The Experts below are selected from a list of 107382 Experts worldwide ranked by ideXlab platform
Fengqi You - One of the best experts on this subject based on the ideXlab platform.
-
data driven decision making under uncertainty integrating Robust Optimization with principal component analysis and kernel smoothing methods
Computers & Chemical Engineering, 2018Co-Authors: Chao Ning, Fengqi YouAbstract:Abstract This paper proposes a novel data-driven Robust Optimization framework that leverages the power of machine learning and big data analytics for decision-making under uncertainty. By applying principal component analysis to uncertainty data, correlations between uncertain parameters are effectively captured, and latent uncertainty sources are identified. These data are then projected onto each principal component to facilitate extracting distributional information of latent uncertainties using kernel density estimation techniques. To explicitly account for asymmetric distributions, we introduce forward and backward deviation vectors into the data-driven uncertainty set, which are further incorporated into novel data-driven static and adaptive Robust Optimization models. The proposed framework not only significantly ameliorates the conservatism of Robust Optimization, but also enjoys computational efficiency and wide-ranging applicability. Three applications on Optimization under uncertainty, including model predictive control, batch production scheduling, and process network planning, are presented to demonstrate the applicability of the proposed framework.
-
Robust Optimization in high dimensional data space with support vector clustering
IFAC-PapersOnLine, 2018Co-Authors: Chao Shang, Fengqi YouAbstract:Abstract Data-driven Robust Optimization has attracted immense attentions. In this work, we propose a data-driven uncertainty set for Robust Optimization under high-dimensional uncertainty. We propose to first decompose the high-dimensional data space into the principal subspace and the residual subspace by employing principal component analysis, and then adopt support vector clustering and classic polyhedral uncertainty set to describe the intricate geometry in the principal subspace and the tiny variations in the residual subspace, respectively, giving rise to a new data-driven uncertainty set. Similar to classic uncertainty sets, the proposed data-driven uncertainty set can also preserve the tractability of Robust Optimization problems. In addition, we establish the probabilistic guarantee theoretically by further calibrating the uncertainty set with an independent dataset, which ensures that the data-driven uncertainty set covers a portion of uncertainty with a given confidence level. Numerical results show the effectiveness of the proposed uncertainty set in reducing conservatism of Robust Optimization problems as well as the fidelity of the established probabilistic guarantee.
-
data driven Robust Optimization based on kernel learning
Computers & Chemical Engineering, 2017Co-Authors: Chao Shang, Xiaolin Huang, Fengqi YouAbstract:Abstract We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven Robust Optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of Robust Optimization problems. The induced Robust counterpart problem retains the same type as the deterministic problem, which provides significant computational benefits. In addition, by exploiting statistical properties of SVC, the fraction of data coverage of the data-driven uncertainty set can be easily selected by adjusting only one parameter, which furnishes an interpretable and pragmatic way to control conservatism and exclude outliers. Numerical studies and an industrial application of process network planning demonstrate that, the proposed data-driven approach can effectively utilize useful information with massive data, and better hedge against uncertainties and yield less conservative solutions.
-
a data driven multistage adaptive Robust Optimization framework for planning and scheduling under uncertainty
Aiche Journal, 2017Co-Authors: Chao Ning, Fengqi YouAbstract:A novel data-driven approach for Optimization under uncertainty based on multistage adaptive Robust Optimization (ARO) and nonparametric kernel density M-estimation is proposed. Different from conventional Robust Optimization methods, the proposed framework incorporates distributional information to avoid over-conservatism. Robust kernel density estimation with Hampel loss function is employed to extract probability distributions from uncertainty data via a kernelized iteratively reweighted least squares algorithm. A data-driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, to organically integrate the multistage ARO framework with uncertainty data. Based on this uncertainty set, we further develop an exact Robust counterpart in its general form for solving the resulting data-driven multistage ARO problem. To illustrate the applicability of the proposed framework, two typical applications in process operations are presented: The first one is on strategic planning of process networks, and the other one on short-term scheduling of multipurpose batch processes. The proposed approach returns 23.9% higher net present value and 31.5% more profits than the conventional Robust Optimization method in planning and scheduling applications, respectively. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4343–4369, 2017
Dimitris Bertsimas - One of the best experts on this subject based on the ideXlab platform.
-
two stage sample Robust Optimization
arXiv: Optimization and Control, 2019Co-Authors: Dimitris Bertsimas, Shimrit Shtern, Bradley SturtAbstract:We investigate a data-driven approach to two-stage stochastic linear Optimization in which an uncertainty set is constructed around each data point. We propose an approximation algorithm for these sample Robust Optimization problems by optimizing a separate linear decision rule for each uncertainty set. We show that the proposed algorithm combines the asymptotic optimality and scalability of the sample average approximation while simultaneously offering improved out-of-sample performance guarantees. The practical value of our method is demonstrated in network inventory management and hospital scheduling.
-
Data-driven Robust Optimization
Mathematical Programming, 2018Co-Authors: Dimitris Bertsimas, Vishal Gupta, Nathan KallusAbstract:The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for Robust Optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and Robust Optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee whenever the constraints and objective function are concave in the uncertainty. We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queueing confirm that our data-driven sets significantly outperform traditional Robust Optimization techniques whenever data are available.
-
data driven Robust Optimization
arXiv: Optimization and Control, 2013Co-Authors: Dimitris Bertsimas, Vishal Gupta, Nathan KallusAbstract:The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for Robust Optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and Robust Optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. \edit{We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queuing confirm that our data-driven sets significantly outperform traditional Robust Optimization techniques whenever data is available.
-
performance analysis of queueing networks via Robust Optimization
Operations Research, 2011Co-Authors: Dimitris Bertsimas, David Gamarnik, Alexander RikunAbstract:Performance analysis of queueing networks is one of the most challenging areas of queueing theory. Barring very specialized models such as product-form type queueing networks, there exist very few results that provide provable nonasymptotic upper and lower bounds on key performance measures. In this paper we propose a new performance analysis method, which is based on the Robust Optimization. The basic premise of our approach is as follows: rather than assuming that the stochastic primitives of a queueing model satisfy certain probability laws---such as i.i.d. interarrival and service times distributions---we assume that the underlying primitives are deterministic and satisfy the implications of such probability laws. These implications take the form of simple linear constraints, namely, those motivated by the law of the iterated logarithm (LIL). Using this approach we are able to obtain performance bounds on some key performance measures. Furthermore, these performance bounds imply similar bounds in the underlying stochastic queueing models. We demonstrate our approach on two types of queueing networks: (a) tandem single-class queueing network and (b) multiclass single-server queueing network. In both cases, using the proposed Robust Optimization approach, we are able to obtain explicit upper bounds on some steady-state performance measures. For example, for the case of TSC system we obtain a bound of the form C(1-ρ)-1 ln ln((1-ρ)-1) on the expected steady-state sojourn time, where C is an explicit constant and ρ is the bottleneck traffic intensity. This qualitatively agrees with the correct heavy traffic scaling of this performance measure up to the ln ln((1-ρ)-1) correction factor.
-
Theory and Applications of Robust Optimization
SIAM Review, 2011Co-Authors: Dimitris Bertsimas, David B Brown, Constantine CaramanisAbstract:In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.
N Alqasas - One of the best experts on this subject based on the ideXlab platform.
-
improving multi objective Robust Optimization under interval uncertainty using worst possible point constraint cuts
Design Automation Conference, 2009Co-Authors: Shapour Azarm, Al S Hashimi, Ali Almansoori, N AlqasasAbstract:Many real-world engineering design Optimization problems are multi-objective and have uncertainty in their parameters. For such problems it is useful to obtain design solutions that are both multi-objectively optimum and Robust. A Robust design is one whose objective and constraint function variations under uncertainty are within an acceptable range. While the literature reports on many techniques in Robust Optimization for single objective Optimization problems, very few papers report on methods in Robust Optimization for multi-objective Optimization problems. The Multi-Objective Robust Optimization (MORO) technique with interval uncertainty proposed in this paper is a significant improvement, with respect to computational effort, over a previously reported MORO technique. In the proposed technique, a master problem solves a relaxed Optimization problem whose feasible domain is iteratively confined by constraint cuts determined by the solutions from a sub-problem. The proposed approach and the synergy between the master problem and sub-problem are demonstrated by three examples. The results obtained show a general agreement between the solutions from the proposed MORO and the previous MORO technique. Moreover, the number of function calls for obtaining solutions from the proposed technique is an order of magnitude less than that from the previous MORO technique.Copyright © 2009 by ASME
David Papp - One of the best experts on this subject based on the ideXlab platform.
-
a cutting surface algorithm for semi infinite convex programming with an application to moment Robust Optimization
Siam Journal on Optimization, 2014Co-Authors: Sanjay Mehrotra, David PappAbstract:We present and analyze a central cutting surface algorithm for general semi-infinite convex Optimization problems and use it to develop a novel algorithm for distributionally Robust Optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of Optimization problems with decreasing levels of risk-aversion, with classic Robust Optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally Robust Optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorit...
-
a cutting surface algorithm for semi infinite convex programming with an application to moment Robust Optimization
2013Co-Authors: Sanjay Mehrotra, David PappAbstract:We present and analyze a central cutting surface algorithm for general semi-infinite convex Optimization problems, and use it to develop a novel algorithm for distributionally Robust Optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as non-polynomial moments can be included in the formulation. We show that this gives rise to a hierarchy of Optimization problems with decreasing levels of risk-aversion, with classic Robust Optimization at one end of the spectrum, and stochastic programming at the other. Although our primary motivation is to solve distributionally Robust Optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with non-differentiable semi-infinite constraints indexed by an infinite-dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems whose constraints are differentiable and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution Optimization method and the central cutting surface algorithm yields a solution to a family of distributionally Robust Optimization problems that are considerably more general than the ones proposed to date.
Chao Ning - One of the best experts on this subject based on the ideXlab platform.
-
deciphering latent uncertainty sources with principal component analysis for adaptive Robust Optimization
2019Co-Authors: Chao NingAbstract:Abstract This paper proposes a novel data-driven Robust Optimization framework that leverages the power of machine learning for decision-making under uncertainty. By performing principal component analysis on uncertainty data, the correlations among uncertain parameters are effectively captured, and latent uncertainty sources are identified. Uncertainty data are then projected onto each principal component to facilitate extracting distributional information of latent uncertainties with kernel density estimation technique. To explicitly account for asymmetric uncertainties, we introduce forward and backward deviation vectors in an uncertainty set. The resulting data-driven uncertainty set is general enough to be employed in adaptive Robust Optimization model. The proposed framework not only significantly ameliorates the conservatism of Robust Optimization but also enjoys computational efficiency and wide applicability. An application of Optimization under uncertainty on batch process scheduling is presented to demonstrate the effectiveness of the proposed general framework. We also investigate a data-driven uncertainty set in a low-dimensional subspace and derive a theoretical bound on the performance gap between ARO solutions due to the dimension reduction of uncertainties.
-
data driven adaptive Robust Optimization framework based on principal component analysis
Advances in Computing and Communications, 2018Co-Authors: Chao NingAbstract:This article proposes a novel data-driven adaptive Robust Optimization (ARO) framework based on principal component analysis (PCA). By performing PCA on uncertainty data, the correlations among uncertain parameters are effectively captured, and principal components are identified. Uncertainty data are then projected onto each principal component, and distributional information is extracted from the projected uncertainty data using kernel density estimation. To explicitly account for asymmetric uncertainties, we introduce forward and backward deviations into uncertainty sets. The proposed data-driven ARO approach enjoys a less conservative solution compared with conventional Robust Optimization methods. A numerical example and an application in process network planning are presented to demonstrate the effectiveness of the proposed approach. Some promising extensions are also made within the proposed framework. Specifically, we investigate a data-driven uncertainty set in a low-dimensional subspace, and derive a theoretical bound on the performance gap between ARO solutions due to the dimension reduction of uncertainties.
-
data driven decision making under uncertainty integrating Robust Optimization with principal component analysis and kernel smoothing methods
Computers & Chemical Engineering, 2018Co-Authors: Chao Ning, Fengqi YouAbstract:Abstract This paper proposes a novel data-driven Robust Optimization framework that leverages the power of machine learning and big data analytics for decision-making under uncertainty. By applying principal component analysis to uncertainty data, correlations between uncertain parameters are effectively captured, and latent uncertainty sources are identified. These data are then projected onto each principal component to facilitate extracting distributional information of latent uncertainties using kernel density estimation techniques. To explicitly account for asymmetric distributions, we introduce forward and backward deviation vectors into the data-driven uncertainty set, which are further incorporated into novel data-driven static and adaptive Robust Optimization models. The proposed framework not only significantly ameliorates the conservatism of Robust Optimization, but also enjoys computational efficiency and wide-ranging applicability. Three applications on Optimization under uncertainty, including model predictive control, batch production scheduling, and process network planning, are presented to demonstrate the applicability of the proposed framework.
-
a data driven multistage adaptive Robust Optimization framework for planning and scheduling under uncertainty
Aiche Journal, 2017Co-Authors: Chao Ning, Fengqi YouAbstract:A novel data-driven approach for Optimization under uncertainty based on multistage adaptive Robust Optimization (ARO) and nonparametric kernel density M-estimation is proposed. Different from conventional Robust Optimization methods, the proposed framework incorporates distributional information to avoid over-conservatism. Robust kernel density estimation with Hampel loss function is employed to extract probability distributions from uncertainty data via a kernelized iteratively reweighted least squares algorithm. A data-driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, to organically integrate the multistage ARO framework with uncertainty data. Based on this uncertainty set, we further develop an exact Robust counterpart in its general form for solving the resulting data-driven multistage ARO problem. To illustrate the applicability of the proposed framework, two typical applications in process operations are presented: The first one is on strategic planning of process networks, and the other one on short-term scheduling of multipurpose batch processes. The proposed approach returns 23.9% higher net present value and 31.5% more profits than the conventional Robust Optimization method in planning and scheduling applications, respectively. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4343–4369, 2017
