Dantzig-Wolfe decomposition and branch-and-price solving in G12

Abstract The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a high-level model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branch-and-price solving. Dantzig-Wolfe decomposition is automatically performed using the additional information given by the model annotations. The obtained models can then be solved using column generation and branch-and-price. G12 supports the selection of specialised subproblem solvers, the aggregation of identical subproblems to reduce symmetries, automatic disaggregation when required by branch-and-bound, the use of specialised subproblem constraint-branching rules, and different master problem solvers including a hybrid solver based on the volume algorithm. We demonstrate the benefits of the G12 framework on three examples: a trucking problem, cutting stock, and two-dimensional bin packi...

• Type: Journal
• Year: 2011
• Where: CONSTRAINTS
• Authors: Jakob Puchinger, Peter J. Stuckey, Mark G. Wallace, Sebastian Brand
• Keywords: Applied Computing, CONSTRAINTS 2011, G12 Project, Master Problem Solvers, Model Annotations