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

    Adversarial Classification via Distributional Robustness with Wasserstein Ambiguity

  • Nam Ho-Nguyen
  • Stephen Wright
    • Categories Nonlinear Optimization, Robust Optimization Tags , , , ,

    We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification, and we explore links to adversarial classification models proposed earlier and to maximum-margin classifiers. We also provide a reformulation of the distributionally robust … Read more

    Γ-counterparts for robust nonlinear combinatorial and discrete optimization

  • Dennis Adelhütte
  • Frauke Liers
    • Categories Robust Optimization Tags , , , , ,

    Γ-uncertainties have been introduced for adjusting the degree of conservatism ofrobust counterparts of (discrete) linear optimization problems under interval uncertainty. Thisarticle’s contribution is a generalization of this approach to (mixed-integer) nonlinear optimizationproblems. We focus on the cases in which the uncertainty is linear but also derive formulationsfor the general case. We present cases where the … Read more

    Robustification of the k-Means Clustering Problem and Tailored Decomposition Methods: When More Conservative Means More Accurate

  • Jan Pablo Burgard
  • Carina Moreira Costa
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , , , ,

    k-means clustering is a classic method of unsupervised learning with the aim of partitioning a given number of measurements into k clusters. In many modern applications, however, this approach suffers from unstructured measurement errors because the k-means clustering result then represents a clustering of the erroneous measurements instead of retrieving the true underlying clustering structure. … Read more

    Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

  • Dirk Lauinger
  • François Vuille
  • Daniel Kuhn
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

    Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner’s expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency … Read more

    Regret in the Newsvendor Model with Demand and Yield Randomness

  • Zhi Chen
  • Weijun Xie
    • Categories Robust Optimization Tags , , , , ,

    We study the fundamental stochastic newsvendor model that considers both demand and yield randomness. It is usually difficult in practice to describe precisely the joint demand and yield distribution, although partial statistical information and empirical data about this ambiguous distribution are often accessible. We combat the issue of distributional ambiguity by taking a data-driven distributionally … 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

    A Robust Optimization Approach to Network Control Using Local Information Exchange

  • Georgios Darivianakis
  • Angelos Georghiou
  • Soroosh Shafieezadeh-Abadeh
  • John Lygeros
    • Categories Robust Optimization Tags

    Designing policies for a network of agents is typically done by formulating an optimization problem where each agent has access to state measurements of all the other agents in the network. Such policy designs with centralized information exchange results in optimization problems that are typically hard to solve, require to establish substantial communication links, and … 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