Sensitivity Analysis in Quantified Interval Constraint Satisfaction Problems

2013 ◽  
Author(s):  
Jie Hu ◽  
Yan Wang
Keyword(s):  
Sensitivity Analysis ◽  
Constraint Satisfaction ◽  
Epistemic Uncertainty ◽  
Constraint Satisfaction Problems ◽  
Vehicle Design ◽  
Design Problems ◽  
Propagation Of Uncertainty ◽  
Interval Constraints ◽  
Interval Constraint ◽  
Interval Valued

Interval is an alternative to probability distribution in quantifying epistemic uncertainty for reliability analysis when there is a lack of data to fit a distribution with good confidence. It only requires the information of lower and upper bounds. The propagation of uncertainty is analyzed by solving interval-valued constraint satisfaction problems (CSPs). By introducing logic quantifiers, quantified constraint satisfaction problems (QCSPs) can capture more semantics and engineering intent than CSPs. Sensitivity analysis (SA) takes into account of variations associated with the structure and parameters of interval constraints to study to which extent they affect the output. In this paper, a global SA method is developed for QCSPs, where the effects of quantifiers and interval ranges on the constraints are analyzed based on several proposed metrics, which indicate the levels of indeterminacy for inputs and outputs as well as unsatisfiability of constraints. Two vehicle design problems are used to demonstrate the proposed approach.

Sensitivity Analysis in Quantified Interval Constraint Satisfaction Problems

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Jie Hu ◽  
Yan Wang ◽  
Aiguo Cheng ◽  
Zhihua Zhong
Keyword(s):  
Sensitivity Analysis ◽  
Constraint Satisfaction ◽  
Information Gain ◽  
Constraint Satisfaction Problems ◽  
Design Parameters ◽  
Design Variables ◽  
Parameter Variations ◽  
Analytical Relations ◽  
Quantifying Uncertainty ◽  
Interval Valued

Interval is an alternative to probability distribution in quantifying uncertainty for sensitivity analysis (SA) when there is a lack of data to fit a distribution with good confidence. It only requires the information of lower and upper bounds. Analytical relations among design parameters, design variables, and target performances under uncertainty can be modeled as interval-valued constraints. By incorporating logic quantifiers, quantified constraint satisfaction problems (QCSPs) can integrate semantics and engineering intent in mathematical relations for engineering design. In this paper, a global sensitivity analysis (GSA) method is developed for feasible design space searching problems that are formulated as QCSPs, where the effects of value variations and quantifier changes for design parameters on target performances are analyzed based on several proposed metrics, including the indeterminacy of target performances, information gain of parameter variations, and infeasibility of constraints. Three examples are used to demonstrate the proposed approach.

scholarly journals Propagation of uncertainty and sensitivity analysis in an integral oil‐gas plume model

2016 ◽  
Vol 121 (5) ◽  
pp. 3488-3501 ◽  
Author(s):  
Shitao Wang ◽  
Mohamed Iskandarani ◽  
Ashwanth Srinivasan ◽  
W. Carlisle Thacker ◽  
Justin Winokur ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Plume Model ◽  
Propagation Of Uncertainty ◽  
Uncertainty And Sensitivity Analysis ◽  
Oil Gas

scholarly journals Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

2013 ◽  
Vol 44 (2) ◽  
pp. 131-156 ◽  
Author(s):  
Laura Climent ◽  
Richard J. Wallace ◽  
Miguel A. Salido ◽  
Federico Barber
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Robust Solutions

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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