We consider two variants of the toll-setting problem in which a traffic authority uses tolls either to maximize revenue or to alleviate bottlenecks in the traffic network. The users of the network are assumed to act according to Wardrop’s user equilibrium so that the overall toll-setting problems are modeled as mathematical problems with equilibrium constraints. … Read more
Robust optimization is an approach for handling uncertainty in optimization problems, in which the uncertainty set determines the conservativeness of the solutions. In this paper, we propose a data-driven uncertainty set using a type of volume-based clustering, which we call Minimum-Volume Norm-Based Clustering (MVNBC). MVNBC extends the concept of minimum-volume ellipsoid clustering by allowing clusters … Read more
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
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
We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. 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, load scenarios within a given … Read more
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
Quadratic optimization (QO) has been studied extensively in the literature due to its applicability in many practical problems. While practical, it is known that QO problems are generally NP-hard. So, researchers developed many approximation methods to find good solutions. In this paper, we analyze QO problems using robust optimization techniques. To this end, we first … Read more
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 squares regression problem. We show that this formulation recovers ridge regression exactly and establishes the missing link between robust optimization and the mean squared error … Read more
We study the continuous-time service network design problem (CTSNDP) under travel time uncertainty, aiming to design a transportation service network along a continuous-time planning horizon, with robust operational efficiency even in the presence of travel time deviations. Incorporating travel time uncertainty holds a great practical value. However, it poses a significant challenge in both problem … Read more
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