Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Solving binary cutting stock problems by column generation and branch-and-bound
Computational Optimization and Applications
Discrete Mathematics
Using Extra Dual Cuts to Accelerate Column Generation
INFORMS Journal on Computing
A proximal trust-region algorithm for column generation stabilization
Computers and Operations Research
A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem
Computers and Operations Research
A Column Generation Algorithm for a Rich Vehicle-Routing Problem
Transportation Science
SearchCol: metaheuristic search by column generation
HM'10 Proceedings of the 7th international conference on Hybrid metaheuristics
Branch and Price for Large-Scale Capacitated Hub Location Problems with Single Assignment
INFORMS Journal on Computing
Stabilized branch-and-price for the rooted delay-constrained steiner tree problem
INOC'11 Proceedings of the 5th international conference on Network optimization
New Stabilization Procedures for the Cutting Stock Problem
INFORMS Journal on Computing
Chebyshev center based column generation
Discrete Applied Mathematics
On routing in large WDM networks
Optical Switching and Networking
Cut-First Branch-and-Price-Second for the Capacitated Arc-Routing Problem
Operations Research
One-Dimensional Cutting Stock Optimization with Usable Leftover: A Case of Low Stock-to-Order Ratio
International Journal of Decision Support System Technology
Exact Algorithms for a Bandwidth Packing Problem with Queueing Delay Guarantees
INFORMS Journal on Computing
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Column generation is one of the most successful approaches for solving large-scale linear programming problems. However, degeneracy difficulties and long-tail effects are known to occur as problems become larger. In recent years, several stabilization techniques of the dual variables have proven to be effective. We study the use of two types of dual-optimal inequalities to accelerate and stabilize the whole convergence process. Added to the dual formulation, these constraints are satisfied by all or a subset of the dual-optimal solutions. Therefore, the optimal objective function value of the augmented dual problem is identical to the original one. Adding constraints to the dual problem leads to adding columns to the primal problem, and feasibility of the solution may be lost. We propose two methods for recovering primal feasibility and optimality, depending on the type of inequalities that are used. Our computational experiments on the binary and the classical cutting-stock problems, and more specifically on the so-called triplet instances, show that the use of relevant dual information has a tremendous effect on the reduction of the number of column generation iterations.