Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition
Transportation Science
The Co-Printing Problem: A Packing Problem with a Color Constraint
Operations Research
Selected Topics in Column Generation
Operations Research
The Profitable Arc Tour Problem: Solution with a Branch-and-Price Algorithm
Transportation Science
Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition
Transportation Science
Circulation of railway rolling stock: a branch-and-price approach
Computers and Operations Research
On column generation formulations for the RWA problem
Discrete Applied Mathematics
An Inexact Bundle Approach to Cutting-Stock Problems
INFORMS Journal on Computing
A branch-and-price algorithm for an integrated production and inventory routing problem
Computers and Operations Research
Exact optimization for the l1-Compressive Sensing problem using a modified Dantzig-Wolfe method
Theoretical Computer Science
Experiments with a generic dantzig-wolfe decomposition for integer programs
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Mixed integer programming models for detailed placement
Proceedings of the 2012 ACM international symposium on International Symposium on Physical Design
A generic view of Dantzig-Wolfe decomposition in mixed integer programming
Operations Research Letters
Automatic decomposition and branch-and-price--a status report
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Optimal solutions for routing problems with profits
Discrete Applied Mathematics
Flexible weekly tour scheduling for postal service workers using a branch and price
Journal of Scheduling
Algorithm 928: A general, parallel implementation of Dantzig--Wolfe decomposition
ACM Transactions on Mathematical Software (TOMS)
Computers and Operations Research
Models for the two-dimensional two-stage cutting stock problem with multiple stock size
Computers and Operations Research
Column Generation for the Minimum Hyperplanes Clustering Problem
INFORMS Journal on Computing
MIP-based detailed placer for mixed-size circuits
Proceedings of the 2014 on International symposium on physical design
Hi-index | 0.00 |
Dantzig-Wolfe decomposition as applied to an integer program is a specific form of problem reformulation that aims at providing a tighter linear programming relaxation bound. The reformulation gives rise to an integer master problem, whose typically large number of variables is dealt with implicitly by using an integer programming column generation procedure, also known as branch-and-price algorithm. There is a large class of integer programs that are well suited for this solution technique. In this paper, we propose to base the Dantzig-Wolfe decomposition of an integer program on the discretization of the integer polyhedron associated with a subsystem of constraints (as opposed to its convexification). This allows us to formulate the integrality restriction directly on the master variables and sets a theoretical framework for dealing with specific issues such as branching or the introduction of cutting planes in the master. We discuss specific branching schemes and their effect on the structure of the column generation subproblem. We give theoretical bounds on the complexity of the separation process and the extent of the modifications to the column generation subproblem. Our computational tests on the cutting stock problem and a generalisation--the cutting strip problem--show that, in practice, all fractional solutions can be eliminated using branching rules that preserve the tractability of the subproblem, but there is a trade-off. between branching efficiency and subproblem tractability.