scholarly journals A CHR-based implementation of known arc-consistency

2005 ◽  
Vol 5 (4-5) ◽  
pp. 419-440 ◽  
Author(s):  
MARCO ALBERTI ◽  
MARCO GAVANELLI ◽  
EVELINA LAMMA ◽  
PAOLA MELLO ◽  
MICHELA MILANO
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
External Environment ◽  
Computation Time ◽  
Constraint Propagation ◽  
Constraint Handling ◽  
Declarative Language ◽  
Propagation Process ◽  
Arc Consistency ◽  
High Level

In classical CLP(FD) systems, domains of variables are completely known at the beginning of the constraint propagation process. However, in systems interacting with an external environment, acquiring the whole domains of variables before the beginning of constraint propagation may cause waste of computation time, or even obsolescence of the acquired data at the time of use. For such cases, the Interactive Constraint Satisfaction Problem (ICSP) model has been proposed (Cucchiara et al. 1999a) as an extension of the CSP model, to make it possible to start constraint propagation even when domains are not fully known, performing acquisition of domain elements only when necessary, and without the need for restarting the propagation after every acquisition. In this paper, we show how a solver for the two sorted CLP language, defined in previous work (Gavanelli et al. 2005) to express ICSPs, has been implemented in the Constraint Handling Rules (CHR) language, a declarative language particularly suitable for high level implementation of constraint solvers.

scholarly journals A Reactive Strategy for High-Level Consistency During Search

2018 ◽  
Author(s):  
Robert J. Woodward ◽  
Berthe Y. Choueiry ◽  
Christian Bessiere
Keyword(s):  
Constraint Satisfaction Problem ◽  
Constraint Propagation ◽  
Search Tree ◽  
Benchmark Problems ◽  
Search Performance ◽  
Arc Consistency ◽  
Backtrack Search ◽  
Reactive Strategy ◽  
Active Research ◽  
High Level

Constraint propagation during backtrack search significantly improves the performance of solving a Constraint Satisfaction Problem. While Generalized Arc Consistency (GAC) is the most popular level of propagation, higher-level consistencies (HLC) are needed to solve difficult instances. Deciding to enforce an HLC instead of GAC remains the topic of active research. We propose a simple and effective strategy that reactively triggers an HLC by monitoring search performance: When search starts thrashing, we trigger an HLC, then conservatively revert to GAC. We detect thrashing by counting the number of backtracks at each level of the search tree and geometrically adjust the frequency of triggering an HLC based on its filtering effectiveness. We validate our approach on benchmark problems using Partition-One Arc-Consistency as an HLC. However, our strategy is generic and can be used with other higher-level consistency algorithms.

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.

A classification and constraint-based framework for configuration

1998 ◽  
Vol 12 (4) ◽  
pp. 383-397 ◽  
Author(s):  
DANIEL MAILHARRO
Keyword(s):  
Constraint Satisfaction ◽  
Domain Knowledge ◽  
Constraint Satisfaction Problem ◽  
Object Oriented ◽  
Classification Problem ◽  
Single Model ◽  
Arc Consistency ◽  
Configuration Problem ◽  
Taxonomic Reasoning ◽  
New Framework

One of the main difficulties with configuration problem solving lies in the representation of the domain knowledge because many different aspects, such as taxonomy, topology, constraints, resource balancing, component generation, etc., have to be captured in a single model. This model must be expressive, declarative, and structured enough to be easy to maintain and to be easily used by many different kind of reasoning algorithms. This paper presents a new framework where a configuration problem is considered both as a classification problem and as a constraint satisfaction problem (CSP). Our approach deeply blends concepts from the CSP and object-oriented paradigms to adopt the strengths of both. We expose how we have integrated taxonomic reasoning in the constraint programming schema. We also introduce new constrained variables with nonfinite domains to deal with the fact that the set of components is previously unknown and is constructed during the search for solution. Our work strongly focuses on the representation and the structuring of the domain knowledge, because the most common drawback of previous works is the difficulty to maintain the knowledge base that is due to a lack of structure and expressiveness of the knowledge representation model. The main contribution of our work is to provide an object-oriented model completely integrated in the CSP schema, with inheritance and classification mechanisms, and with specific arc consistency algorithms.

Extending Fuzzy Constraint Satisfaction Problems

2006 ◽  
Vol 10 (4) ◽  
pp. 465-471 ◽  
Author(s):  
Yasuhiro Sudo ◽  
◽  
Masahito Kurihara ◽  
Tamotsu Mitamura ◽  
◽  
...  
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Computation Time ◽  
Approximate Solutions ◽  
Constraint Satisfaction Problems ◽  
Test Problems ◽  
Hybrid Domain ◽  
Fuzzy Constraint ◽  
Fuzzy Constraint Satisfaction ◽  
Discrete Domains

This paper propose a new type of Fuzzy CSP (Constraint Satisfaction Problem) that have a mixture of discrete and continuous domains, and a Spread-Repair algorithm. In traditional CSP and Fuzzy CSP, values for the variables are chosen from the discrete domains. However, this is often inconvenient when one wants to express real world problems. We show that this model, called HDFCSP (Hybrid Domain Fuzzy CSP), can be solved by Spread-Repair, an extension of the well known iterative improvement algorithms. Experimental results on some test problems show that the algorithm actually has an ability of finding partial approximate solutions with high probability in a computation time much shorter than the traditional, discrete-domain FCSP.

SPECIFIC CONSTRAINT HANDLING IN CONSTRAINT SATISFACTION PROBLEMS

1994 ◽  
Vol 03 (01) ◽  
pp. 79-96
Author(s):  
BING LIU
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Constraint Handling ◽  
Consistency Check ◽  
Arc Consistency ◽  
Individual Constraint ◽  
Network Consistency

Abundant literatures exist on consistency techniques for solving Constraint Satisfaction Problems (CSPs). These literatures, however, focused mainly on finding efficient general techniques to achieve network consistency and to solve CSPs. So far, many techniques have been reported, e.g., node consistency, arc consistency, path consistency, k-consistency, forward checking, lookahead, partial lookahead, etc. Not enough attention has been given to individual constraints, and how constraint specific features may be exploited for more efficient consistency check. Many types of constraints exist in real problems, and each has its own features. These features may allow specific consistency techniques to be designed such that they are more efficient than the general algorithms. To analyze this issue, we divide a consistency algorithm into three parts: (1) activating constraints for check; (2) selecting the next constraint to be checked; and (3) checking the selected constraint. We will discuss how constraint specific features may influence each of these aspects and how special handling techniques may be designed to improve the efficiency. In order to allow these individual constraint handling techniques to be used, a new consistency algorithm is also proposed.

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 Early and Efficient Identification of Useless Constraint Propagation for Alldifferent Constraints

2020 ◽  
Author(s):  
Xizhe Zhang ◽  
Jian Gao ◽  
Yizhi Lv ◽  
Weixiong Zhang
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Propagation ◽  
Constraint Satisfaction Problems ◽  
Benchmark Problem ◽  
Value Assignment ◽  
Arc Consistency ◽  
A Value ◽  
Removable Edge ◽  
Problem Instances ◽  
State Of Art

Constraints propagation and backtracking are two basic techniques for solving constraint satisfaction problems (CSPs). During the search for a solution, the variable and value pairs that do not belong to any solution can be discarded by constraint propagation to ensure generalized arc consistency so as to avoid the fruitless search. However, constraint propagation is frequently invoked often with little effect on many CSPs. Much effort has been devoted to predicting when to invoke constraint propagation for solving a CSP; however, no effective approach has been developed for the alldifferent constraint. Here we present a novel theorem for identifying the edges in a value graph of alldifferent constraint whose removal can significantly reduce useless constraint propagation. We prove that if an alternating cycle exists for a prospectively removable edge that represents a variable-value assignment, the edge (and the assignment) can be discarded without constraint propagation. Based on this theorem, we developed a novel optimizing technique for early detection of useless constraint propagation which can be incorporated in any existing algorithm for alldifferent constraint. Our implementation of the new method achieved speedup by a factor of 1-5 over the state-of-art approaches on 93 benchmark problem instances in 8 domains. Furthermore, the new algorithm is scalable well and runs increasingly faster than the existing methods on larger problems.

scholarly journals MUSE CSP: An Extension to the Constraint Satisfaction Problem

1996 ◽  
Vol 5 ◽  
pp. 239-288
Author(s):  
R. A. Helzerman ◽  
M. P. Harper
Keyword(s):  
Computer Vision ◽  
Constraint Satisfaction ◽  
Speech Processing ◽  
Constraint Satisfaction Problem ◽  
Handwriting Recognition ◽  
Arc Consistency ◽  
Single Instance ◽  
Shared Variables ◽  
Segmentation Algorithms ◽  
Level Information

This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of partially shared variables. Such problems arise naturally in signal processing applications including computer vision, speech processing, and handwriting recognition. For these applications, it is often difficult to segment the data in only one way given the low-level information utilized by the segmentation algorithms. MUSE CSP can be used to compactly represent several similar instances of the constraint satisfaction problem. If multiple instances of a CSP have some common variables which have the same domains and constraints, then they can be combined into a single instance of a MUSE CSP, reducing the work required to apply the constraints. We introduce the concepts of MUSE node consistency, MUSE arc consistency, and MUSE path consistency. We then demonstrate how MUSE CSP can be used to compactly represent lexically ambiguous sentences and the multiple sentence hypotheses that are often generated by speech recognition algorithms so that grammar constraints can be used to provide parses for all syntactically correct sentences. Algorithms for MUSE arc and path consistency are provided. Finally, we discuss how to create a MUSE CSP from a set of CSPs which are labeled to indicate when the same variable is shared by more than a single CSP.

scholarly journals Localization of a Vehicle: A Dynamic Interval Constraint Satisfaction Problem-Based Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Kangni Kueviakoe ◽  
Zhan Wang ◽  
Alain Lambert ◽  
Emmanuelle Frenoux ◽  
Philippe Tarroux
Keyword(s):  
Kalman Filter ◽  
Bayesian Methods ◽  
Constraint Satisfaction ◽  
Measurement Errors ◽  
Constraint Satisfaction Problem ◽  
Constraint Propagation ◽  
Gps Receiver ◽  
Localization Problem ◽  
Vehicle Localization ◽  
Interval Constraint

This paper introduces a new interval constraint propagation (ICP) approach dealing with the real-time vehicle localization problem. Bayesian methods like extended Kalman filter (EKF) are classically used to achieve vehicle localization. ICP is an alternative which provides guaranteed localization results rather than probabilities. Our approach assumes that all models and measurement errors are bounded within known limits without any other hypotheses on the probability distribution. The proposed algorithm uses a low-level consistency algorithm and has been validated with an outdoor vehicle equipped with a GPS receiver, a gyro, and odometers. Results have been compared to EKF and other ICP methods such as hull consistency (HC4) and 3-bound (3B) algorithms. Both consistencies of EKF and our algorithm have been experimentally studied.

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.

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