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Lagrangean-based decomposition algorithms for multicommodity network design problems with penalized constraints

Lagrangean-based decomposition algorithms for multicommodity network design problems with penalized constraints
Lagrangean-based decomposition algorithms for multicommodity network design problems with penalized constraints
This paper discusses problems in the context of multicommodity network design where the additional constraints (such as capacity), rather than being imposed in a strict manner, are allowed to be violated at the expense of additional penalty costs. Such penalized cost structures allow these constraints to be treated as utilization targets and provide a better modelling framework in terms of strategic or tactical level planning of network design, especially in freight transportation systems. However, due to penalized costs, these problems are generally in the form of a nonlinear integer multicommodity network problem. This paper presents two algorithms based on Lagrangean relaxation and decomposition for the solution of such problems. The first is through relaxing flow constraints that results in an arc decomposition, and the second relies upon dualizing the capacity constraints that result in a flow decomposition. It is shown that nonlinearities in the decomposed substructures can be handled in a very efficient manner. Arc decomposition is shown, through computational experiments, to have better convergence properties. Through the proposed algorithms, reasonably good solutions can be obtained for these problems where publicly available state-of-the-art nonlinear optimization codes fail to identify feasible solutions.
CORMSIS-08-06
University of Southampton
Bektas, T.
0db10084-e51c-41e5-a3c6-417e0d08dac9
Chouman, M.
08a55649-be45-4c4c-a4c6-0c0d248fb54f
Crainic, T.G.
8bf6f82d-a944-4530-81a6-cf9b46721256
Bektas, T.
0db10084-e51c-41e5-a3c6-417e0d08dac9
Chouman, M.
08a55649-be45-4c4c-a4c6-0c0d248fb54f
Crainic, T.G.
8bf6f82d-a944-4530-81a6-cf9b46721256

Bektas, T., Chouman, M. and Crainic, T.G. (2008) Lagrangean-based decomposition algorithms for multicommodity network design problems with penalized constraints (Discussion Papers in Centre for Operational Research, Management Science and Information Systems, CORMSIS-08-06) University of Southampton

Record type: Monograph (Discussion Paper)

Abstract

This paper discusses problems in the context of multicommodity network design where the additional constraints (such as capacity), rather than being imposed in a strict manner, are allowed to be violated at the expense of additional penalty costs. Such penalized cost structures allow these constraints to be treated as utilization targets and provide a better modelling framework in terms of strategic or tactical level planning of network design, especially in freight transportation systems. However, due to penalized costs, these problems are generally in the form of a nonlinear integer multicommodity network problem. This paper presents two algorithms based on Lagrangean relaxation and decomposition for the solution of such problems. The first is through relaxing flow constraints that results in an arc decomposition, and the second relies upon dualizing the capacity constraints that result in a flow decomposition. It is shown that nonlinearities in the decomposed substructures can be handled in a very efficient manner. Arc decomposition is shown, through computational experiments, to have better convergence properties. Through the proposed algorithms, reasonably good solutions can be obtained for these problems where publicly available state-of-the-art nonlinear optimization codes fail to identify feasible solutions.

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Published date: April 2008

Identifiers

Local EPrints ID: 55838
URI: https://eprints.soton.ac.uk/id/eprint/55838
PURE UUID: d8605159-8e5e-4e3e-91f5-d1d71e030611
ORCID for T. Bektas: ORCID iD orcid.org/0000-0003-0634-144X

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Date deposited: 12 Aug 2008
Last modified: 14 Mar 2019 01:39

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Contributors

Author: T. Bektas ORCID iD
Author: M. Chouman
Author: T.G. Crainic

University divisions

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