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We study Bayesian inversion for a model elliptic PDE with unknown diffusion coefficient. We provide complexity analyses of several Markov Chain-Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the…

In many operational contexts, solutions to NP-hard combinatorial optimization problems, modeled by means of Mixed-Integer Linear Programming (MILP), may become infeasible due to unpredictable disruptions. Typically, reoptimizing by solving…

The Directed Layering Problem (DLP) solves a step of the widely used layer-based approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, usually a preprocessing step is used that solves the Feedback Arc Set…

The COVID-19 pandemic has been a recent example for the spread of a harmful contagion in large populations. Moreover, the spread of harmful contagions is not only restricted to an infectious disease, but is also relevant to computer viruses…

We propose a novel approach which employs random sampling to generate an accurate non-uniform mesh for numerically solving Partial Differential Equation Boundary Value Problems (PDE-BVP's). From a uniform probability distribution U over a…

For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of…

The balanced connected $k$-partition problem (\textsc{bcp}) is a classic problem, which consists in partitioning the set of vertices of a vertex-weighted connected graph into a collection of~$k$ classes such that each class induces a…

Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of…

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

Graph Coloring Problem (GCP) is an NP-Hard vertex labeling problem in graphs such that no two adjacent vertices can have the same color. Large instances of GCP cannot be solved in reasonable execution times by exact algorithms. Therefore,…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms…

This paper presents a method for time-lapse 3D cell analysis. Specifically, we consider the problem of accurately localizing and quantitatively analyzing sub-cellular features, and for tracking individual cells from time-lapse 3D confocal…

In recent years generative design techniques have become firmly established in numerous applied fields, especially in engineering. These methods are demonstrating intensive growth owing to promising outlook. However, existing approaches are…

Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in K-dimensional space such that the…

Machining process planning (MP) is inherently complex due to structural and geometrical dependencies among part features and machining operations. A key challenge lies in capturing dynamic interdependencies that evolve with distinct part…

This paper investigates the column generation (CG) for solving cutting stock problems (CSP). Traditional CG method, which repeatedly solves a restricted master problem (RMP), often suffers from two critical issues in practice -- the loss of…

This paper considers the generalized maximal covering location problem (GMCLP) which establishes a fixed number of facilities to maximize the weighted sum of the covered customers, allowing customer weights to be positive or negative. Due…

Set covering problem is an important class of combinatorial optimization problems, which has been widely applied and studied in many fields. In this paper, we propose an improved column generation algorithm with neural prediction (CG-P) for…

Defect segmentation is crucial for quality control in advanced manufacturing, yet data scarcity poses challenges for state-of-the-art supervised deep learning. Synthetic defect data generation is a popular approach for mitigating data…