Robust Optimization

A successive linear programming algorithm with non-linear time series for the reservoir management problem

  • Erick Delage
  • Charles Gauvin
  • Michel Gendreau
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    This paper proposes a multi-stage stochastic programming formulation based on affine decision rules for the reservoir management problem. Our approach seeks to find a release schedule that balances flood control and power generation objectives while considering realistic operating conditions as well as variable water head. To deal with the non-convexity introduced by the variable water … Read more

    Optimized Bonferroni Approximations of Distributionally Robust Joint Chance Constraints

  • Shabbir Ahmed
  • Ruiwei Jiang
  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold $\epsilon$, over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to … Read more

    Decomposition Algorithms for Two-Stage Distributionally Robust Mixed Binary Programs

  • Manish Bansal
  • Kuo-Ling Huang
  • Sanjay Mehrotra
    • Categories 0-1 Programming, Robust Optimization, Stochastic Programming

    In this paper, we introduce and study a two-stage distributionally robust mixed binary problem (TSDR-MBP) where the random parameters follow the worst-case distribution belonging to an uncertainty set of probability distributions. We present a decomposition algorithm, which utilizes distribution separation procedure and parametric cuts within Benders’ algorithm or L-shaped method, to solve TSDR-MBPs with binary … Read more

    Robust combinatorial optimization with knapsack uncertainty

  • Michael Poss
    • Categories Combinatorial Optimization, Robust Optimization Tags , , ,

    We study in this paper min max robust combinatorial optimization problems for an uncertainty polytope that is defined by knapsack constraints, either in the space of the optimization variables or in an extended space. We provide exact and approximation algorithms that extend the iterative algorithms proposed by Bertismas and Sim (2003). We also study the … Read more

    Distributionally Robust Stochastic Optimization with Dependence Structure

  • Anton J. Kleywegt
  • Rui Gao
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming

    Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for specifying a set of distributions have been proposed. The choice matters, because it affects the results, and the relative performance of different choices depend on … Read more

    Scenario Reduction Revisited: Fundamental Limits and Guarantees

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Kilian Schindler
  • Wolfram Wiesemann
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , , , ,

    The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure … Read more

    Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric

  • Yongchao Liu
  • Xinmin Yang
  • Jin Zhang
  • Yong Zhao
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Reward-risk ratio (RR) is a very important stock market definition. In recent years, people extend RR model as distributionally robust reward-risk ratio (DRR) to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty. In this paper, we study the DRR model where the ambiguity on the … Read more

    The Robust Uncapacitated Lot Sizing Model with Uncertainty Range

  • Dong Li
  • Dolores Romero Morales
    • Categories (Mixed) Integer Linear Programming, Production and Logistics, Robust Optimization Tags , , ,

    We study robust versions of the uncapacitated lot sizing problem, where the demand is subject to uncertainty. The robust models are guided by three parameters, namely, the total scaled uncertainty budget, the minimum number of periods in which one would like the demand to be protected against uncertainty, and the minimum scaled protection level per … Read more

    A Robust Approach to the Capacitated Vehicle Routing Problem with Uncertain Costs

  • Christoph Buchheim
  • Uwe Clausen
  • Jannis Kurtz
  • Lars Eufinger
    • Categories Combinatorial Optimization, Robust Optimization, Transportation Tags , ,

    We investigate a robust approach for solving the Capacitated Vehicle Routing Problem (CVRP) with uncertain travel times. It is based on the concept of K-adaptability, which allows to calculate a set of k feasible solutions in a preprocessing phase before the scenario is revealed. Once a scenario occurs, the corresponding best solution may be picked … Read more

    Distributionally robust chance constrained optimal power flow with renewables: A conic reformulation

  • Shabbir Ahmed
  • Weijun Xie
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming

    The uncertainty associated with renewable energy sources introduces significant challenges in optimal power flow (OPF) analysis. A variety of new approaches have been proposed that use chance constraints to limit line or bus overload risk in OPF models. Most existing formulations assume that the probability distributions associated with the uncertainty are known a priori or … Read more