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194
Theory and applications of Robust Optimization
, 2007
"... In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most pr ..."
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Cited by 110 (16 self)
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In this paper we survey the primary research, both theoretical and applied, in the field of Robust Optimization (RO). Our focus will be on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying the most prominent theoretical results of RO over the past decade, we will also present some recent results linking RO to adaptable models for multistage decisionmaking problems. Finally, we will highlight successful applications of RO across a wide spectrum of domains, including, but not limited to, finance, statistics, learning, and engineering.
Facility Location under Uncertainty: A Review
 IIE Transactions
, 2004
"... Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made th ..."
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Cited by 77 (7 self)
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Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers in both the logistics and stochastic/robust optimization communities. Indeed, a large number of the approaches that have been proposed for optimization under uncertainty have been applied to facility location problems. This paper reviews the literature...
Tractable approximations of robust conic optimization problems
, 2006
"... In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NPha ..."
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Cited by 70 (14 self)
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In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NPhard. We propose a relaxed robust counterpart for general conic optimization problems that (a) preserves the computational tractability of the nominal problem; specifically the robust conic optimization problem retains its original structure, i.e., robust LPs remain LPs, robust SOCPs remain SOCPs and robust SDPs remain SDPs, and (b) allows us to provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.
Robust game theory
, 2006
"... We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides ..."
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Cited by 55 (0 self)
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We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides an alternative distributionfree equilibrium concept, which we call “robustoptimization equilibrium, ” to that of the ex post equilibrium. We prove that the robustoptimization equilibria of an incompleteinformation game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robustoptimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results.
A Robust Optimization Perspective Of Stochastic Programming
, 2005
"... In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of c ..."
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Cited by 51 (12 self)
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In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. We also propose a tractable robust optimization approach for obtaining robust solutions to a class of stochastic linear optimization problems where the risk of infeasibility can be tolerated as a tradeoff to improve upon the objective value. An attractive feature of the framework is the computational scalability to multiperiod models. We show an application of the framework for solving a project management problem with uncertain activity completion time.
TWOSTAGE ROBUST NETWORK FLOW AND DESIGN UNDER DEMAND UNCERTAINTY
 FORTHCOMING IN OPERATIONS RESEARCH
, 2004
"... We describe a twostage robust optimization approach for solving network flow and design problems with uncertain demand. In twostage network optimization one defers a subset of the flow decisions until after the realization of the uncertain demand. Availability of such a recourse action allows one ..."
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Cited by 47 (3 self)
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We describe a twostage robust optimization approach for solving network flow and design problems with uncertain demand. In twostage network optimization one defers a subset of the flow decisions until after the realization of the uncertain demand. Availability of such a recourse action allows one to come up with less conservative solutions compared to singlestage optimization. However, this advantage often comes at a price: twostage optimization is, in general, significantly harder than singestage optimization. For network flow and design under demand uncertainty we give a characterization of the firststage robust decisions with an exponential number of constraints and prove that the corresponding separation problem is N Phard even for a network flow problem on a bipartite graph. We show, however, that if the secondstage network topology is totally ordered or an arborescence, then the separation problem is tractable. Unlike singlestage robust optimization under demand uncertainty, twostage robust optimization allows one to control conservatism of the solutions by means of an allowed “budget for demand uncertainty.” Using a budget of uncertainty we provide an upper
Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem
, 2011
"... Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we p ..."
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Cited by 45 (3 self)
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Unit commitment, one of the most critical tasks in electric power system operations, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet these challenges, we propose a twostage adaptive robust unit commitment model for the security constrained unit commitment problem in the presence of nodal net injection uncertainty. Compared to the conventional stochastic programming approach, the proposed model is more practical in that it only requires a deterministic uncertainty set, rather than a hardtoobtain probability distribution on the uncertain data. The unit commitment solutions of the proposed model are robust against all possible realizations of the modeled uncertainty. We develop a practical solution methodology based on a combination of Benders decomposition type algorithm and the outer approximation technique. We present an extensive numerical study on the realworld large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.
Extending the Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems
 MATH. PROGRAM. 107, (2006) 63 – 89
, 2006
"... In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the propo ..."
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Cited by 41 (5 self)
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In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance when the data is outside the uncertainty set. The extension of Robust Optimization methodology developed in this paper opens up new possibilities to solve efficiently multistage finitehorizon uncertain optimization problems, in particular, to analyze and to synthesize linear controllers for discrete time dynamical systems.
A robust optimization approach to supply chain management
 Operations Research
, 2003
"... Abstract. 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. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including deman ..."
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Cited by 39 (3 self)
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Abstract. 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. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including demands that are not identically distributed over time and capacity on the echelons and links; (b) it uses very little information on the demand distributions; (c) it leads to qualitatively similar optimal policies (basestock policies) as in dynamic programming; (d) it is numerically tractable for large scale supply chain problems even in networks, where dynamic programming methods face serious dimensionality problems; (e) in preliminary computational experiments, it often outperforms dynamic programming based solutions for a wide range of parameters. 1