This paper investigates the bounds on the expectation of combinatorial optimization given moment information for each individual random variable. A popular approach to solving this problem, known as the marginal moment model (MMM), is to reformulate it as a semidefinite program (SDP). In this paper, we investigate the structure of MMM with up to fourth-order … 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 go beyond the norm and analyze QO problems using robust optimization techniques. … Read more
Dynamic robust optimization deals with sequential, multi-stage decisions in the face of uncertain, worst-case scenarios. To manage its complexity and the curse of dimensionality, decision rules simplify the search for an optimal policy. This paper explores a middle ground between two common decision rules: simple but imprecise constant policies, and accurate but less scalable affine … Read more
Citation Belbasi R., Selvi A., Wiesemann W. (December 2023) It’s all in the mix: Wasserstein machine learning with mixed features. Preprint. Article Download View It's All in the Mix: Wasserstein Machine Learning with Mixed Features
In most health care systems, a primary care physician (PCP) is both the first instance consulted by patients with medical concerns and the instance coordinating patients’ continued access to medical care. Due to the PCP’s pivotal role, we address challenges of a high-quality primary care service by interday appointment scheduling on a tactical decision level. Our … Read more
We consider several hierarchical optimization programs: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs. Multiple adaptive discretization-based algorithms have been published for these program classes in recent decades. However, rigorous numerical performance comparisons between these algorithms are lacking. Indeed, if numerical comparisons are provided at all, they usually compare a small selection of … 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-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
In this paper, we propose ROBIST, a simple, yet effective, data-driven algorithm for optimization under parametric uncertainty. The algorithm first generates solutions in an iterative manner by sampling and optimizing over a relatively small set of scenarios. Then, using statistical testing, the robustness of the solutions is evaluated, which can be done with a much … Read more
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
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