Related papers: Solving Splitted Multi-Commodity Flow Problem by E…
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…
We consider the problem of sparse matrix multiplication by the column row method in a distributed setting where the matrix product is not necessarily sparse. We present a surprisingly simple method for "consistent" parallel processing of…
Capacity sharing networks are typical heterogeneous communication networks widely applied in information and communications technology (ICT) field. In such networks, resources like bandwidth, spectrum, computation and storage are shared…
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
This paper studies the estimation of ranked-list discrete choice models with single and multiple purchases. In this setting, each consumer type is characterized by a ranking over a subset of products and a desired number of purchases, and…
In this article we introduce Graph Generation, an enhanced Column Generation (CG) algorithm for solving expanded linear programming relaxations of mixed integer linear programs. To apply Graph Generation, we must be able to map any given…
In light of the need for design and analysis of intermodal transportation systems, we propose an algorithmic framework to determine the system optimum of an intermodal transportation system. To this end, we model an intermodal…
Column generation and branch-and-price are leading methods for large-scale exact optimization. Column generation iterates between solving a master problem and a pricing problem. The master problem is a linear program, which can be solved…
The Set Partitioning Problem is a combinatorial optimization problem with wide-ranging applicability, used to model various real-world tasks such as facility location and crew scheduling. However, real-world applications often require…
The purpose of this work is to develop an algorithmic optimization approach for a capacitated Multi-Commodity flow problem, where the objective is to minimize the total link costs, where the cost of each arc increases convexly with its…
Column Generation (CG) is an effective and iterative algorithm to solve large-scale linear programs (LP). During each CG iteration, new columns are added to improve the solution of the LP. Typically, CG greedily selects one column with the…
Discrete Optimal Transport problems give rise to very large linear programs (LP) with a particular structure of the constraint matrix. In this paper we present a hybrid algorithm that mixes an interior point method (IPM) and column…
Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is…
We study the problems of multi-person pose segmentation in natural images and instance segmentation in biological images with crowded cells. We formulate these distinct tasks as integer programs where variables correspond to poses/cells. To…
Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…
We consider a fashion discounter distributing its many branches with integral multiples from a set of available lot-types. For the problem of approximating the branch and size dependent demand using those lots we propose a tailored exact…
Research on multi-objective combinatorial optimization and on the Cutting Stock Problem (CSP) has been widely developed over the years. In contrast, the multi-objective Cutting Stock Problem has received limited attention and has been…
Column generation is used alongside Dantzig-Wolfe Decomposition, especially for linear programs having a decomposable pricing step requiring to solve numerous independent pricing subproblems. We propose a filtering method to detect which…