Separable convexification and DCA techniques for capacity and flow assignment problems
P. Mahey; Thai Q. Phong; H. P.L. Luna
RAIRO - Operations Research (2010)
- Volume: 35, Issue: 2, page 269-281
- ISSN: 0399-0559
Access Full Article
top
Abstract
topHow to cite
topMahey, P., Phong, Thai Q., and Luna, H. P.L.. "Separable convexification and DCA techniques for capacity and flow assignment problems." RAIRO - Operations Research 35.2 (2010): 269-281. <http://eudml.org/doc/197823>.
@article{Mahey2010,
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.
},
author = {Mahey, P., Phong, Thai Q., Luna, H. P.L.},
journal = {RAIRO - Operations Research},
keywords = {Network design; DC optimization; capacity and flow assignment.},
language = {eng},
month = {3},
number = {2},
pages = {269-281},
publisher = {EDP Sciences},
title = {Separable convexification and DCA techniques for capacity and flow assignment problems},
url = {http://eudml.org/doc/197823},
volume = {35},
year = {2010},
}
TY - JOUR
AU - Mahey, P.
AU - Phong, Thai Q.
AU - Luna, H. P.L.
TI - Separable convexification and DCA techniques for capacity and flow assignment problems
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 269
EP - 281
AB -
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.
LA - eng
KW - Network design; DC optimization; capacity and flow assignment.
UR - http://eudml.org/doc/197823
ER -
References
top- A. Balakrishnan and S.C. Graves, A composite algorithm for a concave-cost network flow problem. Networks19 (1989) 175-202.
- D.P. Bertsekas and R.G. Gallager, Data Networks. Prentice-Hall (1987).
- J.E. Falk, Lagrange multipliers and nonconvex programs. SIAM J. Control Optim.7 (1969) 534-545.
- L. Fratta, M. Gerla and L. Kleinrock, The flow deviation method: an approach to store-and-forward communication network design. Networks3 (1973) 97-133.
- B. Gavish, Augmented Lagrangian based bounds for centralized network design. IEEE Trans. Comm.33 (1985) 1247-1257.
- B. Gavish and K. Altinkemer, Backbone network design tools with economic tradeoffs. ORSA J. Comput.2/3 (1990) 236-252.
- B. Gavish and I. Neuman, A system for routing and capacity assignment in computer communication networks. IEEE Trans. Comm.37 (1989) 360-366.
- M. Gerla, The Design of Store-and-forward Networks for Computer Communications. Ph.D. Thesis, UCLA (1973).
- M. Gerla and L. Kleinrock, On the topological design of distributed computer networks. IEEE Trans. Comm.25 (1977) 48-60.
- M. Gerla, J.A.S. Monteiro and R. Pazos, Topology design and bandwith allocation in ATM nets. IEEE J. Selected Areas in Communications7 (1989) 1253-1261.
- J.B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms. Springer-Verlag (1993).
- H. Konno, P.T. Thach and H. Tuy, Optimization on Low Rank Nonconvex Structures. Kluwer Academic Publishers, Dordrecht (1997).
- H.P.L. Luna and P. Mahey, Bounds for global optimization of capacity expansion and flow assignment problems. Oper. Res. Lett.26 (2000) 211-216.
- P. Mahey, A. Benchakroun and F. Boyer, Capacity and flow assignment of data networks by generalized Benders decomposition. J. Global Optim. (to appear).
- P. Mahey, A. Ouorou, L. LeBlanc and J. Chifflet, A new proximal decomposition algorithm for routing in telecommunications networks. Networks31 (1998) 227-238.
- A. Ouorou, P. Mahey and J.P. Vial, A survey of algorithms for convex multicommodity flow problems. Management Sci.46 (2000) 126-147.
- P.D. Tao and L.T.H. An, Convex analysis approach to dc programming: Theory, algorithms and applications. Acta Math. Vietnam.22 (1997) 289-355.
- N.T. Quang, Une approche dc en optimisation dans les réseaux. Algorithmes, codes et simulations numériques. Doct. Thesis, Univ. Rouen (1999).
- B. Sanso, M. Gendreau and F. Soumis, An algorithm for network dimensioning under reliability considerations. Ann. Oper. Res.36 (1992) 263-274.
- H. Tuy, S. Ghannadan, A. Migdalas and P. Varbrand, A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of nonlinear variables. Math. Programming72 (1996) 229-258.
- R. Wong, Introduction and recent advances in network design: Models and algorithms, in Transportation Planning Models, edited by M. Florian. Elsevier-North-Holland Publ. (1984).
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.