Theory and applications of robust optimization siam. We also refer the interested reader to the recent book of bental. Bertsimas and sim 2004, which introduce the notion ofabudgetofuncertaintytoreducetheconservatism of robust optimization. We also show that the robust counterpart of an nphard. Introduction to linear optimization by dimitris bertsimas. In the datadriven framework, uncertainty sets are directly constructed from uncertainty data. Robust optimization an overview sciencedirect topics. Robust optimization is a young and active research field that has been mainly developed in the last 15 years. 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. Bertsimas likes his equations though and is sometimes a bit short on explanations. This book is an authoritative reference that will be very useful to researchers working in this area. 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.
A practical guide to robust optimization sciencedirect. Robust optimization is an important sub eld of optimization that deals with uncertainty in the data of optimization problems. Through an illustrative example, we suggest ways of putting robust optimization at work in. Bertsimas second area of research is robust optimization, the goal of which is to propose a tractable theory for optimization under uncertaintytake air traffic control, for example where the uncertainty is mainly to the weather. 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 for environmental and energy planning. Bertsimas and others published introduction to linear optimization find, read and cite all the research you need on researchgate. Theory and applications of robust optimization citeseerx. We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. Dimitris bertsimas at massachusetts institute of technology. Bertsimas and thiele 2006 apply the ideas in bertsimas and sim 2004 to formulate a robust optimization model of inventory control, which can handle. The farkas prize is awarded biannually by informs for the most significant contribution to the field of optimization by a researcher. Dimitris bertsimas author of introduction to linear.
The remainder of the chapter is organized as follows. Whereas stochastic programming assumes there is a probabilistic description of the uncertainty, robust optimization works with a deterministic, setbased description of the uncertainty. We show that the adaptive distributionally robust linear optimization problem can be. Finally, we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network. 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. Tsitsiklis errata sheet last updated on 51507 the errata depend on the printing. Theory and applications of robust optimization jstor.
Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the. Bertsimas and goyal consider a twostage adaptive linear optimization problem under righthand side uncertainty with a minmax objective. Optimization over integers by dimitris bertsimas and a great selection of related books, art and collectibles available now at. Introduction to linear optimization dimitris bertsimas and john n.
The first motivation for robust optimization is data uncertainty for structured mathematical programming problems. Robust optimization the goal of this work is to propose a tractable theory for optimization under uncertainty. The book is used in the doctoral level course, integer and combinatorial optimization at the massachusetts institute of technology. Robust sensitivity analysis of the optimal value of linear. Robust portfolio optimization was introduced by lobo, vandenberghe, boyd and lebret 1998 as a tractable alternative to stochastic programming. The robust optimization approach constructs a solution that is feasible for any realization of. Robust optimization is a relatively new approach to modeling uncertainty in optimization problems. A robust optimization approach to inventory theory. Nemirovski 8 studied robust optimization applied to conic quadratic and semide. In section 2, we discuss a wide array of optimization classes and also uncertainty sets, and we consider the properties of the robust versions. Furthermore, the book has been structured so that the first part could easily be used as the text for a graduate level course in robust optimization. Adaptive distributionally robust optimization management. For tractability considerations, we focus on a class of secondorder conic soc representable ambiguity set, though our results can easily be extended to more general conic.
Pdf theory and applications of robust optimization researchgate. Robust optimization ro is a relatively young methodology, developed mainly in the course of the last 15 years to analyze and optimize the performance of complex systems. Robust optimization princeton series in applied mathematics 9780691143682. The complete recourse assumption is often made in twostage robust optimization to ensure the secondstage problem is feasible. Multistage air traffic flow management under capacity. 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. Dimitris bertsimas is the author of introduction to linear optimization 4. Brown, and constantine caramanis overly conservative and in many cases are very similar to those produced by stochastic methods. A robust optimization approach to inventory theory, with aurelie thiele, operations research, 54, 1, 150168, 2006.
The concept of robust optimization has a relationship with chanceconstrained optimization, where in certain cases there is a direct relationship between a robust optimization model and a chanceconstrained optimization model. It includes classical topics as well as the state of the art, in both theory and practice. 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. 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. Finished well, finished the parts i intended to read a while ago so i dont remember much else. 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. Robust optimization belongs to an important methodology for dealing with optimization problems with data uncertainty. In this chapter, the authors give a brief introduction to important concepts of ro paradigm. Robust discrete optimization under ellipsoidal uncertainty sets, with melvyn sim, april 2004. This problem has been studied in the past using dynamic programming, which suffers from dimensionality problems and assumes full knowledge of the demand distribution. The second motivation of robust optimization is to model stochastic and dynamic optimization problems using uncertainty sets as opposed to probability. Practical robust optimization an introduction lnmb.
Robust optimization made easy with rome 974 operations research 594, pp. This book provides a unified, insightful, and modern treatment of linear optimization, that is, linear programming, network flow problems, and discrete optimization. A good survey on tractability of robust counterparts of convex optimization problems is by bertsimas et al. Robust discrete optimization and network flows springerlink. Robust optimization with multiple ranges optimization online. W e also refer the interested reader to the recent book of bental. Bertsimas, pachamanova, and sim 32 show that robust. 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. Robust linear optimization under general norms, with dessi pachamanova and melvyn sim, operations research letters, 32, 510516, 2004. In a robust optimization approach, the uncertain parameters are assumed to belong to some uncertainty set. In contrast to ro, stochastic optimization starts by assuming the uncertainty has. Adaptive distributionally robust optimization management science. Despite the attractive features of datadriven approaches, most existing publications.
A robust optimization approach to supply chain management. Dimitris bertsimas was awarded the 2008 farkas prize of the informs optimization society, for his research work on robust optimization and its applications. 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. A tight characterization of the performance of static. Stochastic optimization starts by assuming the uncertainty has a probabilistic description. A simpli ed version of this problem, in which the rststage variables are nonexistent, reduces to worstcase linear optimization. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions adapt to the uncertain outcomes as they unfold in stages. Part of the lecture notes in computer science book series lncs, volume 3064. We propose a general methodology based on robust optimization to address the. A datadriven robust optimization approach to operational optimization of industrial steam systems under uncertainty. One major motivation for studying robust optimization is that in many applications the data set is an appropriate notion of parameter uncertainty, e. Datadriven robust optimization has been proposed recently bertsimas et al. A faculty member since 1988, his research interests include optimization, stochastic systems, machine learning, and their application.
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