Efficient handling of universally quantified inequalities

Goldsztejn, Alexandre; Michel, Claude; Rueher, Michel

doi:10.1007/s10601-008-9053-0

Cited by 11 publications

(7 citation statements)

References 26 publications

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“…The basic idea is searching the algebraic solution such that constraints are satisfied. The value y is called an algebraic solution to the constraint f Transactions of the ASME QCSPs were developed, including constraints where all universal quantifiers precede existential ones [51,52], constraints with shared existential variables [53], linear and nonlinear constraints [54,55], and constraints where existential quantifiers precede all universal ones [56]. Quantified set inversion method [21,22] provides three computing rules to solve an interval QCSP by combining the set inversion technique and modal interval [28].…”

Section: Solving Csps the Commonly Used Methods To Solvementioning

confidence: 99%

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

Aminzadeh

Wang

2013

Journal of Mechanical Design

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In complex systems design, multidisciplinary constraints are imposed by stakeholders. Engineers need to search feasible design space for a given problem before searching for the optimum design solution. Searching feasible design space can be modeled as a constraint satisfaction problem (CSP). By introducing logical quantifiers, CSP is extended to quantified constraint satisfaction problem (QCSP) so that more semantics and design intent can be captured. This paper presents a new approach to formulate searching design problems as QCSPs in a continuous design space based on generalized interval, and to numerically solve them for feasible solution sets, where the lower and upper bounds of design variables are specified. The approach includes two major components. One is a semantic analysis which evaluates the logic relationship of variables in generalized interval constraints based on Kaucher arithmetic, and the other is a branch-and-prune algorithm that takes advantage of the logic interpretation. The new approach is generic and can be applied to the case when variables occur multiple times, which is not available in other QCSP solving methods. A hybrid stratified Monte Carlo method that combines interval arithmetic with Monte Carlo sampling is also developed to verify the correctness of the QCSP solution sets obtained by the branch-and-prune algorithm.

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Section: Solving Csps the Commonly Used Methods To Solvementioning

confidence: 99%

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

Aminzadeh

Wang

2013

Journal of Mechanical Design

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“…To know when to perform a bisection on parameter domains, in a similar fashion to the work of Goldsztejn [25], one defines a threshold on the ratio:…”

Section: ) Verificationmentioning

confidence: 99%

Performance analysis and design of parallel kinematic machines using interval analysis

Viegas

Daney

Tavakoli

et al. 2017

Mechanism and Machine Theory

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. Performance analysis and design of parallel kinematic machines using interval analysis. Mechanism and Machine Theory, Elsevier, 2017, 115, pp.218 -236 Abstract-Some design methodologies for Parallel Kinematic Machines (PKM) have been proposed but with limitations regarding two main problems: how to improve multiple properties of different nature such as accuracy, force or singularity poses, and how to check these properties for all poses inside the PKM workspace. To address these problems, this work proposes to formulate the design problem as a feasibility problem and use a data representation which takes into account the uncertainty or variation of the involved parameters. This method, based on interval analysis, allows to evaluate several performance indexes of a PKM design. For validation purposes, this methodology is applied to a PKM, obtaining a continuous set of possible kinematic parameters values for its architecture which is capable of fulfilling several performance requirements over a desired workspace.

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“…The first four tests are similar to standard monotonicity tests[40,33], which were already used in the context of SICs in[30] in a simpler form.…”

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confidence: 99%

A standard branch-and-bound approach for nonlinear semi-infinite problems

Marendet

Goldsztejn

Chabert

et al. 2020

European Journal of Operational Research

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This paper considers nonlinear semi-infinite problems, which contain at least one semi-infinite constraint (SIC). The standard branch-and-bound algorithm is adapted to such problems by extending usual upper and lower bounding techniques for nonlinear inequality constraints to SICs. This is achieved by defining the interval evaluation of parametrized functions and their generalized gradients, by also adapting numerical constraint programming techniques to quantified inequalities, and by introducing linear relaxations and restrictions for SICs. The overall efficiency of our algorithm is demonstrated on a standard set of benchmarks from the literature, in comparison with the best state of the art alternative.

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Efficient handling of universally quantified inequalities

Cited by 11 publications

References 26 publications

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

Performance analysis and design of parallel kinematic machines using interval analysis

A standard branch-and-bound approach for nonlinear semi-infinite problems

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