Robust Optimization

Robust combinatorial optimization problems under locally budgeted interdiction uncertainty against the objective function and covering constraints

  • Alejandro Crema
    • Categories Combinatorial Optimization, Robust Optimization Tags ,

    Recently robust combinatorial optimization problems with budgeted interdiction uncertainty affecting cardinality-based constraints or objective were considered by presenting, comparing and experimenting with compact formulations. In this paper we present a compact formulation for the case in which locally budgeted interdiction uncertainty affects the objective function and covering constraints simultaneously. ArticleDownload View PDF

    An alternating optimization approach for robust optimal control in chromatography

  • Dominik H. Cebulla
  • Andrea Gilch
  • Jan Hendrik Rolfes
  • Christian Kirches
  • Frauke Liers
    • Categories Optimization of Systems modeled by PDEs, Robust Optimization Tags , ,

    Chromatographic separation plays a vital role in various areas, as this technique can deliver high-quality products both in lab- and industrial-scale processes. Economical and also ecological benefits can be expected when optimizing such processes with mathematical methods. However, even small perturbations in the operating conditions can result in significantly altered results, which may lead to … Read more

    Integrated Planning of Drone-Based Disaster Relief: Facility Location, Inventory Prepositioning, and Fleet Operations under Uncertainty

  • Yuyang Ma
  • Karmel S. Shehadeh
  • Man Yiu Tsang
    • Categories Robust Optimization, Transportation

    We introduce a two-stage robust optimization (RO) framework for the integrated planning of a drone-based disaster relief operations problem (DDROP). Given sets of demand points, candidate locations for establishing drone-supported relief facilities, facility types, drone types, and relief items types, our first-stage problem solves the following problems simultaneously: (i) a location problem that determines the … Read more

    Counterfactual explanations with the k-Nearest Neighborhood classifier and uncertain data

  • Emilio Carrizosa
  • Renato De Leone
  • Marica Magagnini
    • Categories Bilevel Optimization, Robust Optimization Tags , , , ,

    Counterfactual Analysis is a powerful tool in Explainable Machine Learning. Given a classifier and a record, one seeks the smallest perturbation necessary to have the perturbed record, called the counterfactual explanation, classified in the desired class. Feature uncertainty in data reflects the inherent variability and noise present in real-world scenarios, and therefore, there is a … Read more

    Distributionally Robust Optimization with Integer Recourse: Convex Reformulations and Critical Recourse Decisions

  • Yiling Zhang
    • Categories Integer Programming, Robust Optimization, Stochastic Programming Tags , , , ,

    The paper studies distributionally robust optimization models with integer recourse. We develop a unified framework that provides finite tight convex relaxations under conic moment-based ambiguity sets and Wasserstein ambiguity sets.  They provide tractable primal representations without relying on sampling or semi-infinite optimization. Beyond tractability, the relaxations offer interpretability that captures the criticality of recourse decisions. … Read more

    Two-Stage Data-Driven Contextual Robust Optimization: An End-to-End Learning Approach for Online Energy Applications

  • Carlos Gamboa
  • Alexandre Street
  • Davi Valladão
  • Bernardo K. Pagnoncelli
    • Categories Energy, Robust Optimization, Stochastic Programming Tags , , ,

    Traditional end-to-end contextual robust optimization models are trained for specific contextual data, requiring complete retraining whenever new contextual information arrives. This limitation hampers their use in online decision-making problems such as energy scheduling, where multiperiod optimization must be solved every few minutes. In this paper, we propose a novel Data-Driven Contextual Uncertainty Set, which gives … Read more

    Effective Solution Algorithms for Bulk-Robust Optimization Problems

  • Christoph Buchheim
  • Enrico Malaguti
  • Michele Monaci
  • Paolo Paronuzzi
  • Pia Schreynemackers
    • Categories 0-1 Programming, Network Optimization, Robust Optimization Tags , , , ,

    Bulk-robust optimization is a recent paradigm for addressing problems in which the structure of a system is affected by uncertainty. It considers the case in which a finite and discrete set of possible failure scenarios is known in advance, and the decision maker aims to activate a subset of available resources of minimum cost so … Read more

    Towards robust optimal control of chromatographic separation processes with controlled flow reversal

  • Dominik H. Cebulla
  • Christian Kirches
  • Andreas Potschka
    • Categories Chemical Engineering, Robust Optimization, Systems governed by Differential Equations Optimization Tags , ,

    Column liquid chromatography is an important technique applied in the production of biopharmaceuticals, specifically for the separation of biological macromolecules such as proteins. When setting up process conditions, it is crucial that the purity of the product is sufficiently high, even in the presence of perturbations in the process conditions, e.g., altered buffer salt concentrations. … Read more

    When Wasserstein DRO Reduces Exactly: Complete Characterization, Projection Equivalence, and Regularization

  • Chenling Huang
  • Jonathan Yu-Meng Li
  • Tiantian Mao
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Wasserstein distributionally robust optimization (DRO), a leading paradigm in data-driven decision-making, entails the evaluation of worst-case risk over a high-dimensional Wasserstein ball–a major computational burden. In this paper, we study when the worst-case risk problem admits an exact reduction to the evaluation of risk over a one-dimensional projected Wasserstein ball—a property we refer to as … Read more

    Data-Driven Contextual Optimization with Gaussian Mixtures: Flow-Based Generalization, Robust Models, and Multistage Extensions

  • YoungChul Yoon
  • Grani A. Hanasusanto
  • Yijie Wang
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of distributions. The inherent complexity of such structures often precludes an explicit functional relationship between the contextual information and the uncertain parameters, limiting the direct applicability of parametric … Read more