Robust Optimization

A Unifying Framework for the Capacitated Vehicle Routing Problem under Risk and Ambiguity

  • Shubhechyya Ghosal
  • Chin Pang Ho
  • Wolfram Wiesemann
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , ,

    We propose a generic model for the capacitated vehicle routing problem (CVRP) under demand uncertainty. By combining risk measures, satisficing measures or disutility functions with complete or partial characterizations of the probability distribution governing the demands, our formulation bridges the popular but often independently studied paradigms of stochastic programming and distributionally robust optimization. We characterize … Read more

    Statistical Inference of Contextual Stochastic Optimization with Endogenous Uncertainty

  • Junyu Cao
  • Rui Gao
    • Categories Robust Optimization, Statistics, Stochastic Programming Tags

    This paper considers contextual stochastic optimization with endogenous uncertainty, where random outcomes depend on both contextual information and decisions. We analyze the statistical properties of solutions from two prominent approaches: predict-then-optimize (PTO), which first predicts a model between outcomes, contexts, and decisions, and then optimizes the downstream objective; and estimate- then-optimize (ETO), which directly estimates … Read more

    Screening with Limited Information: A Dual Perspective and A Geometric Approach

  • Zhi Chen
  • Zhenyu Hu
  • Ruiqin Wang
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    Consider a seller seeking a selling mechanism to maximize the worst-case revenue obtained from a buyer whose valuation distribution lies in a certain ambiguity set. For a generic convex ambiguity set, we show via the minimax theorem that strong duality holds between the problem of finding the optimal robust mechanism and a minimax pricing problem … Read more

    Adjustability in Robust Linear Optimization

  • Ningji Wei
  • Peter Yun Zhang
    • Categories Robust Optimization Tags , ,

    We investigate the concept of adjustability — the difference in objective values between two types of dynamic robust optimization formulations: one where (static) decisions are made before uncertainty realization, and one where uncertainty is resolved before (adjustable) decisions. This difference reflects the value of information and decision timing in optimization under uncertainty, and is related … Read more

    Robust CARA Optimization

  • Li Chen
  • Melvyn Sim
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , ,

    We propose robust optimization models and their tractable approximations that cater for ambiguity-averse decision makers whose underlying risk preferences are consistent with constant absolute risk aversion (CARA). Specifically, we focus on maximizing the worst-case expected exponential utility where the underlying uncertainty is generated from a set of stochastically independent factors with ambiguous marginals. To obtain … Read more

    Adjustable robust optimization with objective uncertainty

  • Boris Detienne
  • Henri Lefebvre
  • Enrico Malaguti
  • Michele Monaci
    • Categories Applications - OR and Management Sciences, Convex Optimization, Robust Optimization Tags , , , , ,

    In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and … Read more

    Sinkhorn Distributionally Robust Optimization

  • Jie Wang
  • Rui Gao
  • Yao Xie
    • Categories Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming

    We study distributionally robust optimization with Sinkhorn distance—a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. To solve the dual reformulation, we develop a stochastic mirror descent algorithm with biased subgradient estimators and derive its computational complexity guarantees. Finally, … Read more

    Effective Scenarios in Multistage Distributionally Robust Optimization with a Focus on Total Variation Distance

  • Hamed Rahimian
  • Güzin Bayraksan
  • Tito Homem-de-Mello
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an “effect” on the optimal value, we investigate the question of how to define and identify critical scenarios for nested multistage DRO problems. Our analysis … Read more

    Data-Driven Distributionally Preference Robust Optimization Models Based on Random Utility Representation in Multi-Attribute Decision Making

  • Jian Hu
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker’s (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our … Read more

    Pareto Robust Optimization on Euclidean Vector Spaces

  • Dennis Adelhütte
  • Christian Biefel
  • Martina Kuchlbauer
  • Jan Hendrik Rolfes
    • Categories Robust Optimization Tags , ,

    Pareto efficiency for robust linear programs was introduced by Iancu and Trichakis. We generalize their approach and theoretical results to robust optimization problems in Euclidean spaces with affine uncertainty. Additionally, we demonstrate the value of this approach in an exemplary manner in the area of robust semidefinite programming (SDP). In particular, we prove that computing … Read more