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Column generation (CG) is one of the most successful approaches for solving large-scale linear programming (LP) problems. Given an LP with a prohibitively large number of variables (i.e., columns), the idea of CG is to explicitly consider…
We consider the problem of developing an efficient multi-threaded implementation of the matrix-vector multiplication algorithm for sparse matrices with structural symmetry. Matrices are stored using the compressed sparse row-column format…
Electric utility companies perform numerous technical interventions every day. Since it is generally not possible to complete all planned interventions within a single day, companies face two objectives: maximizing the total duration of…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
We consider an important problem in the shipping industry known as the liner shipping fleet repositioning problem (LSFRP). We examine a public data set for this problem including many instances which have not previously been solved to…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
This paper presents a new column-and-constraint generation method for two-stage robust mixed-integer programs with finite uncertainty sets. Our method combines and extends speed-up techniques used in previous column-and-constraint…
In many manufacturing processes, batch processing is frequently needed for capacity reasons. This applies both to parallel and serial batching. However, while the serial batch processing is largely studied in the literature, as it is…
In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are usually solved in each iteration. This is true both for Active Set (AS) methods as well as for Interior Point (IP) methods, and for…
We consider the problem of coordinating a fleet of robots in a warehouse so as to maximize the reward achieved within a time limit while respecting problem and robot specific constraints. We formulate the problem as a weighted set packing…
The unit commitment problem is an important optimization problem in the energy industry used to compute the most economical operating schedules of power plants. Typically, this problem has to be solved repeatedly with different data but…
Column generation (CG) is a well-established method for solving large-scale linear programs. It involves iteratively optimizing a subproblem containing a subset of columns and using its dual solution to generate new columns with negative…
Column Generation (CG) is an iterative algorithm for solving linear programs (LPs) with an extremely large number of variables (columns). CG is the workhorse for tackling large-scale \textit{integer} linear programs, which rely on CG to…
Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a sub-problem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of…
Integer programs for resource-constrained project scheduling problems are notoriously hard to solve due to their weak linear relaxations. Several papers have proposed reformulating project scheduling problems via Dantzig-Wolfe decomposition…
During natural or anthropogenic disasters, humanitarian organizations face a series of time-sensitive tasks. One of the tasks involves picking up critical resources (e.g., first aid kits, blankets, water) from warehouses and delivering them…
The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their…
We consider the quantum implementations of the two classical iterative solvers for a system of linear equations, including the Kaczmarz method which uses a row of coefficient matrix in each iteration step, and the coordinate descent method…
Numerous communication networks are emerging to serve the various demands and improve the quality of service. Heterogeneous users have different requirements on quality metrics such as delay and service efficiency. Besides, the networks are…
Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic.…