robust optimization

Algorithmic Differentiation for Piecewise Smooth Functions: A Case Study for Robust Optimization

  • Sabrina Fiege
  • Andreas Griewank
  • Kshitij Kulshreshtha
  • Andrea Walther
    • Categories Nonsmooth Optimization Tags , , ,

    This paper presents a minimization method for Lipschitz continuous, piecewise smooth objective functions based on algorithmic differentiation (AD). We assume that all nondifferentiabilities are caused by abs(), min(), and max(). The optimization method generates successively piecewise linearizations in abs-normal form and solves these local subproblems by exploiting the resulting kink structure. Both, the generation of … 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

    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

    Robust Dual Dynamic Programming

  • Angelos Georghiou
  • Angelos Tsoukalas
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    Multi-stage robust optimization problems, where the decision maker can dynamically react to consecutively observed realizations of the uncertain problem parameters, pose formidable theoretical and computational challenges. As a result, the existing solution approaches for this problem class typically determine subopti- mal solutions under restrictive assumptions. In this paper, we propose a robust dual dynamic programming … Read more

    Adjustable robust strategies for flood protection

  • Dick den Hertog
  • Krzysztof Postek
  • Jarl Kind
  • Chris Pustjens
    • Categories Civil and Environmental Engineering Tags , , ,

    Flood protection is of major importance to many flood-prone regions and involves substantial investment and maintenance costs. Modern flood risk management requires often to determine a cost-efficient protection strategy, i.e., one with lowest possible long run cost and satisfying flood protection standards imposed by the regulator throughout the entire planning horizon. There are two challenges … Read more

    Maximizing a class of utility functions over the vertices of a polytope

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , , , ,

    Given a polytope X, a monotone concave univariate function g, and two vectors c and d, we study the discrete optimization problem of finding a vertex of X that maximizes the utility function c’x + g(d’x). This problem has numerous applications in combinatorial optimization with a probabilistic objective, including estimation of project duration with stochastic … Read more

    A Copositive Approach for Two-Stage Adjustable Robust Optimization with Uncertain Right-Hand Sides

  • Samuel Burer
  • Guanglin Xu
    • Categories Dynamic Programming, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , , ,

    We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We prove that under standard and simple conditions, the two-stage problem can be reformulated as a copositive optimization problem, which … Read more

    Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

  • Grani A. Hanasusanto
  • Daniel Kuhn
    • Categories Robust Optimization Tags , , ,

    Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust and distributionally robust linear programs can often be reformulated exactly as conic programs that scale polynomially with the problem dimensions. Specifically, … 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

    A Tractable Approach for designing Piecewise Affine Policies in Two-stage Adjustable Robust Optimization

  • Aharon Ben-Tal
  • Omar El Housni
  • Vineet Goyal
    • Categories Robust Optimization Tags , ,

    We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of pieces can be exponentially large. A significant challenge in designing a practical piecewise affine policy is constructing good pieces of … Read more