Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Datadriven robust optimization massachusetts institute of. For two univariate probability distributions p 1 and p 2, let f 1 and. What are some good resources to learn about optimization. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are. 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, usa binstitute of image processing and pattern recognition, shanghai jiao tong university, shanghai 200400, china abstract we propose piecewise linear kernelbased support vector clustering svc. Nov 28, 2017 data driven optimization models and algorithms simons institute. Princeton series in applied mathematics, title robust optimization, year 2009 related entries. Laguna, m, applying robust optimization to capacity expansion of one location in telecommunications with demand uncertainty. Lichairprofessorofengineering department ofmanagementscience andengineering stanforduniversity june,2014 yinyu ye june 2014. Will dynardo gmbh robust design optimization methods for industrial applications nafems world congress. Milton stewart school of industrial and systems engineering georgia institute of technology, atlanta georgia 303320205 usa november 2012. The ks distance was used by 17 in defining an ambiguity set for a data driven distributionally robust optimization model. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests.
Robust optimization is designed to meet some major challenges associated with uncertaintyaffected optimization problems. We consider optimal decisionmaking problems in an uncertain environment. The book is indeed good in mathematical theory and only for that. Distributionally robust optimization prob lems have been studied since scarfs 43 seminal treatise on the ambiguityaverse newsvendor problem in 1958, but the. In particular, we consider the case in which the distribution of the input is unknown, yet there is some historical data drawn from the distribution. A company produces two kinds of drugs, drugi and drugii, containing a specific active agent a, which is extracted from raw materials purchased on the market. We introduce a simple uncertainty set for arrival rates based on some structural properties of optimal queueing and routing solutions. Fraction of data coverage can be conveniently adjusted using only one parameter. The new frontier of datadriven price optimization duration. Most dynardo gmbh robust design optimization and catastrophe theory nafems world congress, stockholm 2017. A tutorial on robust optimization, given at the ima. When you optimize parameters for robustness, the optimization solver uses the responses computed using all the uncertain parameter values to.
There are few examples to illustrate the techniques of robust optimization, and most of this content discusses. Cooperative datadriven distributionally robust optimization. Stepbystep analysis on fundamental questions followed by a datadriven optimization plan is enough to get you large gains. Robust data driven vehicle routing 4 article accepted by operations research. Distributionally robust optimization and its tractable.
Datadriven optimization uses observations of the random variables as direct inputs to the mathematical programming problems. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the. On distributionally robust chanceconstrained linear programs. Pdf nowadays, data becomes a critical corporate asset. One major motivation for studying robust optimization is that in many applications the data set is an appropriate notion of parameter uncertainty, e. There are constraints with uncertain parameters that must be satis. Robust design optimization of optothermomechanical systems nafems benchmark magazine, july 2017. Portfolio optimization results are strongly dependent on. Released under the lgpl license, the engine can be used, modified and redistributed free of charge. A practical guide to robust optimization sciencedirect. Ning a set d of possible probability distributions that is assumed to. Table 1 presents the tractable robust counterparts of an uncertain linear optimization problem for different classes of uncertainty sets.
While many books have addressed its various aspects, nonlinear optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Likelihood robust optimization for datadriven problems. Theory and applications of robust optimization 467 since there are more constraints to satisfy and the smaller the loss probability p loss. A distributionally robust variant of value iteration can be cast as. Sep 19, 2015 we consider optimal decisionmaking problems in an uncertain environment. All the algorithms and methods have been coded in a matlab toolbox allowing numerical analysis, reliability analysis, simulation, sensitivity, optimization, robust design and much more. Nevertheless, tractability results are available for special cases.
The transformation to smarter cities brings an array of emerging urbanization challenges. Robust optimization mathematical and statistical sciences. Our data driven robust polynomial optimization method applies to a number of machine learning problems. A compact convex uncertainty set can be efficiently learnt from massive data. In a recent work, delage and ye 2010 study distributionally robust stochastic programs where the mean. Datadriven robust optimization based on kernel learning. The new frontier of data driven price optimization duration. Dec 31, 20 the last decade witnessed an explosion in the availability of data for operations research applications. The benefit of data driven robust optimization for supply chain problems is that behavior of suppliers and consumers can be modeled through historical demand data, and the data associated with past decisions. Modern cities have brought to life unprecedented opportunities and challenges for allocating limited resources in a data. Parameter estimation with expected and residualatrisk criteria. Robust datadriven vehicle routing with time windows. Robust optimization models can be useful in the following situations. Robust optimization belongs to an important methodology for dealing with optimization problems with data uncertainty.
Cuttingset methods for robust convex optimization with. Datadriven distributionally robust optimization using the. The last decade witnessed an explosion in the availability of data for operations research applications. Robust optimization with data driven asymmetric uncertainty. Our datadriven robust polynomial optimization method applies to a number of machine learning problems.
Data driven distributionally robust optimization using the wasserstein metric. The probability distribution of the random variable. Distributionally robust optimization under moment uncertainty. Datadriven robust optimization gtest are based on phidivergences see also 32.
They focus on the case where the uncertain parameters u. Boyd at stanford, this is a rare case where watching live lectures is better than reading a book. Robust optimization with data driven asymmetric uncertainty set construction zukui li, said rahal department of chemical and materials engineering, university of alberta, edmonton, ab, canada t6g1h9 abstract in this paper, we introduced a novel method for asymmetric uncertainty set construction based on the distributional information of. In this paper, we propose a new type of distributionally robust optimization model called the likelihood robust optimization lro model for this class of problems. These robust counterparts are derived using the three steps that are described above. Data driven optimization models and algorithms youtube. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology.
With the development of technologies such as sensor networks, storage devices, and cloud computing, we are able to collect, store, and analyze a large amount of data in real time. Integration of data in optimization methods has made a leap forward in recent years. Distributionally robust optimization and its tractable approximations. I thought that this one would have a more practical view to apply this method. This book is devoted to robust optimization a speci.
Jon macdonald jon macdonald is the founder and president of the good, conversion rate experts who deliver more revenues, customers, and leads. However, we need conic duality instead of lp duality in step 2 to derive the tractable robust counterparts for the conic uncertainty set. Some of the problem parameters are estimates and carry estimation risk. Data driven robust optimization p2 the set u implies a probabilistic guarantee for p. In chemical engineering, various operations and reactor systems can also be optimized through data driven robust optimization. Robust optimization problems where theuncertainty isaprobability. Datadriven robust optimization p2 the set u implies a probabilistic guarantee for p. A new datadriven robust optimization method is proposed based on kernel learning. The ks distance was used by 17 in defining an ambiguity set for a datadriven distributionally robust optimization model. In a general setting, robust optimization deals with optimization problems with two sets of variables, decision variables here denoted x and uncertain variables w. Modern decisionmaking under uncertainty dimtris bertsimas. Aug 10, 2009 robust optimization is designed to meet some major challenges associated with uncertaintyaffected optimization problems.
The primary goal of this preface is to provide the reader with a. There are two kinds of raw materials, rawi and rawii, which can be used as sources of the active agent. Opre201811676 20 study a robust vrptw and propose two models that are solved, respectively, by extending the resource and path inequalities from the deterministic to the robust optimization context and. Distributionally robust optimization dro online linear programming olp least squares with nonconvex regularization lsnr alternating direction method of multipliers admm su. Distributionally robust optimization dro online linear programming olp least squares with nonconvex regularization lsnr alternating direction method of multipliers admm data drivenoptimization yinyuye k. One approach in these cases is to formulate a conservative approximation optimization. Aurelie thieley march 2006 abstract traditional models of decisionmaking under uncertainty assume perfect information, i. The data of optimization problems of real world origin typically is uncertain not. Robust optimization refers to the modeling of optimization problems with data uncertainly. One example arises in markov decision problems where a highdimensional valuefunction is approximated by a lowdimensional polynomial v. Datadriven distributionally robust optimization using the wasserstein metric.
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. 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 can be represented as deterministic variability in the value of the parameters of the problem itself andor its solution. Data driven optimization uses observations of the random variables as direct inputs to the mathematical programming problems. Data driven optimization models and algorithms simons institute. For negative results, which show that some robust optimization problems are for example nphard, see e. Distributionally robust optimization under moment uncertainty 2 operations research 000, pp. Computational tractability is well preserved by the robust counterpart problem. Central themes in ro include understanding how to structure the uncertainty set r with loss probability p loss. Datadriven distributionally robust polynomial optimization. Cooperative datadriven distributionally robust optimization ashish cherukuri jorge corte.
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