Reasoning about conditional constraint specification problems and feature models

2011 ◽  
Vol 25 (2) ◽  
pp. 163-174 ◽  
Author(s):  
Raphael Finkel ◽  
Barry O'Sullivan
Keyword(s):  
Constraint Satisfaction ◽  
Directed Acyclic Graphs ◽  
Constraint Satisfaction Problems ◽  
Product Configuration ◽  
Feature Models ◽  
Model Builder ◽  
A Value ◽  
Acyclic Graphs ◽  
All Solutions ◽  
Constraint Specification

AbstractProduct configuration is a major industrial application domain for constraint satisfaction techniques. Conditional constraint satisfaction problems (CCSPs) and feature models (FMs) have been developed to represent configuration problems in a natural way. CCSPs are like constraint satisfaction problems (CSPs), but they also include potential variables, which might or might not exist in any given solution, as well as classical variables, which are required to take a value in every solution. CCSPs model, for example, options on a car, for which the style of sunroof (a variable) only makes sense if the car has a sunroof at all. FMs are directed acyclic graphs of features with constraints on edges. FMs model, for example, cell phone features, where utility functions are required, but the particular utility function “games” is optional, but requires Java support. We show that existing techniques from formal methods and answer set programming can be used to naturally model CCSPs and FMs. We demonstrate configurators in both approaches. An advantage of these approaches is that the model builder does not have to reformulate the CCSP or FM into a classic CSP, converting potential variables into classical variables by adding a “does not exist” value and modifying the problem constraints. Our configurators automatically reason about the model itself, enumerating all solutions and discovering several kinds of model flaws.

On Considering Constraints of Different Importance in Fuzzy Constraint Satisfaction Problems

1998 ◽  
Vol 06 (05) ◽  
pp. 489-501 ◽  
Author(s):  
Vicenç Torra I Reventós
Keyword(s):  
Constraint Satisfaction ◽  
Real World ◽  
Constraint Satisfaction Problems ◽  
Human Reasoning ◽  
Fuzzy Constraints ◽  
A Value ◽  
Equal Importance ◽  
Real World Applications ◽  
Fuzzy Constraint ◽  
Fuzzy Constraint Satisfaction

Several real-world applications (e.g., scheduling, configuration, …) can be formulated as Constraint Satisfaction Problems (CSP). In these cases, a set of variables have to be settled to a value with the requirement that they satisfy a set of constraints. Classical CSPs are defined only by means of crisp (Boolean) constraints. However, as sometimes Boolean constraints are too strict in relation to human reasoning, fuzzy constraints were introduced. When fuzzy constraints are considered, human reasoning usually performs some compensation between alternatives. Thus other operators than t-norms are advisable. Besides of that, not all constraints can be considered with equal importance. In this paper we show that the WOWA operator can consider both aspects: compensation between constraints and constraints of different importance.

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 Replaceability for Constraint Satisfaction Problems: Algorithms, Inference, and Complexity Patterns

10.29007/wrp9 ◽  
2018 ◽  
Author(s):  
Richard Wallace
Keyword(s):  
Constraint Satisfaction ◽  
Relative Effectiveness ◽  
Constraint Satisfaction Problems ◽  
Scheduling Problems ◽  
Problem Space ◽  
All Solutions ◽  
Disjunctive Constraints ◽  
Neighbourhood Search ◽  
Structured Problems ◽  
Full Search

Replaceability is a form of generalized substitutability whose features make it potentially of great importance for problem simplification. It differs from simple substitutability in that it only requires that substitutable values exist for every solution containing a given value without requiring that the former always be the same. This is the most general form of substitutability that allows inferences from local to global versions of this property. Building on earlier work, this study first establishes that algorithms for localized replaceability (consistent neighbourhood replaceability or CNR algorithms) based on all-solutions neighbourhood search outperform other replaceability algorithms by several orders of magnitude. It also examines the relative effectiveness of different forms of depth-first CNR algorithms. Secondly, it demonstrates an apparent complexity ridge, which does not occur at the same place in the problem space as the complexity areas for consistency or full search algorithms. Thirdly, it continues the study of methods for inferring replaceability in structured problems in order to improve efficiency. Here, it is shown that some strategies for inferring replaceable values can be extended to disjunctive constraints in scheduling problems.

scholarly journals Verifying concurrent multicopy search structures

2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-32
Author(s):  
Nisarg Patel ◽  
Siddharth Krishna ◽  
Dennis Shasha ◽  
Thomas Wies
Keyword(s):  
Data Structures ◽  
General Framework ◽  
Directed Acyclic Graphs ◽  
Separation Logic ◽  
A Value ◽  
Acyclic Graphs ◽  
Multiple Copies ◽  
File Structures ◽  
Search Structure ◽  
Concurrent Separation Logic

Multicopy search structures such as log-structured merge (LSM) trees are optimized for high insert/update/delete (collectively known as upsert) performance. In such data structures, an upsert on key k , which adds ( k , v ) where v can be a value or a tombstone, is added to the root node even if k is already present in other nodes. Thus there may be multiple copies of k in the search structure. A search on k aims to return the value associated with the most recent upsert. We present a general framework for verifying linearizability of concurrent multicopy search structures that abstracts from the underlying representation of the data structure in memory, enabling proof-reuse across diverse implementations. Based on our framework, we propose template algorithms for (a) LSM structures forming arbitrary directed acyclic graphs and (b) differential file structures, and formally verify these templates in the concurrent separation logic Iris. We also instantiate the LSM template to obtain the first verified concurrent in-memory LSM tree implementation.

Formulating constraint satisfaction problems for the inspection of configuration rules

2015 ◽  
Vol 30 (3) ◽  
pp. 313-328
Author(s):  
Anna Tidstam ◽  
Johan Malmqvist ◽  
Alexey Voronov ◽  
Knut Åkesson ◽  
Martin Fabian
Keyword(s):  
Constraint Satisfaction ◽  
Product Family ◽  
Constraint Satisfaction Problems ◽  
Product Configuration ◽  
Computational Performance ◽  
Multiple Configuration ◽  
Future Work ◽  
Rules Set ◽  
Single Configuration ◽  
Important Activity

AbstractProduct configurationis when an artifact from a product family is assembled from a set of predefined components that can only be combined in certain ways. These ways are defined by configuration rules. The product developers inspect the configuration rules when they develop new configuration rules or modify the configuration rules set. The inspection of configuration rules is thereby an important activity to avoid errors in the configuration rules set. Several formulations of constraint satisfaction problems (CSPs) are proposed that facilitate the inspection of configuration rules in propositional logic (IF-THEN, AND, NOT, OR, etc.). Many of the configuration rules are so calledproduction rules; that is, a configuration rule is an IF-THEN expression that fires when the IF condition is met. Several configuration rules build chains that fire during the product configuration. It is therefore important not only to inspect single configuration rules but also to analyze the effect of multiple configuration rules. Formulating the tasks as variations of the CSP can support the inspection activity. More specifically, we address the reformulation of configuration rules, testing of feature variant combinations, and counting of item quantities from an item set. The suggested CSPs are tested on industrial vehicle configuration rules for computational performance. The results show that the time for achieving results from the solving of the CSP is within seconds. Our future work will be to implement the various CSPs into a demonstrator that could be tested by product developers.

CONSTRAINT SATISFACTION PROBLEMS WITH ORDER-SORTED DOMAINS

1995 ◽  
Vol 04 (01n02) ◽  
pp. 55-72 ◽  
Author(s):  
TIBOR KÖKÉNY
Keyword(s):  
Constraint Satisfaction ◽  
Special Class ◽  
Object Oriented ◽  
Constraint Satisfaction Problems ◽  
Constraint Systems ◽  
Arc Consistency ◽  
All Solutions ◽  
Variable Domains ◽  
Natural Support ◽  
Inheritance Hierarchy

In order to improve constraint satisfaction techniques, a promising way is to use special features of constraints and variable domains. This paper examines a special class of CSPs (Constraint Satisfaction Problems) in which a partial order is defined on each domain and the constraints are compatible with these orders. A special arc-consistency algorithm for this case is presented and some questions about finding all solutions are discussed. The presented ideas can be used in constraint systems implemented in an object-oriented language, where inheritance hierarchy of objects is a natural support for the presented CSP type.

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