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An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron
[article]

2020
*
arXiv
*
pre-print

We use the

arXiv:2009.12550v3
fatcat:hzua2wqzvrblvkqvlr42ud72tm
*unsplittable**flow**arc*-*set**polyhedron*of the considered problem as a substructure and generate cutting planes by solving the*separation*problem over it. ... In this paper, we concentrate on generating cutting planes*for*the*unsplittable**capacitated**network**design*problem. ...*Separation*problem*for*the*unsplittable**flow**arc*-*set**polyhedron*In this section, we first study the polyhedral properties of the*unsplittable**flow**arc*-*set**polyhedron*P . ...##
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On splittable and unsplittable flow capacitated network design arc-set polyhedra

2002
*
Mathematical programming
*

We study the polyhedra of splittable and

doi:10.1007/s101070100269
fatcat:kefxv7kls5cblblkmt77s57uem
*unsplittable*single*arc*-*set*relaxations of multicommodity*flow**capacitated**network**design*problems. ... We present a summary of computational experiments with a branch-and-cut*algorithm**for*multicommodity*flow**capacitated**network**design*problems to test the effectiveness of the results presented here empirically ... Experiments with*unsplittable**flow*problems The next*set*of experiments are on the multicommodity*unsplittable**flow**network**design*problem. ...##
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On the minimum cost multiple-source unsplittable flow problem

2007
*
Reserche operationelle
*

The minimum cost multiple-source

doi:10.1051/ro:2007023
fatcat:tkvtyqzgtvgbjfjonilhaou5gy
*unsplittable**flow*problem is studied in this paper. A simple necessary condition to get a solution is proposed. ... A cutting plane*algorithm*is derived using a superadditive approach. The inequalities considered here are valid*for*single knapsack constraints. ... The authors wish to thank the referees*for*a number of insightful comments that have led to a substantially improved paper. ...##
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Multicommodity flow problems with a bounded number of paths: A flow deviation approach

2006
*
Networks
*

A heuristic control of the path generation is then embedded in the original

doi:10.1002/net.20143
fatcat:boiy5nwpczcq7b5n4djn4hqn5q
*algorithm*based on the concepts of cleaning the quasi inactive paths and the reduction of the*flow*width*for*each commodity. ... Numerical experiments show the validity of the approach*for*realistic medium-size*networks*associated with routing problems in broadband communication*networks*with multiple protocols and label-switched ... The problem of minimizing the*flow*on the most congested link is of valuable interest*for*the*design*of data communication*networks*(see [4] ). ...##
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Multi-Commodity Multi-Facility Network Design
[article]

2020
*
arXiv
*
pre-print

The basic inequalities derived from

arXiv:1707.03810v3
fatcat:yur4urx7jfh4dmqw7b3x6awfea
*arc*-*set*, cut-*set*and partition relaxations of the*network*are also extensively utilized with certain modifications in robust and survivable*network**design*problems. ... These are the metric inequalities*for*projecting out continuous*flow*variables, mixed-integer rounding from appropriate base relaxations and shrinking the*network*to a small k-node graph. ... Atamtürk is supported, in part, by grant FA9550-10-1-0168 from the Office of the Assistant Secretary of Defense*for*Research and Engineering. O. ...##
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0–1 reformulations of the multicommodity capacitated network design problem

2009
*
Discrete Applied Mathematics
*

install on each

doi:10.1016/j.dam.2008.04.022
fatcat:756meunr4fgkdey6nfaadsvn6i
*arc*of the*network*. ... 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 ... We are grateful to Serge Bisaillon*for*his help with implementing and testing the*algorithms*. ...##
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The Mcf-separator: detecting and exploiting multi-commodity flow structures in MIPs

2010
*
Mathematical Programming Computation
*

We evaluate the quality of the

doi:10.1007/s12532-010-0015-3
fatcat:sb35hvya5vdx7dzyhlyo5mnd4i
*algorithm*using a large*set*of publicly available*network**design*instances. Section 4 describes our aggregation and*separation*scheme. ... Our*separation*scheme speeds-up the computation*for*a large*set*of mixed integer programs coming from*network**design*problems by a factor two on average. ... The*capacitated**network**design*problem now asks*for*a capacity assignment to the*arcs*plus a feasible*network**flow**for*all commodities that minimizes a given linear (*flow*and/or capacity) cost function ...##
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COLUMN GENERATION BASED ALGORITHMS FOR THE CAPACITATED MULTI-LAYER NETWORK DESIGN WITH UNSPLITTABLE DEMANDS

2017
*
Pesquisa Operacional
*

More precisely,

doi:10.1590/0101-7438.2017.037.03.0545
fatcat:incu6umvhffw5ol42o54wg7kcm
*an**arc*-*flow*formulation is given*for*the problem and used to derive two different paths formulations: non-aggregated and aggregated. ... We investigate a variant of the Multi-Layer*Network**Design*problem where minimum cost capacities have to be installed upon a virtual layer in such a way that (i) a*set*of traffic demands can be routed ... ACKNOWLEDGMENTS Authors are very grateful to the anonymous referees*for*their constructive comments on a previous version of the paper. ...##
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Multicommodity demand flow in a tree and packing integer programs

2007
*
ACM Transactions on Algorithms
*

We also obtain, via this method, improved

doi:10.1145/1273340.1273343
fatcat:okxybkbez5dfjkjrlus2if4fia
*algorithms**for*the line and ring*networks*. Applications and connections to other combinatorial problems are discussed. ... Garg, Vazirani, and Yannakakis had shown that this problem is NP-hard and gave a 2-approximation*algorithm**for*the cardinality case (all profits are 1) via a primal-dual*algorithm*. ... We are grateful to ONR*for*supporting this visit (N00014-02-M-0125). We thank the anonymous reviewers*for*their comments and corrections. ...##
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The Robust Network Loading Problem Under Hose Demand Uncertainty: Formulation, Polyhedral Analysis, and Computations

2011
*
INFORMS journal on computing
*

We study the polyhedral aspects of the NLP under hose demand uncertainty and use the results as the basis of

doi:10.1287/ijoc.1100.0380
fatcat:wur3xi3kzvagtn3jvocbqowxtm
*an*efficient branch-and-cut*algorithm*. ... The results of extensive computational experiments on well-known*network**design*instances are reported. ... Ridha Mahjoub and Hervé Kerivin*for*helpful discussions and three anonymous referees*for*detailed suggestions. ...##
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k-splittable delay constrained routing problem: A branch and price approach

2007
*
2007 6th International Workshop on Design and Reliable Communication Networks
*

We analyze here

doi:10.1109/drcn.2007.4762284
fatcat:f3hzlm2zmrfa7lqxhgj67yv46e
*an**algorithmic*procedure based on branch-and-price*algorithm*and on the*flow*deviation method to solve a nonlinear k -splittable*flow*problem. ... Routing problems, which include a QoS-based path control, play a key role in broadband communication*networks*. ...*capacitated**network*? ...##
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k-Splittable delay constrained routing problem: A branch-and-price approach

2009
*
Networks
*

We analyze here

doi:10.1002/net.20311
fatcat:i3nbifgrsbc5ncsulr3h3ygrxm
*an**algorithmic*procedure based on branch-and-price*algorithm*and on the*flow*deviation method to solve a nonlinear k -splittable*flow*problem. ... Routing problems, which include a QoS-based path control, play a key role in broadband communication*networks*. ...*capacitated**network*? ...##
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Models and algorithms for network design problems

2011
*
4OR
*

Multi-layer

doi:10.1007/s10288-011-0174-8
fatcat:j4iuucjoqvcuxccma5wkfxmkom
*network**design*As the single-layer*capacitated**network**design*problem is complicated enough, most approaches*for*the bi-layer problem consider each layer*separately*: • First, a*network**design*... Formulation Given*an*undirected graph (V, E) and a*set*of commodities Q, with origin s(q), destination t(q), and nominal value d q*for*every q ∈ Q, the*capacitated**network**design*problem aims at installing ...##
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14th International Symposium on Mathematical Programming

1990
*
Mathematical programming
*

If we use a decomposition approach in order to solve a minimization problem we often get

doi:10.1007/bf01580875
fatcat:3jtclwmntzgjxkqs5uecombdaa
*an*objective function in such a w a y that its domain dom 6 = n is not given explicitely to us. ... It is shown that*for*the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral ... present a branch-and-cut*algorithm*to solve*capacitated**network**design*problems. ...##
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Minimum color‐degree perfect b ‐matchings

2020
*
Networks
*

The last speaker of the session will chair the session, with two exceptions

doi:10.1002/net.21974
fatcat:4qgtutmxrrcy7anvxks4fivcii
*for*PhD-only sessions: Combinatorial Optimization (Mon 18, Room PP, 16-17) chaired by R. ...*For*the GVRP-CAFS, we formulated a MILP model and we proposed*an**exact*method to solve it in more reasonable time. ... The proposed*exact*approach solved to optimality all the instances within*an*average computational time of 22 seconds against*an*average of 557 seconds of the MILP model. ...
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