Integer and combinatorial optimization
Integer and combinatorial optimization
Cutting planes and column generation techniques with the projective algorithm
Journal of Optimization Theory and Applications
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
A descent method with linear programming subproblems for nondifferentiable convex optimization
Mathematical Programming: Series A and B
BISON: a fast hybrid procedure for exactly solving the one-dimensional bin packing problem
Computers and Operations Research
Discrete Mathematics
Optimal Integer Solutions to Industrial Cutting-Stock Problems: Part 2, Benchmark Results
INFORMS Journal on Computing
Using Extra Dual Cuts to Accelerate Column Generation
INFORMS Journal on Computing
Computers and Operations Research
Selected Topics in Column Generation
Operations Research
Dual-Optimal Inequalities for Stabilized Column Generation
Operations Research
A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem
Computers and Operations Research
Lagrangian duality applied to the vehicle routing problem with time windows
Computers and Operations Research
Bidimensional packing by bilinear programming
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Recovering an optimal LP basis from an optimal dual solution
Operations Research Letters
Conservative scales in packing problems
OR Spectrum
Hi-index | 0.00 |
In this paper, we deal with a column generation-based algorithm for the classical cutting stock problem. This algorithm is known to have convergence issues, which are addressed in this paper. Our methods are based on the fact that there are interesting characterizations of the structure of the dual problem, and that a large number of dual solutions are known. First, we describe methods based on the concept of dual cuts, proposed by Valério de Carvalho [Valério de Carvalho, J. M. 2005. Using extra dual cuts to accelerate column generation. INFORMS J. Comput.17(2) 175--182]. We introduce a general framework for deriving cuts, and we describe a new type of dual cut that excludes solutions that are linear combinations of some other known solutions. We also explore new lower and upper bounds for the dual variables. Then we show how the prior knowledge of a good dual solution helps improve the results. It tightens the bounds around the dual values and makes the search converge faster if a solution is sought in its neighborhood first. A set of computational experiments on very hard instances is reported at the end of the paper; the results confirm the effectiveness of the methods proposed.