Robust Optimization

Robust Bilevel Optimization with a Wait-and-See Follower: A Column-and-Constraint Generation Approach

  • Henri Lefebvre
  • Johannes Thürauf
    • Categories Bilevel Optimization, Robust Optimization Tags , , , ,

    We study optimistic robust bilevel problems with uncertainty in the follower’s problem, where the follower adopts a so-called wait-and-see approach. In this setting, the leader decides without knowledge of the specific realization of the uncertainty. Then, the uncertainty realizes in a worst-case manner, and afterward the follower makes her own decisions. For this challenging problem … Read more

    Statistical Consistency of Distributionally Robust Optimization

  • Qiao Yi Wang
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    We study the statistical consistency of distributionally robust optimization (DRO) with metric-based ambiguity sets. While convergence of optimal values is well understood, a unified set-valued analysis of feasible regions and solution sets remains largely missing, especially for constrained DRO. We develop a general variational framework based on a collapse principle, which requires that all probability … Read more

    Distributionally Robust Chance-Constrained Optimal Load Shedding Model for Active Distribution Networks Based on KDE

  • Xiaotong Qi
  • Wei Liu
  • Bo Yu
  • Li Yang
    • Categories Applications - Science and Engineering, Energy, Robust Optimization

    With the high penetration of distributed energy resources in active distribution networks(ADNs), forecast errors from renewables and loads pose significant risks of bilateral violations, including overvoltage/undervoltage and line overloads. To address this challenge, this paper proposes a KDE-DRCCO model that integrates kernel density estimation (KDE) with distributionally robust chance-constrained optimization (DRCCO). Leveraging the radial topology … Read more

    KDE Robust Satisficing for Optimal Load Shedding Under Renewable Uncertainty

  • Min Xin Shu
  • Wei Liu
  • Qiao Yi Wang
  • Bo Yu
    • Categories Applications - Science and Engineering, Energy, Robust Optimization Tags , , , ,

    Abstract—Renewable-driven direct-current optimal load shedding (DC-OLS) requires a model that is interpretable to operators, data driven under continuous forecast errors, sensitive to severe security failures, and computationally tractable. This paper develops a budgeted KDE-ϕ-HMCR-RS-OLS framework for that purpose. Robust satisficing (RS) replaces ambiguity-radius tuning with an admissible shedding budget. A one-dimensional KDE reference family with … Read more

    Globalized Adversarial Regret Optimization: Robust Decisions with Uncalibrated Predictions

  • Jannis Kurtz
  • Bart Paul Gerard van Parys
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds in simple settings. However, when predictions lack rigorous error bounds (as is typical of modern machine learning methods) classical robust models often … Read more

    Context-Aware Cluster-Based Multi-Uncertainty-Set Distributionally Robust Chance-Constrained DC Optimal Power Flow

  • Qiao Yi Wang
  • Wei Liu
  • Bo Yu
    • Categories Applications - Science and Engineering, Energy, Robust Optimization Tags , , , , ,

    This paper proposes a context-aware multi-uncertainty-set distributionally robust chance-constrained DC optimal power flow model. Meteorological features are projected to partition the non-convex error support into a context-dependent decomposition of conditional local ambiguity sets, with conditional weights inferred via kernel regression. The minimax problem is reformulated into a finite-dimensional second-order cone program with proven asymptotic consistency. … Read more

    Stochastic set-valued optimization and its application to robust learning

  • Tommaso Giovannelli
  • Jingfu Tan
  • Luis Nunes Vicente
    • Categories Robust Optimization Tags , , ,

    In this paper, we develop a stochastic set-valued optimization (SVO) framework tailored for robust machine learning. In the SVO setting, each decision variable is mapped to a set of objective values, and optimality is defined via set relations. We focus on SVO problems with hyperbox sets, which can be reformulated as multi-objective optimization (MOO) problems … Read more

    Branch-and-Cut for Mixed-Integer Linear Decision-Dependent Robust Optimization

  • Henri Lefebvre
  • Martin Schmidt
  • Simon Stevens
  • Johannes Thürauf
    • Categories Bilevel Optimization, Branch and Cut Algorithms, Robust Optimization Tags , , , , ,

    Decision-dependent robust optimization (DDRO) problems are usually tackled by reformulating them using a strong-duality theorem for the uncertainty set model. If the uncertainty set is, however, described by a mixed-integer linear model, dualization techniques cannot be applied and the literature on solution methods is very scarce. In this paper, we exploit the equivalence of DDRO … Read more

    Risk-Averse Stochastic User Equilibrium on Uncertain Transportation Networks

  • Wencheng Bao
  • Chrysafis Vogiatzis
  • Eleftheria Kontou
    • Categories Network Optimization, Robust Optimization, Transportation Tags , , , , ,

    Extreme weather events, like flooding, disrupt urban transportation networks by reducing speeds and capacities, and by closing roadways. These hazards create regime-dependent uncertainty in link performance and travel-time distribution tails, challenging conventional traffic assignment that relies on the expectation of cost or mean excess of cost summation. This study develops a risk- and ambiguity-aware traffic … Read more

    Dynamic and Robust Allocation of On-Street Parking for Passenger and Delivery Vehicles

  • Alp Darendeliler
  • Barış Yıldız
    • Categories Dynamic Programming, Robust Optimization, Transportation Tags , , , ,

    Problem definition: Curb space has long been a scarce public resource in automobilized cities, serving competing uses for passenger parking and commercial activities. The rapid growth of e-commerce and home deliveries, combined with increasing urban density, has further intensified pressure on this already constrained resource, making effective curbspace management a critical policy challenge. Yet, in … Read more