Defeasibility in CLP( $$\mathcal{Q}$$ ) through generalized slack variables

Holzbaur, Christian; Menezes, Francisco; Barahona, Pedro

doi:10.1007/3-540-61551-2_76

Cited by 11 publications

(8 citation statements)

References 4 publications

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“…This is opposed to, for example, linear constraints over the reals such as in[20], where the slack variables already used by the SIMPLEX algorithm can be used to similarly deactivate constraints.…”

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confidence: 95%

Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints

2007

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Much research in the area of constraint processing has recently been focused on extracting small unsatisfiable "cores" from unsatisfiable constraint systems with the goal of finding minimal unsatisfiable subsets (MUSes). While most techniques have provided ways to find an approximation of an MUS (not necessarily minimal), we have developed a sound and complete algorithm for producing all MUSes of an unsatisfiable constraint system. In this paper, we describe a relationship between satisfiable and unsatisfiable subsets of constraints that we subsequently use as the foundation for MUS extraction algorithms, implemented for Boolean satisfiability constraints. The algorithms provide a framework with which many related subproblems can be solved, including relaxations of completeness to handle intractable instances, and we develop several variations of the basic algorithms to illustrate this. Experimental results demonstrate the performance of our algorithms, showing how the base algorithms run quickly on many instances, while the variations are valuable for producing results on instances whose complete results are intractably large. Furthermore, our algorithms are shown to perform better than the existing algorithms for solving either of the two distinct phases of our approach.

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confidence: 95%

Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints

2007

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“…The use of branch-and-bound methods is widely used for continuous nonconvex problems [19], [38], [39], [28], [26]. The proposed branch-andbound procedure constructs a binary tree based on the partitioning of the hyperrectangle…”

Section: Fractional Programming Formulationmentioning

confidence: 99%

“…In [26], the authors proposed a method to remove constraints in order to obtain a feasible set, based on an hierarchical classification of constraints. Another possibility is to remove a minimal set of constraints.…”

Section: Introductionmentioning

confidence: 99%

On optimal zero-preserving corrections for inconsistent linear systems

et al. 2009

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This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose objective function is a sum of fractional functions. A branch-and-bound algorithm for solving this nonconvex program is proposed, based on suitably overestimating the denominator function for computing lower bounds. Computational experience is presented to demonstrate the efficacy of this approach.

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“…This work is thus closely related to Partial Constraint Satisfaction in finite domains. In the context of Hierarchical Constraint Logic Programming, Holzbaur, Menezes and Barahona [11] showed how to find minimal conflict sets (equivalent to IISs) incrementally, i.e., upon the addition of a constraint to a set of feasible constraints, that makes the new set infeasible. Much less work was developed, to our knowledge, regarding the correction of linear constraints.…”

Section: Introductionmentioning

confidence: 99%

“…Let us consider again the problem instance(11) presented in Example 2.1. From condition (23) we know that the size of CC must be at least 3.…”

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confidence: 99%

A Framework for Optimal Correction of Inconsistent Linear Constraints

Amaral

Barahona

2005

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The problem of inconsistency between constraints often arises in practice as the result, among others, of the complexity of real models or due to unrealistic requirements and preferences. To overcome such inconsistency two major actions may be taken: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as Bmodel correction^is the problem we address in this article in the context of linear constraints over the reals. The correction of the right hand side alone, which is very close to a fuzzy constraints approach, was one of the first proposals to deal with inconsistency, as it may be mapped into a linear problem. The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, that provide corrections with quite rigid patterns, the optimization of the important Frobenius norm was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global minimizer.

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Defeasibility in CLP( $$\mathcal{Q}$$ ) through generalized slack variables

Cited by 11 publications

References 4 publications

Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints

Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints

On optimal zero-preserving corrections for inconsistent linear systems

A Framework for Optimal Correction of Inconsistent Linear Constraints

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