scholarly journals Binary Encodings of Non-binary Constraint Satisfaction Problems: Algorithms and Experimental Results

2005 ◽  
Vol 24 ◽  
pp. 641-684 ◽  
Author(s):  
N. Samaras ◽  
K. Stergiou
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Binary Representation ◽  
Binary Constraints ◽  
Arc Consistency ◽  
Binary Problem ◽  
Binary Constraint ◽  
Binary Problems ◽  
Standard Techniques

A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques. Alternatively, the non-binary problem can be translated into an equivalent binary one. In this case, it is generally accepted that the translated problem can be solved by applying well-established techniques for binary CSPs. In this paper we evaluate the applicability of the latter approach. We demonstrate that the use of standard techniques for binary CSPs in the encodings of non-binary problems is problematic and results in models that are very rarely competitive with the non-binary representation. To overcome this, we propose specialized arc consistency and search algorithms for binary encodings, and we evaluate them theoretically and empirically. We consider three binary representations; the hidden variable encoding, the dual encoding, and the double encoding. Theoretical and empirical results show that, for certain classes of non-binary constraints, binary encodings are a competitive option, and in many cases, a better one than the non-binary representation.

STRONG DOMAIN FILTERING CONSISTENCIES FOR NON-BINARY CONSTRAINT SATISFACTION PROBLEMS

2008 ◽  
Vol 17 (05) ◽  
pp. 781-802 ◽  
Author(s):  
KOSTAS STERGIOU
Keyword(s):  
Empirical Study ◽  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problems ◽  
Worst Case ◽  
Generic Algorithm ◽  
Binary Constraints ◽  
Binary Constraint

Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with non-binary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong domain filtering consistencies for non-binary constraints and theoretically compare their pruning power. We prove that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for domain filtering consistencies in non-binary CSPs. We show how this algorithm can be instantiated to enforce some of the proposed consistencies and analyze the worst-case complexities of the resulting algorithms. Finally, we make a preliminary empirical study.

PREPROCESSING QUANTIFIED CONSTRAINT SATISFACTION PROBLEMS WITH VALUE REORDERING AND DIRECTIONAL ARC AND PATH CONSISTENCY

2008 ◽  
Vol 17 (02) ◽  
pp. 321-337 ◽  
Author(s):  
KOSTAS STERGIOU
Keyword(s):  
Constraint Satisfaction ◽  
Early Stage ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Combinatorial Problems ◽  
Arc Consistency ◽  
Solution Methods ◽  
Speed Up ◽  
Phase Transition Region ◽  
The Impact

The Quantified Constraint Satisfaction Problem (QCSP) is an extension of the CSP that can be used to model combinatorial problems containing contingency or uncertainty. It allows for universally quantified variables that can model uncertain actions and events, such as the unknown weather for a future party, or an opponent's next move in a game. Although interest in QCSPs is increasing in recent years, the development of techniques for handling QCSPs is still at an early stage. For example, although it is well known that local consistencies are of primary importance in CSPs, only arc consistency has been extended to quantified problems. In this paper we contribute towards the development of solution methods for QCSPs in two ways. First, by extending directional arc and path consistency, two popular local consistencies in constraint satisfaction, to the quantified case and proposing an algorithm that achieves these consistencies. Second, by showing how value ordering heuristics can be utilized to speed up computation in QCSPs. We study the impact of preprocessing QCSPs with value reordering and directional quantified arc and path consistency by running experiments on randomly generated problems. Results show that our preprocessing methods can significantly speed up the QCSP solving process, especially on hard instances from the phase transition region.

The Goldilocks problem

2003 ◽  
Vol 17 (1) ◽  
pp. 3-11 ◽  
Author(s):  
TUDOR HULUBEI ◽  
EUGENE C. FREUDER ◽  
RICHARD J. WALLACE
Keyword(s):  
Constraint Satisfaction ◽  
Feasible Solution ◽  
Constraint Satisfaction Problem ◽  
Real Life ◽  
Constraint Satisfaction Problems ◽  
Major Focus ◽  
Huge Number ◽  
Arc Consistency ◽  
A Value ◽  
Practical Standpoint

Constraint-based reasoning is often used to represent and find solutions to configuration problems. In the field of constraint satisfaction, the major focus has been on finding solutions to difficult problems. However, many real-life configuration problems, although not extremely complicated, have a huge number of solutions, few of which are acceptable from a practical standpoint. In this paper we present a value ordering heuristic for constraint solving that attempts to guide search toward solutions that are acceptable. More specifically, by considering weights that are assigned to values and sets of values, the heuristic can guide search toward solutions for which the total weight is within an acceptable interval. Experiments with random constraint satisfaction problems demonstrate that, when a problem has numerous solutions, the heuristic makes search extremely efficient even when there are relatively few solutions that fall within the interval of acceptable weights. In these cases, an algorithm that is very effective for finding a feasible solution to a given constraint satisfaction problem (the “maintained arc consistency” algorithm or MAC) does not find a solution in the same weight interval within a reasonable time when it is run without the heuristic.

scholarly journals A Variable Depth Search Algorithm for Binary Constraint Satisfaction Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
N. Bouhmala
Keyword(s):  
Constraint Satisfaction ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Wide Spectrum ◽  
Constraint Satisfaction Problem ◽  
Practical Interest ◽  
Constraint Satisfaction Problems ◽  
Variable Depth ◽  
The Past ◽  
Binary Constraint

The constraint satisfaction problem (CSP) is a popular used paradigm to model a wide spectrum of optimization problems in artificial intelligence. This paper presents a fast metaheuristic for solving binary constraint satisfaction problems. The method can be classified as a variable depth search metaheuristic combining a greedy local search using a self-adaptive weighting strategy on the constraint weights. Several metaheuristics have been developed in the past using various penalty weight mechanisms on the constraints. What distinguishes the proposed metaheuristic from those developed in the past is the update ofkvariables during each iteration when moving from one assignment of values to another. The benchmark is based on hard random constraint satisfaction problems enjoying several features that make them of a great theoretical and practical interest. The results show that the proposed metaheuristic is capable of solving hard unsolved problems that still remain a challenge for both complete and incomplete methods. In addition, the proposed metaheuristic is remarkably faster than all existing solvers when tested on previously solved instances. Finally, its distinctive feature contrary to other metaheuristics is the absence of parameter tuning making it highly suitable in practical scenarios.

scholarly journals Bipartite Encoding: A New Binary Encoding for Solving Non-Binary CSPs

2020 ◽  
Author(s):  
Ruiwei Wang ◽  
Roland H.C. Yap
Keyword(s):  
Constraint Satisfaction ◽  
State Of The Art ◽  
Constraint Satisfaction Problems ◽  
Special Structure ◽  
Large Set ◽  
Hidden Variable ◽  
Binary Constraints ◽  
Arc Consistency ◽  
Binary Encoding

Constraint Satisfaction Problems (CSPs) are typically solved with Generalized Arc Consistency (GAC). A general CSP can also be encoded into a binary CSP and solved with Arc Consistency (AC). The well-known Hidden Variable Encoding (HVE) is still a state-of-the-art binary encoding for solving CSPs. We propose a new binary encoding, called Bipartite Encoding (BE) which uses the idea of partitioning constraints. A BE encoded CSP can achieve a higher level of consistency than GAC on the original CSP. We give an algorithm for creating compact bipartite encoding for non-binary CSPs. We present a AC propagator on the binary constraints from BE exploiting their special structure. Experiments on a large set of non-binary CSP benchmarks with table constraints using the Wdeg, Activity and Impact heuristics show that BE with our AC propagator can outperform existing state-of-the-art GAC algorithms (CT, STRbit) and binary encodings (HVE with HTAC).

scholarly journals A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

2011 ◽  
Vol 21 (4) ◽  
pp. 733-744 ◽  
Author(s):  
Marlene Arangú ◽  
Miguel Salido
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Real Life ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Fine Grained ◽  
Arc Consistency ◽  
Life Problems ◽  
Programming Techniques ◽  
Np Complete

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

scholarly journals Constraint programming viewed as rule-based programming

2001 ◽  
Vol 1 (6) ◽  
pp. 713-750 ◽  
Author(s):  
KRZYSZTOF R. APT ◽  
ERIC MONFROY
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Constraint Satisfaction Problems ◽  
Rule Based ◽  
Local Consistency ◽  
Arc Consistency ◽  
Computation Process ◽  
Rule Based Approach ◽  
Rule Consistency

We study here a natural situation when constraint programming can be entirely reduced to rule-based programming. To this end we explain first how one can compute on constraint satisfaction problems using rules represented by simple first-order formulas. Then we consider constraint satisfaction problems that are based on predefined, explicitly given constraints. To solve them we first derive rules from these explicitly given constraints and limit the computation process to a repeated application of these rules, combined with labeling. We consider two types of rule here. The first type, that we call equality rules, leads to a new notion of local consistency, called rule consistency that turns out to be weaker than arc consistency for constraints of arbitrary arity (called hyper-arc consistency in Marriott & Stuckey (1998)). For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. The second type of rules, that we call membership rules, yields a rule-based characterization of arc consistency. To show feasibility of this rule-based approach to constraint programming, we show how both types of rules can be automatically generated, as CHR rules of Frühwirth (1995). This yields an implementation of this approach to programming by means of constraint logic programming. We illustrate the usefulness of this approach to constraint programming by discussing various examples, including Boolean constraints, two typical examples of many valued logics, constraints dealing with Waltz's language for describing polyhedral scenes, and Allen's qualitative approach to temporal logic.

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