structure is easier to implement and maintain than the lists of supported values used in AC6. On the other hand, similarly to the lists of supported values used in AC6, it allows AC2001 to stop the search for supports as soon as possible. The search for a new support for a value on a constraint does not check again values before the current support which were previously proved as incompatible with the considered value. In spite of the fact that AC2011 has the same asymptotic time and space complexity as AC6, it can provide speed-ups in practical experiments because of its simplicity.
En savoir plus

144 En savoir plus

Forbidden patterns in constraint satisfaction problems

Forbidden patterns in constraint satisfaction problems

Some problems cannot be solved by any algorithm. It is the case for instance of the Halting Problem (Turing, 1936). Other problems can be solved by some algorithm, but the time required to do so would be so long, millions of years for the current best computers, that it is often not worth the effort. One such example is the problem of whether or not two different regular expressions represent the same language (Meyer & Stockmeyer, 1972). Fortunately, a lot of problems, including most problems which arise in everyday life, can be solved in a relatively affordable time. They are in NP, the set of problems solvable in polynomial time by a non-deterministic Turing machine. Most work in computer science, or at least most work with the intent of solving problems, focuses on problems from NP. If P6=NP, then NP-Complete problems, the hardest to solve problems in NP, are not solvable in polynomial time, and may require algorithms with an exponential running time to be solved completely. However, by focusing on a single NP-Complete problem, one can still manage to find polynomial time algorithms which give interesting results. This can be done by only focusing on a subset of all possible instances of this problem. If successful, this approach leads to a tractable class. This can also be done by approximating, the act of finding a solution to the problem which is non-optimal, but close enough to be useful. One such work is (Raghavendra, 2008). Additionally, one can use selected randomized algorithms. Such algorithms can give an optimal solution in a polynomial time for any instance, but with a probability of only 1-, with  very small (Motwani & Raghavan, 1995).
En savoir plus

130 En savoir plus

An Extensive Evaluation of Portfolio Approaches for Constraint Satisfaction Problems

An Extensive Evaluation of Portfolio Approaches for Constraint Satisfaction Problems

characterizing each CSP, and the selection algorithms used for deciding the solver(s) to run on a given CSP. A. Dataset, Solvers and Features In order to build and test a good portfolio approach it is fundamental to gather an adequate dataset of CSPs. The data sample should capture a significant variety of problems encoded in the same language. Although nowadays the CP community has not yet agreed on a standard modelling language, MiniZinc [33] is probably the most used and supported language to model CP problems. However, the biggest existing dataset of CSPs we aware is the one used in the 2008 International Constraint Solver Competition (ICSC) [49]. These instances are encoded in the XML-based language XCSP [41]. In [2] an empirical evaluation on such a dataset was conducted. Here we take a step forward by exploiting the xcsp2mzn [3] compiler we developed for converting XCSP to MiniZinc. This allowed us to use a bigger benchmark of 8600 CSPs: 6944 instances of ICSC converted by xcsp2mzn, and 1656 native MiniZinc instances coming from the MiniZinc 1.6 benchmarks and the MiniZinc Challenge 2012.
En savoir plus

8 En savoir plus

Harnessing tractability in constraint satisfaction problems

Harnessing tractability in constraint satisfaction problems

original goal of explaining the performance of CSP and SAT solvers, and have attracted significant attention in the following years [125][56][72]. When approaching strong backdoors, one must make a clear distinction be- tween the solving phase, where the backdoor is known, and the computation of the backdoor. If a nontrivial backdoor B is already known then regardless of its size it is a useful information for a constraint solver, which can invoke a dedicated algorithm whenever the backtracking search procedure has assigned every variable in B (we omit small additional technical requirements here; variables outside B may have been assigned as well and the instance may have been reduced by aux- iliary inference, such as consistency algorithms). In fact, if the backdoor size k is quite large this approach is likely to be more efficient in practice than a straight de- composition of the instance into |D| k subproblems. For example, if a CSP instance has 150 variables a backdoor of size 40 provides an uncompetitive decomposition but can still allow a general backtracking algorithm to prune a large number of branches, even if the backdoor is not used to guide the branching heuristic. As a direct consequence, improving the worst-case complexity of the solving phase is important but not critical for the usefulness of the framework.
En savoir plus

138 En savoir plus

Tractability in constraint satisfaction problems: a survey

Tractability in constraint satisfaction problems: a survey

a constraint graph in the form of a tree provides no more information than we would obtain by applying arc consistency to the original instance I. Many tractable classes of CSP are automatically solved in polynomial time by any algorithm which maintains (generalised) arc consistency during search: we can notably cite the class of instances with max-closed constraints [113], the class of instances whose constraints are max-closed after independent permutations of each domain [93] and the class of binary instances satisfying the broken-triangle property [58]. Simi- larly, Valued CSPs with submodular constraints are automatically solved by establish- ing OSAC (Optimal Soft Arc Consistency) [57]. Present-day solvers do not explicitly look for tractable classes, but by analysis of the algorithms they use it is sometimes possible to show that they automatically solve certain tractable classes. For instance, translating CSP instances with max-closed constraints [113] or CSP instances with connected row-convex constraints [75] into SAT instances using the order encoding produces instances that fall into known tractable classes of SAT which are solved ef- ficiently by modern clause-learning SAT-solvers [145,109]. Tractable classes that are automatically solved by standard algorithms are nevertheless useful since proving that the solver will always execute in polynomial time in a given application provides a potentially important guarantee of efficiency.
En savoir plus

34 En savoir plus

Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree

Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree

All three algorithms that we present in this work follow the same broad outline, while the details are different in each case. To produce an assignment that beats a random assignment, the idea is to partition the variables in to two sets (F, G) with F standing for ‘Fixed’ and G standing for ‘Greedy’ (in Section 4, these correspond to [n] \ U and U respectively). The variables in F are assigned independent and uniform random bits and the variables in G are assigned values greedily based on the values already assigned to F . We will refer to constraints with exactly one variable from G as active constraints. The design of the greedy assignments and their analysis is driven by two key objectives.
En savoir plus

15 En savoir plus

Tractability in Constraint Satisfaction Problems: A Survey

Tractability in Constraint Satisfaction Problems: A Survey

Many tractable classes of CSP are automatically solved in polynomial time by any algorithm which maintains (generalised) arc consistency during search: we can notably cite the class of instances with max-closed constraints [113], the class of instances whose constraints are max-closed after independent permutations of each domain [93] and the class of binary instances satisfying the broken-triangle property [58]. Simi- larly, Valued CSPs with submodular constraints are automatically solved by establish- ing OSAC (Optimal Soft Arc Consistency) [57]. Present-day solvers do not explicitly look for tractable classes, but by analysis of the algorithms they use it is sometimes possible to show that they automatically solve certain tractable classes. For instance, translating CSP instances with max-closed constraints [113] or CSP instances with connected row-convex constraints [75] into SAT instances using the order encoding produces instances that fall into known tractable classes of SAT which are solved ef- ficiently by modern clause-learning SAT-solvers [145,109]. Tractable classes that are automatically solved by standard algorithms are nevertheless useful since proving that the solver will always execute in polynomial time in a given application provides a potentially important guarantee of efficiency.
En savoir plus

34 En savoir plus

Improvement and Integration of Counting-Based Search Heuristics in Constraint Programming

Improvement and Integration of Counting-Based Search Heuristics in Constraint Programming

7.2 Limits and Constraints It would be strange to say that our improvements of counting algorithms in Section 3 have limitations. We proposed better algorithms in both theory and practice; they have better asymptotic complexities and are faster in our benchmarks when choosing hard instances. One could argue that our approach for avoiding systematic recomputation has the limitation that it has lower precision, but we see it more as a trade off between speed and precision. In my opinion, limitations arise when considering practical matters, which comes from the choice of a paradigm — counting-based search — and its actual implementation in Gecode. While generic and powerful, using counting-based search indeed limits the constraints we can use for modeling in practice. In other words, the problems we can solve are limited by the constraints we support (using CBS with some uninstrumented constraints is possible, but it is less effective because we miss solution densities). Furthermore, supporting a new constraint is difficult: we have to design a new counting algorithm and provide an efficient implementation. As CP solvers support a lot of different constraints, designing counting algorithms is a long-term project. This is a price we must pay for having a family of generic branching heuristics that performs well and adapts to the problem formulation.
En savoir plus

72 En savoir plus

Binarisation for valued constraint satisfaction problems

Binarisation for valued constraint satisfaction problems

One important class of valued constraint languages are the submodular languages [ 45 ]. It is known that VCSP instances where all constraints are submodular can be solved in polynomial time, although the algorithms that have been proposed to achieve this in the general case are rather intricate and difficult to implement [ 27 , 44 ]. In the special case of binary submodular constraints a much simpler algorithm can be used to find a minimising assignment of values, based on a standard max-flow algorithm [ 15 ]. Our results in this paper show that this simpler algorithm can be used to obtain exact solutions to arbitrary VCSP instances with submodular constraints (from a finite language) in polynomial time.
En savoir plus

25 En savoir plus

Binarisation for valued constraint satisfaction problems

Binarisation for valued constraint satisfaction problems

One important class of valued constraint languages are the submodular languages [ 45 ]. It is known that VCSP instances where all constraints are submodular can be solved in polynomial time, although the algorithms that have been proposed to achieve this in the general case are rather intricate and difficult to implement [ 27 , 44 ]. In the special case of binary submodular constraints a much simpler algorithm can be used to find a minimising assignment of values, based on a standard max-flow algorithm [ 15 ]. Our results in this paper show that this simpler algorithm can be used to obtain exact solutions to arbitrary VCSP instances with submodular constraints (from a finite language) in polynomial time.
En savoir plus

26 En savoir plus

Global Inverse Consistency for Interactive Constraint Satisfaction

Global Inverse Consistency for Interactive Constraint Satisfaction

7 Conclusion We have analysed the problems that arise in applications that require the interactive resolution of a constraint problem by a human user. The central notion is global inverse consistency of the network because it ensures that the person who interactively solves the problem is not given the choice to select values that do not lead to solutions. We have shown that deciding, computing, or restoring global inverse consistency, and other related problems are all NP-hard. We have proposed several algorithms for enforcing global inverse consistency and we have shown that the best version is efficient enough to be used in an interactive setting on several configuration and design problems. This is a great advantage compared to existing techniques usually used in configurators. As opposed to techniques maintaining arc consistency, our algorithms give an exact picture of the values remaining feasible. As opposed to compiling offline the problem as a multi-valued decision diagram, our algorithms can deal with constraint networks that change over time (e.g., an extra non-unary constraint posted by a customer who does not want to buy a car with more than 100,000 miles except if it is a Volvo). We have finally extended our contribution to the inverse consistency of tuples, which is useful at the modelling phase of configuration problems.
En savoir plus

17 En savoir plus

A study of constraint programming heuristics for the car-sequencing problem

A study of constraint programming heuristics for the car-sequencing problem

Univ de Toulouse, LAAS, F-31400 Toulouse, France Abstract In the car-sequencing problem, a number of cars has to be sequenced on an assembly line respecting several constraints. This problem was addressed by both Operations Research (OR) and Constraint Programming (CP) com- munities, either as a decision problem or as an optimization problem. In this paper, we consider the decision variant of the car sequencing problem and we propose a systematic way to classify heuristics for solving it. This classification is based on a set of four criteria, and we consider all relevant combinations for these criteria. Some combinations correspond to common heuristics used in the past, whereas many others are novel. Not surprisingly, our empirical evaluation confirms earlier findings that specific heuristics are very important for efficiently solving the car-sequencing problem (see for in- stance [17]), in fact, often as important or more than the propagation method. Moreover, through a criteria analysis, we are able to get several new insights into what makes a good heuristic for this problem. In particular, we show that the criterion used to select the most constrained option is critical, and the best choice is fairly reliably the “load” of an option. Similarly, branching on the type of vehicle is more efficient than branching on the use of an option. Overall, we can therefore indicate with a relatively high confidence which is the most robust strategy, or at least outline a small set of potentially best strategies.
En savoir plus

29 En savoir plus

Portfolio Approaches for Constraint Optimization Problems

Portfolio Approaches for Constraint Optimization Problems

2 Solution quality evaluation When satisfaction problems are considered, the definition and the evaluation of a portfolio solver is straightforward. Indeed, the outcome of a solver run for a given time on a given instance can be either ’solved’ (i.e., a solution is found or the unsatisfiability is proven) or ’not solved’ (i.e., the solver does not say anything about the problem). Building and evaluating a CSP solver is then conceptually easy: the goal is to maximize the number of solved instances, solving them as fast as possible. Unfortunately, in the COP world the dichotomy solved/not solved is no longer suitable. A COP solver in fact can provide sub-optimal solutions or even give the optimal one without being able to prove its optimality. Moreover, in order to speed up the search COP solvers could be executed in a non-independent way. Indeed, the knowledge of a sub-optimal solution can be used by a solver to further prune its search space, and therefore to speed up the search process. Thus, the independent (even parallel) execution of a sequence of solvers may differ from a “cooperative” execution where the best solution found by a given solver is used as a lower bound by the solvers that are launched afterwards.
En savoir plus

21 En savoir plus

An approach to solving constraint satisfaction problems using asynchronous teams of autonomous agents

An approach to solving constraint satisfaction problems using asynchronous teams of autonomous agents

Other approaches try to use qualitative reasoning systems instead of the low level detailed representation to capture the functional behavior of design [For88]. Such[r]

147 En savoir plus

Pattern-based constraint satisfaction and logic puzzles

Pattern-based constraint satisfaction and logic puzzles

4. CSP Resolution Theories Before we try to capture CSP Resolution Theories in a logical formalism, we must establish a clear distinction between a logical theory of the CSP itself (as it has been formulated in chapter 3, with no reference to candidates) and theories related to the resolution methods (which we consider from now on as being based on the progressive elimination of candidates). These two kinds of theories correspond to two options: are we just interested in formulating a set of axioms describing the constraints a solution of a given CSP instance (if it has any) must satisfy or do we want a theory that somehow applies to intermediate states in the resolution process? To maintain this distinction as clearly as possible, we shall consistently use the expressions “CSP Theory” for the first type and “CSP Resolution Theory” for the second type. Section 4.1 elaborates on this distinction. Since it has been shown in chapter 3 that formulating the first theory is straightforward, theories of the second kind will remain as our main topic of interest in the present book. Nevertheless, it will be necessary to clarify the relationship between the two types of theories and between their respective basic notions (“value” and “candidate”).
En savoir plus

487 En savoir plus

Algebraic Algorithms for Matching and Matroid Problems

Algebraic Algorithms for Matching and Matroid Problems

For nonbipartite matching, we obtain a simple, purely algebraic algorithm with running time Onω where n is the number of vertices and ω is the matrix multiplication exponent.. This reso[r]

25 En savoir plus

Show all 10000 documents...