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This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
Multilevel/multigrid methods is one of the most popular approaches for solving a large sparse linear system of equations, typically, arising from the discretization of partial differential equations. One critical step in the…
We present a branch-cut-and-price framework to solve Cutting Stock Problems with strong relaxations using Set Covering (Packing) Formulations, which are solved by column generation. The main contributions of this paper include an extended…
Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…
Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…
For clustering of an undirected graph, this paper presents an exact algorithm for the maximization of modularity density, a more complicated criterion to overcome drawbacks of the well-known modularity. The problem can be interpreted as the…
Column Generation (CG) is a popular method dedicated to enhancing computational efficiency in large scale Combinatorial Optimization (CO) problems. It reduces the number of decision variables in a problem by solving a pricing problem. For…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
We present a neural network-enhanced column generation (CG) approach for a parallel machine scheduling problem. The proposed approach utilizes an encoder-decoder attention model, namely the transformer and pointer architectures, to develop…
The bin packing problem exists widely in real logistic scenarios (e.g., packing pipeline, express delivery), with its goal to improve the packing efficiency and reduce the transportation cost. In this NP-hard combinatorial optimization…
We consider a class of linear-programming based estimators in reconstructing a sparse signal from linear measurements. Specific formulations of the reconstruction problem considered here include Dantzig selector, basis pursuit (for the case…
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Freighter airlines need to recover both aircraft and cargo schedules when disruptions happen. This process is usually divided into three sequential decisions to recovery flights, aircraft, and cargoes. This study focuses on the integrated…
Robots performing tasks in warehouses provide the first example of wide-spread adoption of autonomous vehicles in transportation and logistics. The efficiency of these operations, which can vary widely in practice, are a key factor in the…
We tackle the problem of accelerating column generation (CG) approaches to set cover formulations in operations research. At each iteration of CG we generate a dual solution that approximately solves the LP over all columns consisting of a…
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…
Ising machines are expected to solve combinatorial optimization problems faster than the existing integer programming solvers. These problems, particularly those encountered in practical situations, typically involve inequality constraints.…