Optimal power flow opf tools are routinely used to schedule and continuously dispatch controllable generators and loads to balance the system with minimal costs and losses. The conference booklet contains full details of the conference program as well as other useful information. 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. When robust statistics meets with robust optimization. Then, we make distributionally robust decisions that hedge against the worstcase distributions within the ambiguity set.
Section 2 presents the model of datadriven distributionally robust polynomial optimization dro for short. Datadriven optimization for intelligent and efficient transport. Robustness of datadriven cvar optimization using smoothing technique by johnny chow aresearchpaper presented to the university of waterloo in partial ful. Datadriven robust optimzation an introduction to developing smart uncertainty sets mohammad namakshenas research fellow at choir march 18, 2019. Robust optimization problems where theuncertainty isaprobability. Datadriven distributionally robust polynomial optimization. The probability distribution of the random variable. First, adopting a worstcase approach regularizes the optimization problem and thereby mitigates the optimizer s curse characteristic for stochastic.
Robust optimization allows for the modeling of an uncertainty set and ensures that the chosen solution can handle any possible realization based on this uncertainty set. We introduce a new notion of datadriven distributional robustness. First, adopting a worstcase approach regularizes the optimization problem and thereby mitigates the optimizer. Datadriven robust optimization for crude oil blending. Leveraging big data for robust process operation under.
Research proposed a datadriven adaptive robust optimization method for operational optimization. The agents aim to cooperatively find, using their collected data, a solution with guaranteed outofsample performance. Research proposed a datadriven adaptive robust optimization method for operational optimization of an industrial steam system under. Datadriven optimization under distributional uncertainty. First, the blending effect model is used to extract uncertainties of oil components from production data. Introduction robust optimization is a popular approach to optimization. We propose piecewise linear kernelbased support vector clustering svc as a new approach tailored to data driven robust optimization. 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. Datadriven distributionally robust optimization using the wasserstein metric 2 distributionally robust optimization has the following striking bene ts. We study new datadriven distributionally robust optimization.
This set is a ball around a density function estimated from data samples, i. Robustness of datadriven cvar optimization using smoothing. Datadriven decision making under uncertainty integrating. By solving a quadratic program, the distributional geometry.
We consider robust optimization for polynomial optimization problems where the uncertainty set is a set of candidate probability density functions. We investigate a datadriven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose. Datadriven distributionally robust optimization using the. 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. By leveraging a dirichlet process mixture model, a datadriven uncertainty. As a result, it can utilize characteristic properties of systematically collected data to optimize certain features of any given system. Such methods include sample average approximation, estimatethenoptimize policies, datadriven robust optimization. Integration of data in optimization methods has made a leap forward in recent years. The purpose of this tutorial is to illustrate the capabilities of the robust and datadriven optimization. Pishvaee,data driven robust optimization, in robust and constrained optimization. Keywords robust optimization datadriven optimization chanceconstraints. We investigate a data driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint. Introduction robust optimization is a popular approach to optimization under uncertainty. The approach is flexible and widely applicable, and robust optimization.
When machine learning meets robust optimization ufrgs. In this paper, we combine the polynomial and uncertain features and consider polynomial robust optimization. Distributionally robust optimization under moment uncertainty. Robust optimization problems where the uncertainty is a probability. Jun 05, 2017 and discrete optimization, data science and application, algorithm design and analysis, computational gamemarket equilibrium, metric distance geometry, dynamic resource allocation, and stochastic and robust decision making, etc.
The application of robust optimization in power systems. A case study of production scheduling in ethylene plant. Robust optimization with data driven asymmetric uncertainty. The purpose of this tutorial is to present a mathematical framework that is wellsuited to the limited information available in reallife problems and captures the decisionmakers attitude towards uncertainty. Datadriven distributionally robust optimization using the 119 amongallmetricbasedambiguitysetsstudiedtodate,thekullbackleiblerambiguity set has attracted. Data driven robust optimization is useful in chemical engineering because of the complexity of design problems. 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.
Uncertainty in optimization can be difficult to deal with. Robust optimization is an important sub eld of optimization that deals with uncertainty in the data of optimization problems. Data driven optimization models and algorithms youtube. Datadriven robust optimization with known marginal distributions rui gao, anton j. Datadriven robust credit portfolio optimization for. Computational evidence in portfolio management and queueing confirm that our datadriven sets significantly outperform traditional robust optimization techniques whenever data are available. Largescale industrial energy systems optimization under.
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. Experiments with robust optimization columbia university. Datadriven distributionally robust optimal power flow for. Datadriven robust optimization based on kernel learning.
Datadriven robust optimization massachusetts institute of. He is an informs the institute for operations research and the management science fellow. A datadriven robust optimization ddro approach is proposed to optimize crude oil blending under uncertainty. Computational evidence in portfolio management and queueing confirm that our data driven sets significantly outperform traditional robust optimization techniques whenever data are available. Accepted contributions included in the conference program will appear in the ecso 2017 booklet. Leveraging tools from large deviations theory, we prove that this meta optimization problem admits a unique solution. Develop a system level control framework, to incorporate data information with realtime control decisions, balance vacant taxis with. Cooperative datadriven distributionally robust optimization ashish cherukuri jorge cort. Datadriven robust optimization gtest are based on phidivergences see also 32. 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. Datadriven adaptive robust unit commitment under wind. Sep 19, 2015 we consider optimal decisionmaking problems in an uncertain environment.
The best predictorprescriptor pair is obtained by solving a distributionally robust optimization problem over all distributions within a given relative entropy distance from the empirical distribution of the data. Datadriven robust optimization for steam systems in ethylene. A datadriven robust optimization ddro methodology is proposed to deal with uncertainty in the optimization of steam system in an ethylene plant. Distributionally robust optimization under moment uncertainty 2 operations research 000, pp. Datadriven and distributionally robust optimization and applications part 12.
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. Send your exam by mail in pdf by monday 23032020 at 8pm. 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 main contribution of this paper is that we propose a datadriven robust portfolio optimization model based on relative entropy constraints combined with instancebased risk assessment. Cooperative datadriven distributionally robust optimization. Datadriven robust optimization model the uncertain parameters, the enthalpies of the inlet h st in u st 1 and extraction steams h st ext u st 2, are calculated by iapwsif97 based on. Robust optimization in electric power system operations duration. For example, data driven robust optimization can be used in complex supply chain optimization. Follow the moneyball method of datadriven testing and optimization, and youll be on your way to the world series of increased revenues in no time. Data driven distributionally robust optimization using the wasserstein metric. Algorithms and uncertainty sets for datadriven robust.
Datadriven robust optimization is useful in chemical engineering because of the complexity of design problems. Do you agree that a datadriven approach is a must for making your roi shine. Dec 31, 20 the last decade witnessed an explosion in the availability of data for operations research applications. Stephens, m edf statistics for goodness of fit and some.
Datadriven robust optimization under correlated uncertainty. We introduce a simple uncertainty set for arrival rates based on some structural properties of optimal queueing and routing solutions. Computational evidence in portfolio management and queueing confirm that our datadriven sets significantly outperform traditional robust optimization techniques whenever data. 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. Send your exam by mail in pdf by monday 23 032020 at 8pm. A novel datadriven adaptive robust optimization framework fill the knowledge gap datadriven decision making under uncertainty 2. In this paper, we propose an e ective data driven approach for robust optimization. The data driven optimization for intelligent and efficient transport doit project takes advantage of the advances in emerging big data technologies to analyse this data with the aim of improving decision making in the transportation industry. Based upon this uncertainty set, we propose a data driven robust optimization framework, which includes both a data driven static robust optimization model and a data driven aro model. Section 3 situates our work in the context of the literature. Datadriven robust optimization for steam systems in. Datadriven distributionally robust optimization using the wasserstein metric. A notable merit of the proposed uncertainty set is that it flexibly adapts to the intrinsic structure and complexity of uncertainty data. Datadriven distributionally robust optimization for power.
The approach is to formulate a datadriven distributionally robust optimization. Likelihood robust optimization for datadriven problems. Robust optimization methodology and applications 455 cones k1. The last decade witnessed an explosion in the availability of data for operations research applications. Datadriven static robust optimization bertsimas et al. This may somewhat explain the scarce of applications of machine learning models in robust optimization all this time.
It is about following a scientific, datadriven approach. This paper proposes a novel datadriven adaptive robust optimization aro framework for the unit commitment uc problem integrating wind power into smart grids. Data driven distributionally robust optimization using the wasserstein metric 3 computational e ort is reported to be considerable, and there is no guarantee to nd the global optimum. Robust optimization and polynomial optimization are already an important topic in machine learning and operations research. 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. Robust optimization, uncertainty set, datadriven methods, support. The transformation to smarter cities brings an array of emerging urbanization challenges. Nov 28, 2017 data driven optimization models and algorithms simons institute. Distributionally robust optimization dro online linear programming olp least squares with nonconvex regularization lsnr alternating direction method of multipliers admm su. Event locations and floor plan pdf of the floor plan tuesday. Datadriven distributionally robust optimization using the wasserstein metric 2 distributionally robust optimization has the following striking benets. Datadriven robust optimization with known marginal. Selim mankai, france ipag lab, ipag business school.
We show that common datadriven methods may perform poorly in this new setting, despite their provably good performance in the traditional largesample regime. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis. All the algorithms and methods have been coded in a matlab toolbox allowing numerical analysis, reliability analysis, simulation, sensitivity, optimization, robust. Pdf nowadays, data becomes a critical corporate asset. They focus on the case where the uncertain parameters u. Keywords robust optimization datadriven optimization chance constraints. The new frontier of data driven price optimization duration. Distributionally robust optimization dro online linear programming olp least squares with nonconvex regularization lsnr alternating direction method of multipliers admm. We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Mar 31, 2020 smart ab testing is more than just about testing random ideas. Under this framework, the objective and constraint functions. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are. Datadriven and distributionally robust optimization and applications part 12 duration. In contrast to previous work on distributionally robust optimization that focuses on certain parameters e.
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