Santanu S. Dey For mixed-integer programs (MIPs), strong branching is a highly effective variable selection method to reduce the number of nodes in the branch-and-bound algorithm. Extending it to nonlinear problems is conceptually simple but practically limited. Branching on a binary variable fixes the variable to 0 or 1, whereas branching on a continuous variable requires an additional … Read more
In this paper, we study the set \(\mathcal{S}^\kappa = \{ (x,y)\in\mathcal{G}\times\mathbb{R}^n : y_j = x_j^\kappa , j=1,\dots,n\}\), where \(\kappa > 1\) and the ground set \(\mathcal{G}\) is a nonempty polytope contained in \( [0,1]^n\). This nonconvex set is closely related to separable standard quadratic programming and appears as a substructure in potential-based network flow problems … Read more
Multicommodity capacitated network design (MCND) models can be used to optimize the consolidation of shipments within e-commerce fulfillment networks. In practice, fulfillment networks require that shipments with the same origin and destination follow the same transfer path. This unsplittable flow requirement complicates the MCND problem, requiring integer programming (IP) formulations with binary variables replacing continuous … Read more
Many operations related optimization problems involve repeatedly solving similar mixed integer linear programming (MILP) instances with the same constraint matrix but differing objective coefficients and right-hand-side values. The goal of this paper is to generate good cutting-planes for such instances using historical data. Gomory mixed integer cuts (GMIC) for a general MILP can be parameterized … Read more
The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language processing, and speech analysis. Despite its popularity, CCA can encounter challenges in explaining correlations between two variable sets within high-dimensional data contexts. … Read more
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a subset of variables with a pre-specified size that … Read more
We present a trilevel interdiction model for optimally segmenting the Supervisory Control and Data Acquisition (SCADA) network controlling an electric power grid. In this formulation, we decide how to partition nodes of the SCADA network in order to minimize the shedding of load from a worst-case cyberattack, assuming that the grid operator has the opportunity … Read more
We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split disjunctions. ArticleDownload View PDF
Full strong-branching (henceforth referred to as strong-branching) is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an analysis of the performance of the strong-branching rule both from a theoretical and a computational perspective. On … Read more
A classical approach for obtaining valid inequalities for a set involves weighted aggregations of the inequalities that describe such set. When the set is described by linear inequalities, thanks to the Farkas lemma, we know that every valid inequality can be obtained using aggregations. When the inequalities describing the set are two quadratics, Yildiran showed … Read more