Robust Optimization

Partial Policy Iteration for L1-Robust Markov Decision Processes

  • Chin Pang Ho
  • Marek Petrik
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags ,

    Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the transition probabilities significantly increases the computational complexity of solving robust MDPs, which severely limits their scalability. This paper describes new efficient algorithms for solving the … Read more

    Modeling Multi-stage Decision Making under Incomplete and Uncertain Information

  • Viktor Bindewald
  • Fabian Dunke
  • Stefan Nickel
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , ,

    We propose a new universal framework for multi-stage decision making under limited information availability. It is developed as part of a larger research project which aims at providing analytical methods to compare and evaluate different models and algorithms for multi-stage decision making. In our setting, we have an open time horizon and limited information about … Read more

    ROC++: Robust Optimization in C++

  • Phebe Vayanos
  • Qing Jin
  • George Elissaios
    • Categories Optimization Software and Modeling Systems, Robust Optimization Tags , , , , , ,

    Over the last two decades, robust optimization has emerged as a popular means to address decision-making problems affected by uncertainty. This includes single- and multi-stage problems involving real-valued and/or binary decisions, and affected by exogenous (decision-independent) and/or endogenous (decision-dependent) uncertain parameters. Robust optimization techniques rely on duality theory potentially augmented with approximations to transform a … Read more

    Vehicle Repositioning under Uncertainty

  • Qinshen Tang
  • Yu Zhang
  • Minglong Zhou
    • Categories Applications - OR and Management Sciences, Robust Optimization, Transportation Tags , ,

    We consider a general multi-period repositioning problem in vehicle-sharing networks such as bicycle-sharing systems, free-float car-sharing systems, and autonomous mobility-on-demand systems. This problem is subject to uncertainties along multiple dimensions – including demand, travel time, and repositioning duration – and faces several operational constraints such as the service level and cost budget. We propose a … Read more

    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