Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2013, Special Issue (2013), Article ID 678783, 11 pages.
A Hybrid Approach of Bundle and Benders Applied Large Mixed Linear Integer Problem
Placido Rogerio Pinheiro and Paulo Roberto Oliveira
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Abstract
Consider a large mixed integer linear problem where structure of the constraint matrix is sparse, with independent blocks, and coupling constraints and variables. There is one of the groups of constraints to make difficult the application of Benders scheme decomposition. In this work, we propose the following algorithm; a Lagrangian relaxation is made on the mentioned set of constraints; we presented a process heuristic for the calculation of the multiplier through the resolution of the dual problem, structured starting from the bundle methods. According to the methodology proposed, for each iteration of the algorithm, we propose Benders decomposition where quotas are provided for the value function and $\epsilon $-subgradient.
Article information
Source
J. Appl. Math. Volume 2013, Special Issue (2013), Article ID 678783, 11 pages.
Dates
First available in Project Euclid: 14 March 2014
Permanent link to this document
http://projecteuclid.org/euclid.jam/1394807423
Digital Object Identifier
doi:10.1155/2013/678783
Mathematical Reviews number (MathSciNet)
MR3082031
Zentralblatt MATH identifier
1271.90049
Citation
Pinheiro, Placido Rogerio; Oliveira, Paulo Roberto. A Hybrid Approach of Bundle and Benders Applied Large Mixed Linear Integer Problem. J. Appl. Math. 2013, Special Issue (2013), Article ID 678783, 11 pages. doi:10.1155/2013/678783. http://projecteuclid.org/euclid.jam/1394807423.
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