We consider robust shortest path problems, where the aim is to find a path that optimizes the worstcase performance over an uncertainty set containing all relevant. Datadriven distributionally robust polynomial optimization. This electronic textbook is a studentcontributed opensource text covering a variety of topics on process optimization. Hedman, robust corrective topology control for system reliability. Robust optimization robust optimization is a field of optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that. In this paper, we combine the polynomial and uncertain features and consider polynomial robust optimization. Under this framework, the objective and constraint functions are only assumed to belong to certain sets in function space the socalled \uncertainty sets. The models proposed in this paper fall within the scope of datadriven distributionally robust optimization 7, 16, 20, 23. How we measure reads a read is counted each time someone views a publication summary such as the. Datadriven distributionally robust optimization using the. A datadriven robust optimization approach to operational optimization of industrial steam systems under uncertainty. A datadriven robust optimization ddro methodology is proposed to deal with uncertainty in the optimization of steam system in an ethylene plant. The integration of wind energy into the power grid is challenging because of its variability, which causes high ramp events that may threaten the reliability and efficiency of power systems.
Welcome to the northwestern university process optimization open textbook. Despite the attractive features of datadriven approaches, most existing publications in this area are restricted to static robust optimization. The purpose of this tutorial is to illustrate the capabilities of the robust and datadriven optimization. Likelihood robust optimization for datadriven problems. In robust optimization, random variables are modeled as uncertain parameters belonging to a convex uncertainty set, and the decision maker protects the system against the worst case within that set. Distributionally robust optimization dro online linear programming olp least squares with nonconvex regularization lsnr alternating direction method of multipliers admm su. Datadriven and robust optimization approaches to call centers, with x. Under this framework, the objective and constraint functions are only assumed. The solution method to many robust program involves creating a deterministic equivalent, called the robust counterpart. Robust optimization is a distinct approach to optimizations problems that allows for the incorporation of uncertainty. Datadriven distributionally robust optimization using the 117 radiusoftheambiguityset,themodelercanthuscontrolthedegreeofconservatismof the underlying optimization problem.
Robust optimization methodology and applications 457 k is or is not polyhedral, we see that the optimal value inpiy is equal to the one in the solvable dual problem max. Robust approaches to uncertain vector optimization. For two univariate probability distributions p 1 and p 2, let f 1 and. They focus on the case where the uncertain parameters u. Processes free fulltext datadriven robust optimization for. Datadriven and distributionally robust optimization and applications part 22 duration. Sloan school of management massachusetts institute of technology cambridge usa. Distributionally robust optimization dro online linear programming olp least squares with nonconvex regularization lsnr alternating direction method of multipliers admm. Totestforpracticalperformance,weleverageauniquedatasetfroma cancer center. Algorithms and uncertainty sets for datadriven robust.
Robust optimization problems where theuncertainty isaprobability. In robust optimization, random variables are modeled as uncertain parameters belonging to a convex uncertainty set and the decisionmaker protects the system against the worst case within that set. School of operations research and information engineering cornell university and cornell tech new. Praise for robust portfolio optimization and management in the half century since harry markowitz introduced his elegant theory for selecting portfolios, investors and scholars have extended and refined its application to a wide range of realworld problems, culminating in the contents of this masterful book. In the datadriven framework, uncertainty sets are directly constructed from uncertainty data. There are several ways to apply robust optimization and the choice of form is. A datadriven robust optimization approach to scenariobased stochastic model. Datadriven robust optimization based on kernel learning. Keywords robust optimization datadriven optimization chanceconstraints.
The ks distance was used by 17 in defining an ambiguity set for a datadriven distributionally robust optimization model. The argument is based on the fact that a separate analysis allows obtaining. Robust optimization and polynomial optimization are already an important topic in machine learning and operations research. Theory and applications of robust optimization siam. Datadriven appointmentscheduling under uncertainty. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis. In this paper, we propose a novel distributionally robust.
The application of robust optimization in power systems. Datadriven robust optimization gtest are based on phidivergences see also 32. Distributionally robust optimization reference delage, e. Datadriven distributionally robust stochastic control of. If the radius drops to zero, then the ambiguity setshrinkstoasingletonthatcontainsonlythenominaldistribution,inwhichcasethe. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. On the power of robust solutions in twostage stochastic and adaptive optimization. Datadriven robust optimization with application to portfolio management, working papers 2014104, department of research, ipag business school. An alternative streamline of datadriven optimization is the distributionally robust optimization, which utilizes both data and hypothesis tests to construct the ambiguity set including. How the moneyball method can grow revenue jon macdonald whether your current roi is something to brag about or something to worry about, the. Datadriven robust optimization mathematical programming.
Datadriven robust optimization for steam systems in. The goal is to make a decision that is feasible no matter. Dimitris bertsimas, vishal gupta, nathan kallus submitted on 31 dec 20, last revised 23 nov 2014 this version, v2 abstract. In this case, we might ask for probabilistic guarantees for the robust so. First, adopting a worstcase approach regularizes the optimization problem and thereby mitigates the optimizer s curse characteristic for stochastic programming.
Data driven robust security constraint unit commitment, working paper. Datadriven distributionally robust optimization using the wasserstein metric 2 distributionally robust optimization has the following striking bene ts. Data driven robust optimization 7 delage and ye 8 prov ed that the robust counterpart of the problem 2 according to u can be formulated as a semidefinite program sdp. Robust optimization is an important sub eld of optimization that deals with uncertainty in the data of optimization problems.
Azizimj hyperparameter robust simulation optimization star 0 code issues pull requests hyperparameter tuning using a robust simulation optimization. Datadriven robust optimization p2 the set u implies a probabilistic guarantee for p. The last decade witnessed an explosion in the availability of data for operations research applications. These methods are also relevant to datadriven optimization methods. Datadriven robust optimization has been proposed recently bertsimas et al. The approach is flexible and widely applicable, and robust optimization. Data driven robust optimization moahammad namakshenas and mir saman pishvaee, school of industrial engineering, iran university of science and technology, tehran, iran chapter 2. The practical difficulty of a robust program depends on if its robust. Financial signal processing and machine learning wiley. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Robust optimization an overview sciencedirect topics. Distributionally robust optimization under moment uncertainty with application to datadriven problems.
Datadriven robust optimization based on kernel learning chao shanga, xiaolin huangb, fengqi you,a asmith school of chemical and biomolecular engineering, cornell university, ithaca, new york 14853. Data driven robust optimization chapter pdf available january 2019. Ambiguous risk measures and optimal robust portfolios. Pishvaee, data driven robust optimization, in robust and constrained optimization. Introduction robust optimization is a popular approach to optimization under uncertainty. This book is devoted to robust optimization a speci.
A datadriven robust optimization approach to scenariobased. Cooperative datadriven distributionally robust optimization. Datadriven robust optimization with application to. The primary goal of this preface is to provide the reader. To the large set of methods available to solve this type of problems, a recent addition is datadriven distributionally robust optimization, see. This entails the development of a datadriven robust optimization approach with noveluncertaintysets. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. Datadriven distributionally robust optimization using the wasserstein metric.