Error Estimations for Indirect Measurements: Randomized vs. Deterministic Algorithms for “Black-Box” Programs

Kreinovich, Vladik; Trejo, Raul A.

doi:10.1007/978-1-4615-0013-1_17

Cited by 16 publications

(10 citation statements)

References 30 publications

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“…Important observations and explanations about the methods are discussed in detail in Section 4.3. The seminal paper on CD is Kreinovich and Trejo (2001). More details can be found in Kreinovich and Ferson (2004) and Kreinovich et al (2007).…”

Section: Worst-case Searchmentioning

confidence: 99%

“…In the second step, we need to solve an optimisation problem subject to polyhedral constraints to actually find the worst-case scenario. We propose a solution approach that is computationally very attractive and can be easily parallelised, inspired by the simulationbased Cauchy deviates method for interval uncertainty (see Kreinovich and Trejo, 2001; Kreinovich and Ferson, 2004;Kreinovich et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Simulated polyhedral clouds in robust optimisation

Fuchs

2012

IJRS

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Past studies of uncertainty handling with polyhedral clouds have already shown strength in dealing with higher dimensional uncertainties in robust optimisation, even in case of partial ignorance of statistical information. However, the number of function evaluations necessary to quantify and propagate the uncertainties has been too high to be useful in many real-life applications with respect to limitations of computational cost. In this paper, we propose a simulation-based approach for optimisation over a polyhedron, inspired by the Cauchy deviates method. Thus, we achieve a computationally efficient method to compute worst-case scenarios with polyhedral clouds which we embed in a robust optimisation problem formulation. We apply the method to two test cases from space system design.

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Section: Worst-case Searchmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulated polyhedral clouds in robust optimisation

Fuchs

2012

IJRS

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“…In this section we present an approach inspired by the Cauchy deviates method (CD) for interval uncertainty [14,13,12], i.e.,…”

Section: Worst-case Searchmentioning

confidence: 99%

“…In the second step, to actually find the worst-case scenario, we need to solve an optimization problem subject to polyhedral constraints. For very high-dimensional problems we propose a solution approach that is computationally very attractive and can be easily parallelized, inspired by the simulation based Cauchy deviates method for interval uncertainty [14,13,12].…”

Section: Introductionmentioning

confidence: 99%

Simulation Based Uncertainty Handling With Polyhedral Clouds

Fuchs¹

2010

Proceedings of the 4th International Workshop on Reliable Engineering Computing Robust Design – Coping With Hazards, Risk and U

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Abstract. Past studies of uncertainty handling with polyhedral clouds have already shown strength in dealing with higher dimensional uncertainties in robust optimization, even in case of partial ignorance of statistical information. However, in thousands or more dimensions current implementations would still be computationally too expensive to be useful in real-life applications.In this paper we propose a simulation based approach for optimization over a polyhedron, inspired by the Cauchy deviates method. Thus we achieve a computationally efficient method to use polyhedral clouds also in very high dimensions.

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“…[49]: Finding an upper bound on the variance is NP-hard, a lower bound can be found in quadratic time. The field of applications of interval uncertainty for uncertainty handling is vast, e.g., [23], [53], [67], [68], [79].…”

Section: Safety Marginsmentioning

confidence: 99%

Clouds, p-boxes, Fuzzy Sets, and Other Uncertainty Representations in Higher Dimensions

Fuchs

2009

Acta Cybern

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Uncertainty modeling in real-life applications comprises some serious problems such as the curse of dimensionality and a lack of sufficient amount of statistical data.In this paper we give a survey of methods for uncertainty handling and elaborate the latest progress towards real-life applications with respect to the problems that come with it. We compare different methods and highlight their relationships. We introduce intuitively the concept of potential clouds, our latest approach which successfully copes with both higher dimensions and incomplete information.

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Error Estimations for Indirect Measurements: Randomized vs. Deterministic Algorithms for “Black-Box” Programs

Cited by 16 publications

References 30 publications

Simulated polyhedral clouds in robust optimisation

Simulated polyhedral clouds in robust optimisation

Simulation Based Uncertainty Handling With Polyhedral Clouds

Clouds, p-boxes, Fuzzy Sets, and Other Uncertainty Representations in Higher Dimensions

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