Heuristic Methods for Mixed-Integer, Linear, and Γ-Robust Bilevel Problems

Due to their nested structure, bilevel problems are intrinsically hard to solve–even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. To tackle the Γ-robust counterpart of the bilevel … Read more

A Max-Min-Max Algorithm for Large-Scale Robust Optimization

Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO to large-scale decision problems. In this paper, we devise a first-order algorithm for solving RO based on a novel max-min-max perspective. … Read more

Adjustable Robust Nonlinear Network Design under Demand Uncertainties

We study network design problems for nonlinear and nonconvex flow models under demand uncertainties. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, demand scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear … Read more

Frequency regulation with storage: On losses and profits

Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage operators who sell frequency regulation power to grid operators and trade electricity on day-ahead markets. Mathematically, we treat future … Read more

Robust Regression over Averaged Uncertainty

We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least-squared regression problem. We show that this formulation surprisingly recovers ridge regression and establishes the missing link between robust optimization and the mean squared error approaches … Read more

Robust Continuous-Time Service Network Design under Travel Time Uncertainty

The continuous-time service network design problem (CTSNDP) has wide applications in the field of transportation, but it is complicated by travel time uncertainty resulting from unpredictable traffic conditions. Incorporating uncertain travel times poses a significant challenge, as time-indexed mixed-integer linear programming (MILP) formulations commonly used to solve the CTSNDP with deterministic travel times become impractical. … Read more

The Robust Bike Sharing Rebalancing Problem: Formulations and a Branch-and-Cut Algorithm

Bike Sharing Systems (BSSs) offer a sustainable and efficient urban transportation solution, bringing flexible and eco-friendly alternatives to city logistics. During their operation, BSSs may suffer from unbalanced bike distribution among stations, requiring rebalancing operations throughout the system. The inherent uncertain demand at the stations further complicates these rebalancing operations, even when performed during downtime. … Read more

Learning Optimal Classification Trees Robust to Distribution Shifts

We consider the problem of learning classification trees that are robust to distribution shifts between training and testing/deployment data. This problem arises frequently in high stakes settings such as public health and social work where data is often collected using self-reported surveys which are highly sensitive to e.g., the framing of the questions, the time … Read more

Robust Optimization Under Controllable Uncertainty

Applications for optimization with uncertain data in practice often feature a possibility to reduce the uncertainty at a given query cost, e.g., by conducting measurements, surveys, or paying a third party in advance to limit the deviations. To model this type of applications we introduce the concept of optimization problems under controllable uncertainty (OCU). For … Read more

Delay-Resistant Robust Vehicle Routing with Heterogeneous Time Windows

We consider a robust variant of the vehicle routing problem with heterogeneous time windows (RVRP-HTW) with a focus on delay-resistant solutions. Here, customers have different availability time windows for every vehicle and must be provided with a preferably tight appointment window for the planned service. Different vehicles are a possibility to model different days on … Read more