In this paper we provide a survey of recent contributions from operations research and. Floudas department of chemical and biological engineering, princeton university princeton, nj 08544 abstract robust counterpart optimization techniques are studied in this paper. Unfortunately there is few books that deals with robust optimization. A general robustoptimization formulation for nonlinear. Jumper robust optimization with jump jumper julia for. This book examines a novel framework, termed active robust optimization, and its unique features, provides the tools for evaluation, comparison and. When you optimize parameters for robustness, the optimization solver uses the responses computed using all the uncertain parameter values to. It is an extension of the robust optimization framework proposed by bental and nemirovski 1998, who study convex optimization while taking into account uncertainty in the data. Convex optimization and applications april 24, 2008 lecture24. July, 2004 revise june 2005 abstract most research in robust optimization has so far been focused on inequalityonly, convex conic programming with simple linear models for uncertain parameters. Robust portfolio optimization was introduced by lobo, vandenberghe, boyd and lebret 1998 as a tractable alternative to stochastic programming.
In particular, we study a class of coherent risk measures, called distortion risk measures, which give rise to polyhedral uncertainty sets of a special structure that is tractable in the context of robust optimization. N2 in this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for random variables termed the forward and backward deviations. This book is devoted to robust optimization a specific and relatively novel methodology for handling optimization problems with uncertain. A practical guide to robust optimization sciencedirect. Robust optimization princeton series in applied mathematics. It is therefore remarkable that reallife applications of robust optimization are still lagging behind. When you optimize parameters for robustness, the optimization solver uses the responses computed using all the uncertain parameter values to adjust the design variable values. In this section we learn how to apply optimization methods to determine a robust design. Solving robust problems multiple methods exist in the literature for solving robust optimization problems, and it is beyond the scope of this manual to go into too many details. Fortuitously, a general approach to robust design can be formulated in terms of optimization techniques, further extending the usefulness of these methods. Adjustable robust optimization for scheduling of batch. Focus on methodology demonstration for extreme cases, e. Convex optimization and applications april 24, 2008.
T1 adjustable robust optimization for scheduling of batch processes under uncertainty. Many practical optimization problems, however, are nonlinear and. A robust design is a design which can tolerate variation. Released under the lgpl license, the engine can be used, modified and redistributed free of charge. Our approach first reparameterizes the primitive uncertainties and then applies the affinely adjustable robust counterpart proposed in the literature, in which recourse decisions are restricted to be linear in terms of the primitive. Robust optimization is a relatively new approach to modeling uncertainty in optimization problems. 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 a comprehensive survey sciencedirect. The simplest example is markowitz portfolio optimization. I thought that this one would have a more practical view to apply this method. Robust optimization and applications rutgers university. There are several ways to apply robust optimization and the choice of form is.
For a recent account of the application of model uncertainty and robust optimization in economics and. Model uncertainty, robust optimization and learning 2 informspittsburgh 2006, c 2006 informs 1994, garlappi, uppal and wang 2005, hansen and sargent 2001, 2001, 2003. 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. On robust optimization article in journal of optimization theory and applications 1673 september 20 with 17 reads how we measure reads. One approach in these cases is to formulate a conservative approximation optimization. Pachamanova third author is an expert, as well as some relatively advanced stat methods such as robust statistics and bayesian estimation. For negative results, which show that some robust optimization problems are for example nphard, see e. While interest in research in robust optimization has increased in recent years, several factors hindered its algorithmic development. I am using optimizations techniques for my research work on. Constructing uncertainty sets for robust linear optimization. An essential book for anyone working on optimization and decision making under uncertainty, robust optimization also makes an ideal graduate.
Robust optimization is an emerging area in research that allows addressing. Both books discuss some latest optimization techniques however, this one has much more details on a modern method for handling uncertainty called robust optimization, in which dr. His methods have earned him the most wellknown brand in the field of design of experiments. A comparison of these approaches with aro is presented in table 1 and further discussed below. T1 a robust optimization perspective on stochastic programming. Jan 12, 2015 robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is a field of optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty. Princeton series in applied mathematics, title robust optimization, year 2009 related entries.
Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a. Model uncertainty, robust optimization and learning. While we have seen that the robust counterparts will usually turn the original linear or quadratic problem into nonlinear ones, the focus of recent research is on the question to identify conditions and uncertainty sets resulting in systems which can be solved efficiently, i. You can use simulink design optimization software to incorporate the parameter uncertainty to test the robustness of your design. Robust optimization using machine learning for uncertainty sets. In addition to surveying the most prominent theoretical. Uncertainty sets, formulations and probabilistic guarantees zukui li, christodoulos a. The aim of the taguchi design is to make a product or process more stable in the face of variations over which we have little or no control, for example, making sure that an engine. In contrast to existing surveys, our paper focuses on one of the most rapid and important areas, the construction of robust. A new robust optimization approach for scheduling under uncertainty.
Genichi taguchi, a japanese engineer, published his first book on experimental design in 1958. Although it provides almost everything i looked for, i see ben tals book goes deeper in the underpinnings of the subjects i looked for, which is what i. In this paper, we introduce the extended affinely adjustable robust counterpart to modeling and solving multistage uncertain linear programs with fixed recourse. One factor is the miss of a set of benchmark instances that better compare algorithm performance and eliminate the need to reproduce instances. Our focus will be on the computational attractiveness of ro approaches, as well as the modeling power and broad applicability of the methodology. Whereas stochastic programming assumes there is a probabilistic description of the uncertainty, robust optimization works with a deterministic, setbased description of the uncertainty. Theory and applications of robust optimization 467 since there are more constraints to satisfy and the smaller the loss probability p loss. September 28, 2016 with the recent extensions of the optimizer framework, it was just too simple to add basic support for samplescenario based optimization of uncertain programs. Additionally, basic versions of ro assume hard constraints, i. Central themes in ro include understanding how to structure the uncertainty set r with loss probability p loss. In the case of discrete distributions with rational probabilities, which is useful in practical settings when we are sampling.
Computers and chemical engineering, 28, 10691085, is extended in order to consider uncertainty described by a known probability distribution. Can anybody suggest good books on robust optimization and stochastic optimization which has examples with any optimization software. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Can anybody suggest good books on robust optimization and. Robust optimization in practice effectiveness of robust optimization in intensitymodulated proton therapy planning for head and neck cancers example. The field of robust mathematical programming has received increasing interest during the last five years. Aug 10, 2009 robust optimization is designed to meet some major challenges associated with uncertaintyaffected optimization problems.
Robust optimization ro, on the other hand, does not assume that probability distributions are known, but instead it assumes that the uncertain data resides in a socalled uncertainty set. The book is indeed good in mathematical theory and only for that. Distribution, random, scenario optimization updated. Robust optimization using machine learning for uncertainty. Since model 3 is a nonlinear one, it is particularly not attractive for solving robust discrete optimization models. A new robust optimization approach for scheduling under. Because of our goal to solve problems of the form 1. In this work we try to bring the eld of robust optimization further, in an e ort to bring theory and practice one step closer together. Robust optimization mathematical and statistical sciences. A tutorial on robust optimization, given at the ima.
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. Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization noesis solutions noesis solutions. Theory and applications of robust optimization dimitris bertsimas. Hows robust optimization and stochastic programming used. A robust optimization perspective on stochastic programming. In this paper we survey the primary research, both theoretical and applied, in the area of robust optimization ro. September 28, 2016 with the recent extensions of the optimizer framework, it was just too simple to add basic support for samplescenario based optimization of uncertain programs to illustrate the ideas, we will start with some pure clasical yalmip code to show how a circle can be. Robust optimization princeton series in applied mathematics 9780691143682.
Brown y, constantine caramanis z july 6, 2007 abstract in this paper we survey the primary research, both theoretical and applied, in the. Robust optimization made easy with rome 974 operations research 594, pp. The robust optimization approach constructs a solution that is feasible for any realization of. Robust optimization is designed to meet some major challenges associated with uncertaintyaffected optimization problems. Cuttingset methods for robust convex optimization with. I am trying to implement the following optimization from this paper in matlab using fmincon. Our focus will be on the computational attractiveness of ro approaches, as well. A general robustoptimization formulation for nonlinear programming yin zhang. N2 in this work, we hedge against the uncertainty in the of batch process scheduling by using a novel two.
1141 386 896 1178 428 1334 521 766 292 1358 461 735 808 436 834 865 1001 229 626 1146 658 157 499 932 960 930 1263 661 871 625 1 1138 447 1378 1435 236 245 1020 475 1211 170 360