Related papers: The Ensemble Approach of Column Generation for Sol…
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…
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…
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…
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…
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…
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…
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…
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…
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…
Column generation is often used to solve multi-commodity flow problems. A program for column generation always includes a module that solves a linear equation. In this paper, we address three major issues in solving linear problem during…
Graph Generation is a recently introduced enhanced Column Generation algorithm for solving expanded Linear Programming relaxations of mixed integer linear programs without weakening the expanded relaxations which characterize these methods.…
The minimum sum-of-squares clustering problem (MSSC), also known as $k$-means clustering, refers to the problem of partitioning $n$ data points into $k$ clusters, with the objective of minimizing the total sum of squared Euclidean distances…
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…
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…
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…
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…
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…
We propose a new inexact column-and-constraint generation (i-C&CG) method to solve two-stage robust optimization problems. The method allows solutions to the master problems to be inexact, which is desirable when solving large-scale and/or…
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 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…