On feasibility conditions of multicommodity flows in networks

Onaga, Kenji; Kakusho, Osamu

doi:10.1109/tct.1971.1083312

Cited by 111 publications

(47 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The projection results in an exponential formulation in the space of the capacity variables and the variables used to dualize the capacity constraints. The formulation does not rely on general metric inequalities [41,50,54] but is solely based on network cuts such that the corresponding separation can be handled by standard max-flow-min-cut [3].…”

Section: Dominationmentioning

confidence: 99%

Robust network design: Formulations, valid inequalities, and computations

2013

View full text Add to dashboard Cite

Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of [21]. We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness.To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge.For realistic networks and live traffic measurements we compare the formulations and report on the speed up by the valid inequalities. We study the "price of robustness" and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods.

show abstract

Section: Dominationmentioning

confidence: 99%

Robust network design: Formulations, valid inequalities, and computations

2013

View full text Add to dashboard Cite

show abstract

“…These inequalities, called semimetric inequalities, were introduced in [33,52]. They can be seen as a generalization of the maximum flow/minimum cut theorem.…”

Section: Resolution a Linear Programming Routing Problemmentioning

confidence: 99%

Acceleration of cutting‐plane and column generation algorithms: Applications to network design

Ben‐Ameur

Neto

2006

Networks

View full text Add to dashboard Cite

Most of integer, convex, and large-scale linear problems are solved using cutting plane and column generation algorithms. Therefore, to handle large-size problems and to reduce the computing times, it may be very useful to accelerate cutting plane algorithms. We show in this article that we can achieve this goal by choosing good separation points. Focus is given on problems for which we have an exact separation oracle. An in-out algorithm is proposed, and the convergence is proved under some general assumptions. Computational experiments related to three classes of problems, survivable network design, multicommodity flow problems, and random linear programs, clearly point out the savings of time allowed by the simple in-out approach proposed in this article.

show abstract

“…As the routing cost satisfies the triangle inequality, these constraints guarantee that the traffic of a commodity uses the direct link between the hubs of its origin and destination if its origin and destination are assigned to different hubs. Constraints (7) imply that the traffic on arc ( j, l ) should be at least the sum of the traffic of commodities whose origins are assigned to node j and whose destinations are assigned to node l. We sometimes refer to the traffic on the backbone links as capacity to be able to follow the terminology of flows and cuts.…”

Section: Multicommodity Flow Linearization and Its Projectionsmentioning

confidence: 99%

“…The first method used by Mirchandani [6] is a direct projection. This method leads to inequalities known as the metric inequalities (see Iri [4] and Onaga and Kakusho [7]). Mirchandani [6] studies the extreme rays of the resulting cone for the single commodity and multicommodity cases.…”

Section: Multicommodity Flow Linearization and Its Projectionsmentioning

confidence: 99%

Projecting the flow variables for hub location problems

Labbé

Yaman

2004

Networks

View full text Add to dashboard Cite

We consider two formulations for the uncapacitated hub location problem with single assignment (UHL), which use multicommodity flow variables. We project out the flow variables and determine some extreme rays of the projection cones. Then we investigate whether the corresponding inequalities define facets of the UHL polyhedron. We also present two families of facet defining inequalities that dominate some projection inequalities. Finally, we derive a family of valid inequalities that generalizes the facet defining inequalities and that can be separated in polynomial time.

show abstract

On feasibility conditions of multicommodity flows in networks

Cited by 111 publications

References 0 publications

Robust network design: Formulations, valid inequalities, and computations

Robust network design: Formulations, valid inequalities, and computations

Acceleration of cutting‐plane and column generation algorithms: Applications to network design

Projecting the flow variables for hub location problems

Contact Info

Product

Resources

About