Robust Optimization

On deterministic reformulations of distributionally robust joint chance constrained optimization problems

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

    A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exceeding a prespecified threshold. In a distributionally robust joint chance constrained optimization problem (DRCCP), the joint chance constraint is required to hold for all probability distributions of the stochastic parameters from … Read more

    Ambiguous Risk Constraints with Moment and Unimodality Information

  • Ruiwei Jiang
  • Bowen Li
  • Johanna L. Mathieu
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    Optimization problems face random constraint violations when uncertainty arises in constraint parameters. Effective ways of controlling such violations include risk constraints, e.g., chance constraints and conditional Value-at-Risk (CVaR) constraints. This paper studies these two types of risk constraints when the probability distribution of the uncertain parameters is ambiguous. In particular, we assume that the distributional … Read more

    Quadratic Two-Stage Stochastic Optimization with Coherent Measures of Risk

  • Rodrigues Brian
  • Lizhi Liao
  • Jie Sun
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming

    A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second … Read more

    Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization

  • Jonathan Yu-Meng Li
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags ,

    Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be evaluated in closed form when only the first … Read more

    Stochastic and robust optimal operation of energy-efficient building with combined heat and power systems

  • Ping Liu
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , ,

    Energy efficiency and renewable energy become more attractive in smart grid. In order to efficiently reduce global energy usage in building energy systems and to improve local environmental sustainability, it is essential to optimize the operation and the performance of combined heat and power (CHP) systems. In addition, intermittent renewable energy and imprecisely predicted customer … Read more

    Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

  • Melvyn Sim
  • Huan Xu
  • Zhi Chen
    • Categories Robust Optimization Tags ,

    We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinitely … Read more

    Designing Response Supply Chain Against Bioattacks

  • David Simchi-Levi
  • Peter Yun Zhang
  • Nikolaos Trichakis
    • Categories Applications - OR and Management Sciences, Robust Optimization, Supply Chain Management

    Bioattacks, i.e., the intentional release of pathogens or biotoxins against humans to cause serious illness and death, pose a significant threat to public health and safety due to the availability of pathogens worldwide, scale of impact, and short treatment time window. In this paper, we focus on the problem of prepositioning inventory of medical countermeasures … Read more

    Improved Handling of Uncertainty and Robustness in Set Covering Problems

  • Christina Büsing
  • Dirk Degel
  • Arie M.C.A. Koster
  • Pascal Lutter
  • Brigitte Werners
    • Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Robust Optimization Tags , , ,

    This paper studies the emergency service facility location problem in an uncertain environment. The main focus is the integration of uncertainty regarding the covered area due to uncertain traveling times. Previous approaches only consider either probabilistic or fuzzy optimization to cope with uncertainty. However, in many real-world problems the required statistical parameters are not precisely … Read more

    Dice-sion Making under Uncertainty: When Can a Random Decision Reduce Risk?

  • Erick Delage
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming

    Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions which depend on a randomization device producing uniformly distributed samples that are independent of all … Read more

    Adjustable Robust Optimization via Fourier-Motzkin Elimination

  • Dick den Hertog
  • Melvyn Sim
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    We demonstrate how adjustable robust optimization (ARO) problems with fixed recourse can be casted as static robust optimization problems via Fourier-Motzkin elimination (FME). Through the lens of FME, we characterize the structures of the optimal decision rules for a broader class of ARO problems. A scheme based on a blending of classical FME and a … Read more