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0-1 Reformulations of the Multicommodity Capacitated Network Design Problem

Antonio, Frangioni and Bernard, Gendron (2009) 0-1 Reformulations of the Multicommodity Capacitated Network Design Problem. Discrete Applied Mathematics, 157/20 (6). pp. 1229-1241. ISSN 0166-218X

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    We study 0-1 reformulations of the multicommodity capacitated network design problem, which is usually modeled with general integer variables to represent design decisions on the number of facilities to install on each arc of the network. The reformulations are based on the multiple choice model, a generic approach to represent piecewise linear costs using 0-1 variables. This model is improved by the addition of extended linking inequalities, derived from variable disaggregation techniques. We show that these extended linking inequalities for the 0-1 model are equivalent to the residual capacity inequalities, a class of valid inequalities derived for the model with general integer variables. In this paper, we compare two cutting-plane algorithms to compute the same lower bound on the optimal value of the problem: one based on the generation of residual capacity inequalities within the model with general integer variables, and another based on the addition of extended linking inequalities to the 0-1 reformulation. To further improve the computational results of the latter approach, we develop a column-and-row generation approach; the resulting algorithm is shown to be competitive with the approach relying on residual capacity inequalities.

    Item Type: Article
    Uncontrolled Keywords: Multicommodity Capacitated Network Design, Reformulation, Valid Inequalities, Cutting-Plane Method, Column Generation.
    Subjects: Area01 - Scienze matematiche e informatiche > MAT/09 - Ricerca operativa
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA
    Depositing User: Prof. Antonio Frangioni
    Date Deposited: 02 Jul 2009
    Last Modified: 20 Dec 2010 11:56
    URI: http://eprints.adm.unipi.it/id/eprint/484

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