Robust Optimization

A Semi-Infinite Programming Approach for Distributionally Robust Reward-Risk Ratio Optimization with Matrix Moments Constraints

  • Yongchao Liu
  • Rudabeh Meskarian
  • Huifu Xu
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Reward-risk ratio optimization is an important mathematical approach in finance. In this paper, we revisit the model by considering a situation where an investor does not have complete information on the distribution of the underlying uncertainty and consequently a robust action is taken against the risk arising from ambiguity of the true distribution. We propose … Read more

    Single-Commodity Robust Network Design with Finite and Hose Demand Sets

  • Valentina Cacchiani
  • Frauke Liers
  • Andrea Lodi
  • Michael Juenger
  • Daniel Schmidt
    • Categories Branch and Cut Algorithms, Network Optimization, Robust Optimization Tags , , ,

    We study a single-commodity Robust Network Design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of … Read more

    Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection

  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Robust Optimization

    We introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic projection. It is well-known that deriving an explicit description of a projected polytope is NP-hard. Our approach does not require an explicit description of the projection, … Read more

    Safe Approximations of Chance Constraints Using Historical Data

  • Dick den Hertog
  • Ihsan Yanıkoğlu
    • Categories Robust Optimization, Stochastic Programming

    This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, … Read more

    A Composite Risk Measure Framework for Decision Making under Uncertainty

  • Pengyu Qian
  • Zaiwen Wen
  • Zizhuo Wang
    • Categories Robust Optimization, Stochastic Programming

    In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution of uncertain model parameters, and the outer risk measure quantifies the risk that occurs when estimating … Read more

    On the Adaptivity Gap in Two-stage Robust Linear Optimization under Uncertain Constraints

  • Pranjal Awasthi
  • Vineet Goyal
  • Brian Lu
    • Categories Approximation Algorithms, Robust Optimization

    In this paper, we study the performance of static solutions in two-stage adjustable robust packing linear optimization problem with uncertain constraint coefficients. Such problems arise in many important applications such as revenue management and resource allocation problems where demand requests have uncertain resource requirements. The goal is to find a two-stage solution that maximizes the … Read more

    Robust Binary Optimization using a Safe Tractable Approximation

  • Ruken Duzgun
  • Aurelie Thiele
    • Categories Robust Optimization Tags , ,

    We present a robust optimization approach to 0-1 linear programming with uncertain objective coefficients based on a safe tractable approximation of chance constraints, when only the first two moments and the support of the random parameters is known. We obtain nonlinear problems with only one additional (continuous) variable, for which we discuss solution techniques. The … Read more

    Min-max-min robustness: a new approach to combinatorial optimization under uncertainty based on multiple solutions

  • Christoph Buchheim
  • Jannis Kurtz
    • Categories Combinatorial Optimization, Integer Programming, Robust Optimization

    In the classical min-max approach to robust combinatorial optimization, a single feasible solution is computed that optimizes the worst case over a given set of considered scenarios. As is well known, this approach is very conservative, leading to solutions that in the average case are far from being optimal. In this paper, we present a … Read more

    The Value of Flexibility in Robust Location-Transportation Problems

  • Amir Ardestani-Jaafari
  • Erick Delage
    • Categories Facility Planning and Design, Robust Optimization, Transportation Tags , , , , ,

    This article studies a multi-period capacitated fixed-charge location-transportation problem in which, while the location and capacity of each facility need to be determined immediately, the determination of final production and distribution of products can be delayed until actual orders are received in each period. In contexts where little is known about future demand, robust optimization, … Read more