Robust optimization for environmental and energy planning. The last decade witnessed an explosion in the availability of data for operations research applications. In this paper, we propose a framework for robust modeling of linear programming problems using uncertainty sets described by an arbitrary norm. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. The network models were validated by the partners, as well. In 2002, the assets of dynamic ideas were sold to american express. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the. Theory and applications of robust optimization dimitris bertsimas, david b. In recent years, he has worked in robust optimization, healthcare, and finance. Our focus is on the computational attractiveness of ro approaches, as well as th. I thought that this one would have a more practical view to apply this method.
Books from the 2nd or 3d printing can be identi ed by the entry \second printing or \third printing below the isbn number in the page in the front. Introduction to linear optimization dimitris bertsimas and john n. 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. The farkas prize is awarded biannually by informs for the most significant contribution to the field of optimization by a researcher. We propose a general methodology based on robust optimization to address the. There are few examples to illustrate the techniques of robust optimization, and most of this content discusses. Lncs 3064 a robust optimization approach to supply chain. Theory and applications of robust optimization siam. 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. We propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution, and is computationally tractable both practically and theoretically.
The book is used in the doctoral level course, integer and combinatorial optimization at the massachusetts institute of technology. A faculty member since 1988, his research interests include optimization, stochastic systems, machine learning, and their application. The book is indeed good in mathematical theory and only for that. Through an illustrative example, we suggest ways of putting robust optimization at work in environmental and energy optimization models. October 27, 2010 abstract in this paper we survey the primary research, both theoretical and applied, in the area of robust optimization ro.
Robust optimization with simulated annealing, with omid nohadani, journal of global optimization, 2009. Whereas stochastic programming assumes there is a probabilistic description of the uncertainty, robust optimization works with a deterministic, setbased description of the uncertainty. Part i covers robust, sparse, nonlinear, holistic regression and extensions. Different uncertainty sets, including those studied in literature i. Emphasis is on methodology and the underlying mathematical structures.
It manages to bring out the beauty of the subject and provides enough exercises to test and build your understanding. Parrilo, mathematics of operations research, may 2010. Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Both areas are practically significant as real world problems have very often both continuous and discrete variables and have elements of uncertainty that need to be addressed in a tractable manner. Robust optimization by melvyn sim submitted to the sloan school of management on may 14, 2004, in partial ful. Bertsimas, pachamanova, and sim 32 show that robust. Dimitris bertsimas at massachusetts institute of technology. Robust linear optimization under general norms, with dessi pachamanova and melvyn sim, operations research letters, 32, 510516, 2004. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we. Machine learning under a modern optimization lens dynamic ideas.
The robust optimization approach constructs a solution that is feasible for any realization of. Optimization methods sloan school of management mit. Theory and applications of robust optimization jstor. In recent years, he has worked in robust optimization, statistics, healthcare, transportation and finance. Through an illustrative example, we suggest ways of putting robust optimization at work in. A robust optimization approach to inventory theory, with aurelie thiele, operations research, 54, 1, 150168, 2006. This is a really nice book that can serve as a starting point in optimization.
Both areas are practically significant as real world problems have very often both continous and discrete variables and have elements of uncertainty that need to be addressed in a tractable manner. A practical guide to robust optimization sciencedirect. Contrast for example with books that are populated with why. While there are many highoptimization ro came from the robust control community, ro is a distinct. Dimitris bertsimas was awarded the 2008 farkas prize of the informs optimization society, for his research work on robust optimization and its applications. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. The goal of the present chapter is to introduce a relatively new field, known as robust optimization, as an alternative to traditional methods and formulations. This book is impressive for theory, every thing you ever wanted to know or how to avoid some other is here. This book is devoted to robust optimization a specific and.
Dimitris bertsimas is the author of introduction to linear optimization 4. A breakthrough approach to creative problem solving, innovation, and change. Extensions of integer optimization includes chapters 12 and, and treats mixed integer optimization and robust discrete optimization. Tsitsiklis, john and a great selection of similar new, used and collectible books available now at great prices. We also refer the interested reader to the recent book of bental. A robust optimization approach to supply chain management dimitris bertsimas and aur. The book provides a unified, insightful, and modern treatment of the theory of integer optimization. There are several ways to apply robust optimization and the choice of form is typical of the problem that is being solved. Robert weismantel and a great selection of related books, art and collectibles available now at. Theory and applications of robust optimization citeseerx. Tsitsiklis errata sheet last updated on 51507 the errata depend on the printing. Introduction to linear optimization hardcover feb 1 1997.
Bertsimass mit webpage states that his current research is focused on robust optimization and its motivation is two fold 1 tackling data uncertainty for structured mathematical programming problems and 2 modeling stochastic and dynamic optimization problems using uncertainty sets as opposed to probability distributions. In contrast to ro, stochastic optimization starts by assuming the uncertainty has. Optimality of affine policies in multistage robust optimization, with dan a. Robust optimization belongs to an important methodology for dealing with optimization problems with data uncertainty. Introduction to linear optimization dimitris bertsimas. Our focus is on the computational attractiveness of ro approaches, as well as the modeling power and broad applicability of the methodology. Part of the lecture notes in computer science book series lncs, volume 3064. This book is direct, didactic, and spends 2 pages when the author thinks it is necessary. Tsitsiklis errata sheet last updated on 62510 the errata depend on the printing. Robust discrete optimization under ellipsoidal uncertainty sets, with melvyn sim, april 2004. We provide an example showing that the feasibility set delimited by 2 is in general nonconvex, which contrasts with the convexity of. We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain. Dimitris bertsimas is the boeing leaders for global operations professor of management, a professor of operations research, and codirector of the operations research center at mit. Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper.
Adaptive robust optimization for the security constrained unit commitment problem d bertsimas, e litvinov, xa sun, j zhao, t zheng ieee transactions on power systems 28 1, 5263, 2012. Our focus is on the computational attractiveness of ro approaches, as well as the. A robust optimization approach to supply chain management. Robust linear optimization under general norms sciencedirect. This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Pdf theory and applications of robust optimization researchgate. Im a civil engineer, actually studying for masters degree in hydraulic engineering, working with the creation of and model to use robust optimization for operation of hydroelectric power plants. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are. Robust optimization princeton series in applied mathematics 9780691143682. Robust optimization ro is an active research field that has been mainly developed in the course of last twenty years. Dimitris bertsimas author of introduction to linear. One major motivation for studying robust optimization is that in many applications the data set is an appropriate notion of parameter uncertainty, e. Extensions of integer optimization includes chapters and 14, and treats mixed integer optimization and robust discrete optimization.
Introduction to linear optimization by dimitris bertsimas. The goal of robust optimization is to find solutions that are immune to uncertainty of parameters in a given mathematical optimization problem. Robust discrete optimization and network flows springerlink. Robust combinatorial optimization with variable budgeted uncertainty 3 protecting the associated ambiguous chance constraint with the same probability. We explicitly characterize the robust counterpart as a convex optimization problem that involves the dual norm of the given norm. A tutorial on robust optimization, given at the ima. Part iv shows the power of optimization over randomization in design of experiments, exceptional responders, stable regression and the bootstrap. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. Wireless network design all the presented results are strongly based on discussions with experts from our industrial partners, such as. A comparison of monte carlo tree search and rolling horizon optimization for. Bertsimas was a cofounder of dynamic ideas, llc, which developed portfolio management tools for asset management.
The analytics edge provides a unified, insightful, modern and entertaining treatment of analytics. Brown, and constantine caramanis overly conservative and in many cases are very similar to those produced by stochastic methods. Datadriven robust optimization mathematical programming. Robust counterpart formulations for linear optimization. I teach to industrial engineering students, so i have to use other books for the application, but for the theory, everything is covered here, even more, in the book are several simple rules to avoid tipical problems of the simplex method or transportation problems, or integer forms. Practical robust optimization an introduction lnmb. Tsitsiklis, john and a great selection of similar new, used and collectible books. Adaptive robust optimization for the security constrained unit commitment problem d.
The second motivation of robust optimization is to model stochastic and dynamic optimization problems using uncertainty sets as opposed to probability. In particular, when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty, we propose a. His research interests include optimization, stochastic systems, data mining, and their application. The book covers the science of using data to build models, improve decisions, and ultimately add value to institutions and individuals. Introduction to linear optimization athena scientific series in optimization and neural computation, 6 9781886529199 by dimitris bertsimas. Robust optimization is an emerging area in research that allows addressing different optimization problems and specifically industrial optimization problems where there is a degree of uncertainty in some of the variables involved. Bertsimas and sim show that the robust counterpart is still an lp. Aug 10, 2009 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. Unfortunately there is few books that deals with robust optimization. Robust combinatorial optimization with variable budgeted. Fundaments of robust optimization multiband uncertainty in robust optimization an application. Dimitris bertsimas is the boeing leaders for global operations professor of management, a professor of operations research, and the associate dean for the master of business analytics at mit.
In section 2, we discuss a wide array of optimization classes and also uncertainty sets, and we consider the properties of the robust versions. Princeton series in applied mathematics, title robust optimization, year 2009 related entries. Dimitris bertsimas, mit sloan school of management. Part ii contains optimal classification and regression trees. The book provides an original treatment of machine learning ml using convex, robust and mixed integer optimization that leads to solutions to central ml problems at large scale that can be found in secondsminutes, can be certified to be optimal in minuteshours, and outperform classical heuristic approaches in outofsample experiments. Robust optimization is a relatively new approach to modeling uncertainty in optimization problems. Stochastic optimization starts by assuming the uncertainty has a probabilistic description. Introduction to linear optimization errata sheet errata in.
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