We study the Regularized A-Optimal Design (RAOD) problem, which selects a subset of \(k\) experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian experimental design, sensor placement, and cold-start recommendation. We prove its NP-hardness via a reduction from the independent set problem. … Read more
We investigate convexification in convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step function. First, we derive the convex hull for the epigraph of a quadratic function defined by a rank-one matrix. Using this rank-one convexification, we … Read more
Interactive optimization leverages the strengths of optimization frameworks alongside the expertise of human users. Prior research in this area tends to either ask human users for the same type of information, or when varying information is requested, users must manually modify the optimization model directly. These limitations restrict the incorporation of wider human knowledge into … Read more
Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more
This paper proposes a globally converging cutting-plane algorithm for solving multistage stochastic mixed-integer programs with general mixed-integer state variables. We demonstrate the generation process of Lagrangian cuts and show that Lagrangian cuts capture the convex envelope of value functions on a restricted region. To approximate nonconvex value functions to exactness, we propose to iteratively add … Read more
In this work, we present the first 2-index stage-based formulation for the Flying Sidekick Traveling Salesman Problem (FSTSP). Additionally, we propose a Construct-Merge-Solve & Adapt (CMSA) algorithm designed to generate high-quality feasible solutions. Experimental results demonstrate that the proposed algorithm consistently produces good solutions in a fraction of the time required by state-of-the-art mixed-integer linear … Read more
Climate change is increasingly impacting power system operations, not only through more frequent extreme weather events but also through shifts in routine weather patterns. Factors such as increased temperatures, droughts, changing wind patterns, and solar irradiance shifts can impact both power system production and transmission and electric load. The current power system was not designed … Read more
A Surgery Pre-Admission Testing (PAT) clinic is a hospital unit designed to serve pre-operative patients by gathering critical patient information and performing procedure-specific tests to prepare them for surgery. Patients may require multiple tests, each conducted by a specialized nurse. A patient must be assigned to a room before starting any test and must stay … Read more
Graphons generalize graphs and define a limit object of a converging graph sequence. The notion of graphons allows for a generic representation of coupled network dynamical systems. We are interested in approximating optimal switching controls for graphon dynamical systems. To this end, we apply a decomposition approach comprised of a relaxation and a reconstruction step. … Read more
Data collection in application domains like agriculture and environmental science requires the deployment of sensors in large remote areas. These use cases challenge the traditional optimal experimental design (OED) formulation from statistics by their scale as well as the presence of complex operational constraints, such as that data is collected along the trajectory of a … Read more