distributionally robust optimization

Building Load Control using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

  • Yiling Zhang
  • Jin Dong
    • Categories 0-1 Programming, Robust Optimization Tags , , , ,

    Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. However, the time-varying PV generation is not perfectly known when the system operator decides the HVAC control schedules. To consider the unknown uncertain PV generation, in this paper, we formulate a distributionally robust … Read more

    Computationally Efficient Approximations for Distributionally Robust Optimization

  • Jianqiang Cheng
  • Ruiwei Jiang
  • Meysam Cheramin
  • Kai Pan
    • Categories Stochastic Programming Tags , , ,

    Distributionally robust optimization (DRO) is a modeling framework in decision making under uncertainty where the probability distribution of a random parameter is unknown while its partial information (e.g., statistical properties) is available. In this framework, the unknown probability distribution is assumed to lie in an ambiguity set consisting of all distributions that are compatible with … Read more

    A Distributionally Robust Optimization Approach for Stochastic Elective Surgery Scheduling with Limited Intensive Care Unit Capacity

  • Rema Padman
  • Karmel S. Shehadeh
    • Categories (Mixed) Integer Linear Programming, Scheduling, Stochastic Programming Tags , , , , ,

    In this paper, we study the decision process of assigning elective surgery patients to available surgical blocks in multiple operating rooms (OR) under random surgery durations, random postoperative length-of-stay in the intensive care unit (ICU), and limited capacity of ICU. The probability distributions of random parameters are assumed to be ambiguous, and only the mean … Read more

    On Linear Optimization over Wasserstein Balls

  • Daniel Kuhn
  • Wolfram Wiesemann
  • Man-Chung Yue
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under … Read more

    Dual Decomposition of Two-Stage Distributionally Robust Mixed-Integer Programming under the Wasserstein Ambiguity Set

  • Kibaek Kim
    • Categories (Mixed) Integer Linear Programming, Robust Optimization, Stochastic Programming Tags , ,

    We develop a dual decomposition of two-stage distributionally robust mixed-integer programming (DRMIP) under the Wasserstein ambiguity set. The dual decomposition is based on the Lagrangian dual of DRMIP, which results from the Lagrangian relaxation of the nonanticipativity constraints and min-max inequality. We present two Lagrangian dual problem formulations, each of which is based on different principle. We show … Read more

    Distributionally Robust Optimization Approaches for a Stochastic Mobile Facility Routing and Scheduling Problem

  • Karmel S. Shehadeh
    • Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Robust Optimization Tags , , , ,

    We study a mobile facility (MF) routing and scheduling problem in which probability distributions of the time-dependent demand for MF services is unknown. To address distributional ambiguity, we propose and analyze two distributionally robust MF routing and scheduling (DMFRS) models that seek to minimize the fixed cost of establishing the MF fleet and maximum expected … Read more

    Distributionally Robust Optimization under Distorted Expectations

  • Jun Cai
  • Jonathan Yu-Meng Li
  • Tiantian Mao
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , ,

    Distributionally robust optimization (DRO) has arose as an important paradigm to address the issue of distributional ambiguity in decision optimization. In its standard form, DRO seeks an optimal solution against the worst-possible expected value evaluated based on a set of candidate distributions. In the case where a decision maker is not risk neutral, the most … Read more

    The Value of Randomized Strategies in Distributionally Robust Risk Averse Network Interdiction Games

  • Erick Delage
  • Utsav Sadana
    • Categories Applications - OR and Management Sciences, Game Theory, Robust Optimization Tags , , ,

    Conditional Value at Risk (CVaR) is widely used to account for the preferences of a risk-averse agent in the extreme loss scenarios. To study the effectiveness of randomization in interdiction games with an interdictor that is both risk and ambiguity averse, we introduce a distributionally robust network interdiction game where the interdictor randomizes over the … Read more

    Distributionally Robust Bottleneck Combinatorial Problems: Uncertainty Quantification and Robust Decision Making

  • Shabbir Ahmed
  • Weijun Xie
  • Jie Zhang
    • Categories Stochastic Programming Tags , , , ,

    In a bottleneck combinatorial problem, the objective is to minimize the highest cost of elements of a subset selected from the combinatorial solution space. This paper studies data-driven distributionally robust bottleneck combinatorial problems (DRBCP) with stochastic costs, where the probability distribution of the cost vector is contained in a ball of distributions centered at the … Read more

    Multistage Distributionally Robust Mixed-Integer Programming with Decision-Dependent Moment-Based Ambiguity Sets

  • Siqian Shen
  • Xian Yu
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , ,

    We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical … Read more