Robust Optimization

Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures

Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags , , , ,

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of … Read more

Model-Uncertainty-Aware Residuals-Based Sample Average Approximation

Categories Robust Optimization, Stochastic Programming Tags , , ,

We consider a contextual stochastic optimization (CSO) problem, where one has observations of the uncertain parameters together with concurrent observations of covariates, and the goal is to choose decisions that minimize expected cost conditioned on new covariate observations. The empirical residuals-based sample average approximation (ER-SAA) of the CSO problem constructs scenarios of uncertainty by combining … Read more

Advanced Geometrical Test for Interval Branch and Bound methods

Categories Global Optimization, Robust Optimization Tags , , , ,

The Interval Branch and Bound (IBB) method is a widely used approach for solving nonlinear programming problems, especially when a rigorous solution is required. It uses Interval Arithmetic to handle rounding errors. Although numerous variants of the IBB method have been proposed in the literature, relatively few implementations incorporate Karush-Kuhn-Tucker or Fritz-John (FJ) optimality conditions … Read more

De-risking solutions to optimization problems

Categories Bilevel Optimization, Convex and Nonsmooth Optimization, Robust Optimization Tags

We develop a cutting-plane methodology that adjusts solutions to optimization problems so as to reduce features that bring about exposure to risk, such as concentration of assets or resources. The methodology is agnostic to the representation of risk but has provably good attributes. Our procedure aims to reduce the appropriate risk metric without accruing a … Read more

Robust Network Design for Potential-Based Flows with Controllable Elements

Categories (Mixed) Integer Nonlinear Programming, Bilevel Optimization, Robust Optimization Tags , , , ,

We study adjustable robust network design for potential-based flows with controllable elements under load uncertainty. The resulting problem combines discrete here-and-now expansion decisions with wait-and-see operational decisions governed by nonconvex flow constraints. Moreover, controllable elements introduce adjustable integer decisions, which are algorithmically challenging. We equivalently characterize robust feasibility and robust optimality of a fixed network … Read more

PyROS: The Pyomo Robust Optimization Solver

Categories Nonlinear Optimization, Optimization Software and Modeling Systems, Robust Optimization Tags , , , ,

We present PyROS, a Python-based meta-solver that automates a generalized cutting-set algorithm for the solution of nonconvex two-stage robust optimization (RO) problems with uncertain equality constraints. Freely available through the open-source optimization software package Pyomo, PyROS is designed to operate on a user-provided deterministic model and uncertainty set, such that a solution to the RO … Read more

Distributionally Robust Optimization with General Uncertainty Structure

Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags , , , , , ,

We develop an exact solution framework for a broad class of Distributionally Robust Optimization (DRO) problems with general uncertainty structure. Within the class of moment- and confidence-set-based ambiguity sets, existing exact methods are largely limited to max-of-affine functions under ambiguity sets with strictly nested confidence sets. To enlarge this scope while preserving tractability, we introduce … Read more

Scalable Finite Adaptability via Polyhedral Partition and Learning

Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , ,

We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty … Read more

Distributionally Robust Optimization via Targeted Integral Probability Metrics for General Data Processes

Categories Optimization in Data Science, Robust Optimization, Stochastic Programming Tags , , , , , ,

Distributionally robust optimization (DRO) provides a principled framework for decision-making under distributional uncertainty. Classical data-driven DRO frameworks typically construct ambiguity sets from distributional information, such as moment constraints, divergence neighborhoods, or Wasserstein balls, specified before the downstream loss is considered. We propose a task-aware DRO framework based on targeted integral probability metrics. The ambiguity set … Read more

Betweenness Central Nodes Under Uncertainty: An Absorbing Markov Chain Approach

Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Robust Optimization Tags , , , , , , ,

We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This … Read more