期刊
DISCRETE APPLIED MATHEMATICS
卷 112, 期 1-3, 页码 73-99出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/S0166-218X(00)00310-3
关键词
multicommodity capacitated fixed-charge network design; Lagrangian relaxation; sub-gradient methods; bundle methods
To efficiently derive bounds for large-scale instances of the capacitated fixed-charge network design problem, Lagrangian relaxations appear promising. This paper presents the results of comprehensive experiments aimed at calibrating and comparing bundle and subgradient methods applied to the optimization of Lagrangian duals arising from two Lagrangian relaxations. This study substantiates the fact that bundle methods appear superior to subgradient approches because they converge faster and are more robust relative to different relaxations, problem characteristics, and selection of the initial parameter values. It also demonstrates that effective lower bounds may be computed efficiently for large-scale instances of the capacitated fixed-charge network design problem. Indeed, in a fraction of the time required by a standard simplex approach to solve the linear programming relaxation, the methods we present attain very high-quality solutions. (C) 2001 Elsevier Science B.V. All rights reserved.
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