two-stage problems

Distributionally Robust Optimization with Decision-Dependent Information Discovery

  • Qing Jin
  • Angelos Georghiou
  • Phebe Vayanos
  • Grani A. Hanasusanto
    • Categories Robust Optimization Tags , , , , ,

    We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). … Read more

    A Lagrangian Dual Method for Two-Stage Robust Optimization with Binary Uncertainties

  • Anirudh Subramanyam
    • Categories Robust Optimization Tags , , ,

    This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only … Read more

    Data-Driven Two-Stage Conic Optimization with Zero-One Uncertainties

  • Mohamed El Tonbari
  • Kibaek Kim
  • Anirudh Subramanyam
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    We address high-dimensional zero-one random parameters in two-stage convex conic optimization problems. Such parameters typically represent failures of network elements and constitute rare, high-impact random events in several applications. Given a sparse training dataset of the parameters, we motivate and study a distributionally robust formulation of the problem using a Wasserstein ambiguity set centered at … Read more

    A Primal-Dual Lifting Scheme for Two-Stage Robust Optimization

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

    Two-stage robust optimization problems, in which decisions are taken both in anticipation of and in response to the observation of an unknown parameter vector from within an uncertainty set, are notoriously challenging. In this paper, we develop convergent hierarchies of primal (conservative) and dual (progressive) bounds for these problems that trade off the competing goals … Read more

    K-Adaptability in Two-Stage Mixed-Integer Robust Optimization

  • Chrysanthos E. Gounaris
  • Anirudh Subramanyam
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional problems that require a finite-dimensional approximation, and (ii) the presence of discrete recourse decisions typically prohibits duality-based solution schemes. We address the first challenge by studying … 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

    K-Adaptability in Two-Stage Robust Binary Programming

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Integer Programming, Robust Optimization Tags , ,

    Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multi-stage problems with continuous recourse. This paper takes a step towards extending the robust optimization methodology to problems with integer recourse, which … Read more

    Applying oracles of on-demand accuracy in two-stage stochastic programming – a computational study

  • Csaba I. Fábián
  • Achim Koberstein
  • Leena Suhl
  • Christian Wolf
    • Categories Optimization Software Benchmark, Stochastic Programming Tags , , ,

    Traditionally, two variants of the L-shaped method based on Benders’ decomposition principle are used to solve two-stage stochastic programming problems: the single-cut and the multi-cut version. The concept of an oracle with on-demand accuracy was originally proposed in the context of bundle methods for unconstrained convex optimzation to provide approximate function data and subgradients. In … Read more

    REDUCTION OF TWO-STAGE PROBABILISTIC OPTIMIZATION PROBLEMS WITH DISCRETE DISTRIBUTION OF RANDOM DATA TO MIXED INTEGER PROGRAMMING PROBLEMS

  • Andrey Kibzun
  • Vladimir I. Norkin
  • Andrey Naumov
    • Categories (Mixed) Integer Nonlinear Programming, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We consider models of two-stage stochastic programming with a quantile second stage criterion and optimization models with a chance constraint on the second stage objective function values. Such models allow to formalize requirements to reliability and safety of the system under consideration, and to optimize the system in extreme conditions. We suggest a method of … Read more