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Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within…
Charged particle transport is an important energy transport mode in the combustion process of inertial confinement fusion plasma. On the one hand, charged particles inside the hot spot have a strong non-equilibrium effect, so it is…
A recent trend in the design of FPT algorithms is exploiting the half-integrality of LP relaxations. In other words, starting with a half-integral optimal solution to an LP relaxation, we assign integral values to variables one-by-one by…
Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…
With the development of the Internet of Vehicles (IoV), vehicle wireless communication poses serious cybersecurity challenges. Faulty information, such as fake vehicle positions and speeds sent by surrounding vehicles, could cause vehicle…
A novel unconstrained optimization model named weighted trace-penalty minimization (WTPM) is proposed to address the extreme eigenvalue problem arising from the Full Configuration Interaction (FCI) method. Theoretical analysis shows that…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
In this paper, we study the problem of optimal multi-robot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type…
Multi-Agent Path Finding is a fundamental problem in robotics and AI, yet most existing formulations treat planning and execution separately and address variants of the problem in an ad hoc manner. This paper presents a system-level…
Logistics has gained great attentions with the prosperous development of commerce, which is often seen as the classic optimal vehicle routing problem. Meanwhile, electric vehicle (EV) has been widely used in logistic fleet to curb the…
In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
Understanding city-scale vehicular mobility and trip patterns is essential to addressing many problems, from transportation and pollution to public safety, among others. Using spatio-temporal analysis of vehicular mobility, promising…
In this article, we present a novel formulation for the load-dependent traveling salesman problem (LD-TSP), in which travel cost (or energy expended) depends on the vehicle's current load. This problem is relevant for package delivery and…
From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things…
Hydrogen is an energy vector, and one possible way to reduce CO 2 emissions. This paper focuses on a hydrogen transport problem where mobile storage units are moved by trucks between sources to be refilled and destinations to meet demands,…
Some of today's most significant challenges in urban environments concern individual mobility and rapid parcel delivery. With the surge of e-commerce and the ever-increasing volume of goods to be handled, new logistic solutions are in high…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…