A Decomposition Technique for Solving {Max-CSP} (original) (raw)
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A Decomposition Technique for Max-CSP
European Conference on Artificial Intelligence, 2008
The objective of the Maximal Constraint Satisfaction Problem (Max-CSP) is to find an instantiation which minimizes the number of constraint violations in a constraint network. In this paper, inspired from the concept of inferred disjunctive constraints intro- duced by Freuder and Hubbe, we show that it is possible to exploit the arc-inconsistency counts, associated with each value of a net-
Enhancements of Branch and Bound Methods for the Maximal Constraint Satisfaction Problem
1996
Two methods are described for enhancing performance of branch and bound methods for overconstrained CSPs. These methods improve either the upper or lower bound, respectively, during search, so the two can be combined. Upper bounds are improved by using heuristic repair methods before search to find a good solution quickly, whose cost is used as the initial upper bound. The method for improving lower bounds is an extension of directed arc consistency preprocessing, used in conjunction with forward checking. After computing directed arc consistency counts, inferred counts are computed for all values based on minimum counts for values of adjacent variables that are later in the search order. This inference process can be iterated, so that counts are cascaded from the end to the beginning of the search order, to augment the initial counts. Improvements in time and effort are demonstrated for both techniques using random problems.
Algorithms for Constraint Satisfaction Problems (CSPs
Many problems in AI can be modeled as constraint satisfaction problems (CSPs). Hence the development of e ective solution techniques for CSPs is an important research problem. Forward checking (FC) with some other heuristics has been traditionally considered to be the best algorithm for solving CSPs while recently there have been a number of claims that maintaining arc consistency (MAC) is more e cient on large and hard CSPs. In this thesis, we p r o vide a systematic comparison empirically of the performances of the MAC a n d F C algorithms on large and hard CSPs. In particular, we compare their performance with regard to the size, constraint density and constraint t i g h tness of the problems. Though there is a trend that MAC e v entually outperforms FC on hard problems as we increase the problem size, we found that the superiority o f M A C o ver FC w ould not be revealed on the hard problems with low constraint t i g h tness and high constraint density u n til the size of these problems is quite large. We also devised a new FC algorithm | FC4, which s h o ws good performance on the hard problems with low constraint tightness and high constraint density. iv I w ould also like to thank Jean-Charles Regin of ILOG for providing his programs, and his assistance in my understanding his algorithms.
AC2001-OP: an arc-consistency algorithm for constraint satisfaction problems
Trends in Applied Intelligent Systems, 2010
Arc-consistency algorithms are widely used to prune the search space of Constraint Satisfaction Problems (CSPs). One of the most well-known arc-consistency algorithms for filtering CSPs is AC3. This algorithm repeatedly carries out revisions and requires support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, that is, they cannot delete any value and they require a lot of checks and are time-consuming. We present AC3-OP, an optimized and reformulated version of AC3 that reduces the number of constraint checks and prunes the same CSP search space with arithmetic constraints. In inequality constraints, AC3-OP, checks the binary constraints in both directions (full arc-consistency), but it only propagates new constraints in one direction. Thus, it avoids checking redundant constraints that do not filter any value of the variable's domain. The evaluation section shows the improvement of AC3-OP over AC3 in random instances.
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Artificial Intelligence: Methodology, Systems, and …, 2004
Nowadays, many real problem in Artificial Intelligence can be modeled as constraint satisfaction problems (CSPs). A general rule in constraint satisfaction is to tackle the hardest part of a search problem first. In this paper, we introduce a parameter (τ ) that measures the constrainedness of a search problem. This parameter represents the probability of the problem being feasible. A value of τ = 0 corresponds to an over-constrained problem and no states are expected to be solutions. A value of τ = 1 corresponds to an under-constrained problem which every state is a solution. This parameter can also be used in a heuristic to guide search. To achieve this parameter, a sample in finite population is carried out to compute the tightnesses of each constraint. We take advantage of this tightnesses to classify the constraints from the tightest constraint to the loosest constraint. This heuristic may accelerate the search due to inconsistencies can be found earlier and the number of constraint checks can significantly be reduced.
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Abstract A constraint satisfaction problem (CSP) involves a set of variables, a domain of potential values for each variable, and a set of constraints, which specifies the acceptable combinations of values. One popular approach is to represent the original problem as a constraint network where nodes represent variables and arcs represent constraints between variables. Node consistency and arc consistency techniques are first applied to prune the domains of variables.
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A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems
International Journal of Applied Mathematics and Computer Science, 2011
Constraint programming is a powerful software technology for solving many real-life problems. Many of these problems can be modeled as constraint satisfaction problems (CSPs) and can be solved using constraint programming techniques. However, solving a CSP is NP-Complete so that filtering techniques to reduce the search space are still necessary. Arcconsistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, that is, it must be ensured in both directions of the constraint (direct constraint and inverse constraint). Two of the most wellknown and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and they require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, that is, they cannot delete any value and they consume a lot of checks and time.
New look-ahead schemes for constraint satisfaction
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This paper presents new look-ahead schemes for backtracking search when solving constraint satisfaction problems. The look-ahead schemes compute a heuristic for value ordering and domain pruning, which influences variable orderings at each node in the search space. As a basis for a heuristic, we investigate two tasks, both harder than the CSP task. The first is finding the solution with min-number of conflicts. The second is counting solutions. Clearly each of these tasks also finds a solution to the CSP problem, if one exists, or decides that the problem is inconsistent. Our plan is to use approximations of these more complex tasks as heuristics for guiding search for a solution of a CSP task. In particular, we investigate two recent partitionbased strategies that approximate variable elimination algorithms, Mini-Bucket-Tree Elimination and Iterative Join-Graph Propagation (ijgp). The latter belong to the class of belief propagation algorithm that attracted substantial interest due to their surprising success for probabilistic inference. Our preliminary empirical evaluation is very encouraging, demonstrating that the countingbased heuristic approximated by by IJGP yields a very focused search even for hard problems.
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Local consistency properties and algorithms for enforcing them are central to the success of Constraint Processing. In this paper, we explore how to exploit the structure of the problem on the performance of the algorithm for enforcing consistency. We propose various strategies for managing the propagation queue of an algorithm for enforcing consistency, and empirically compare their effectiveness for solving CSPs with backtrack search and full lookahead. We focus our investigations on consistency algorithms that operate on the dual graph of a CSP and demonstrate the importance of exploiting a tree decomposition of the dual graph. Further, we note that exploiting structure is particularly striking on unsatisfiable instances. We conjecture that the approach for queue-management strategies benefits virtually all other propagation algorithms.