EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Issue RAIRO Oper. Res.
Volume 35, Number 2, April-June 2001
Page(s) 269 - 281
DOI 10.1051/ro:2001114

DOI: 10.1051/ro:2001114


RAIRO Oper. Res. 35 (2001) 269-281

Separable convexification and DCA techniques for capacity and flow assignment problems

P. Mahey1, 2, Thai Q. Phong1, 3 and H.P.L. Luna4

1  LIMOS-CNRS, Université Blaise Pascal, Aubière, France; (mahey@sp.isima.fr) (tqphong@sp.isima.fr)
2  This work was partially supported by France Telecom RD, CTI99-1B-281.
3  On leave from: Da Nang University, Vietnam.
4  DCC-ICeX, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil; (pacca@dcc.ufmg.br)

(Received May, 1999.)

Abstract
We study a continuous version of the capacity and flow assignment problem (CFA) where the design cost is combined with an average delay measure to yield a non convex objective function coupled with multicommodity flow constraints. A separable convexification of each arc cost function is proposed to obtain approximate feasible solutions within easily computable gaps from optimality. On the other hand, DC (difference of convex functions) programming can be used to compute accurate upper bounds and reduce the gap. The technique is shown to be effective when topology is assumed fixed and capacity expansion on some arcs is considered.

Résumé
On étudie ici une version continue du problème de dimensionnement et routage dans un réseau de communications, dans lequel les coûts de conception sont combinés aux mesures de délai moyen d'acheminement, engendrant un problème de multiflots avec une fonction objectif non convexe. On propose un encadrement de la valeur optimale par convexification séparable sur les arcs, d'une part, et par calcul d'optima locaux issus d'un modèle DC (différence de fonctions convexes) des fonctions de coût. Cette dernière technique permet de réduire la distance à la valeur optimale et on illustre son efficacité sur des problèmes d'expansion de capacités.


Key words: Network design, DC optimization, capacity and flow assignment.


© EDP Sciences 2001


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.