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Uncertain data

About: Uncertain data is a research topic. Over the lifetime, 2933 publications have been published within this topic receiving 62270 citations.


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BookDOI
27 Jun 2011
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
Abstract: The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods.The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest. Review of First Edition:"The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)

5,398 citations

Journal ArticleDOI
TL;DR: It is shown that the RC of an LP with ellipsoidal uncertainty set is computationally tractable, since it leads to a conic quadratic program, which can be solved in polynomial time.

1,809 citations

Journal ArticleDOI
TL;DR: In this paper, a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty is proposed, which only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data.
Abstract: Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a two-stage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hard-to-obtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.

1,454 citations

Journal ArticleDOI
TL;DR: The Affinely Adjustable Robust Counterpart (AARC) problem is shown to be, in certain important cases, equivalent to a tractable optimization problem, and in other cases, having a tight approximation which is tractable.
Abstract: We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (‘‘non-adjustable variables’’), while the other part are variables that can be chosen after the realization (‘‘adjustable variables’’). We extend the Robust Optimization methodology ([1, 3-6, 9, 13, 14]) to this situation by introducing the Adjustable Robust Counterpart (ARC) associated with an LP of the above structure. Often the ARC is significantly less conservative than the usual Robust Counterpart (RC), however, in most cases the ARC is computationally intractable (NP-hard). This difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data. The ensuing Affinely Adjustable Robust Counterpart (AARC) problem is then shown to be, in certain important cases, equivalent to a tractable optimization problem (typically an LP or a Semidefinite problem), and in other cases, having a tight approximation which is tractable. The AARC approach is illustrated by applying it to a multi-stage inventory management problem.

1,407 citations

Proceedings ArticleDOI
09 Jun 2003
TL;DR: This paper addresses the important issue of measuring the quality of the answers to query evaluation based upon uncertain data, and provides algorithms for efficiently pulling data from relevant sensors or moving objects in order to improve thequality of the executing queries.
Abstract: Many applications employ sensors for monitoring entities such as temperature and wind speed. A centralized database tracks these entities to enable query processing. Due to continuous changes in these values and limited resources (e.g., network bandwidth and battery power), it is often infeasible to store the exact values at all times. A similar situation exists for moving object environments that track the constantly changing locations of objects. In this environment, it is possible for database queries to produce incorrect or invalid results based upon old data. However, if the degree of error (or uncertainty) between the actual value and the database value is controlled, one can place more confidence in the answers to queries. More generally, query answers can be augmented with probabilistic estimates of the validity of the answers. In this paper we study probabilistic query evaluation based upon uncertain data. A classification of queries is made based upon the nature of the result set. For each class, we develop algorithms for computing probabilistic answers. We address the important issue of measuring the quality of the answers to these queries, and provide algorithms for efficiently pulling data from relevant sensors or moving objects in order to improve the quality of the executing queries. Extensive experiments are performed to examine the effectiveness of several data update policies.

632 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202315
202238
2021147
2020126
2019139
2018149