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

Liang Chen and Wei-Kun Chen and Mu-Ming Yang and Yu-Hong Dai
2020 arXiv   pre-print
We use the 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 .  ... 
arXiv:2009.12550v3 fatcat:hzua2wqzvrblvkqvlr42ud72tm

On splittable and unsplittable flow capacitated network design arc-set polyhedra

Alper Atamtürk, Deepak Rajan
2002 Mathematical programming  
We study the polyhedra of splittable and 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.  ... 
doi:10.1007/s101070100269 fatcat:kefxv7kls5cblblkmt77s57uem

On the minimum cost multiple-source unsplittable flow problem

Meriema Belaidouni, Walid Ben-Ameur
2007 Reserche operationelle  
The minimum cost multiple-source 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.  ... 
doi:10.1051/ro:2007023 fatcat:tkvtyqzgtvgbjfjonilhaou5gy

Multicommodity flow problems with a bounded number of paths: A flow deviation approach

Christophe Duhamel, Philippe Mahey
2006 Networks  
A heuristic control of the path generation is then embedded in the original 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] ).  ... 
doi:10.1002/net.20143 fatcat:boiy5nwpczcq7b5n4djn4hqn5q

Multi-Commodity Multi-Facility Network Design [article]

Alper Atamturk, Oktay Gunluk
2020 arXiv   pre-print
The basic inequalities derived from 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.  ... 
arXiv:1707.03810v3 fatcat:yur4urx7jfh4dmqw7b3x6awfea

0–1 reformulations of the multicommodity capacitated network design problem

Antonio Frangioni, Bernard Gendron
2009 Discrete Applied Mathematics  
install on each 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.  ... 
doi:10.1016/j.dam.2008.04.022 fatcat:756meunr4fgkdey6nfaadsvn6i

The Mcf-separator: detecting and exploiting multi-commodity flow structures in MIPs

Tobias Achterberg, Christian Raack
2010 Mathematical Programming Computation  
We evaluate the quality of the 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  ... 
doi:10.1007/s12532-010-0015-3 fatcat:sb35hvya5vdx7dzyhlyo5mnd4i

COLUMN GENERATION BASED ALGORITHMS FOR THE CAPACITATED MULTI-LAYER NETWORK DESIGN WITH UNSPLITTABLE DEMANDS

Amal Benhamiche, A. Ridha Mahjoub, Nancy Perrot, Eduardo Uchoa
2017 Pesquisa Operacional  
More precisely, 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.  ... 
doi:10.1590/0101-7438.2017.037.03.0545 fatcat:incu6umvhffw5ol42o54wg7kcm

Multicommodity demand flow in a tree and packing integer programs

Chandra Chekuri, Marcelo Mydlarz, F. Bruce Shepherd
2007 ACM Transactions on Algorithms  
We also obtain, via this method, improved 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.  ... 
doi:10.1145/1273340.1273343 fatcat:okxybkbez5dfjkjrlus2if4fia

The Robust Network Loading Problem Under Hose Demand Uncertainty: Formulation, Polyhedral Analysis, and Computations

Ayşegül Altın, Hande Yaman, Mustafa Ç. Pınar
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 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.  ... 
doi:10.1287/ijoc.1100.0380 fatcat:wur3xi3kzvagtn3jvocbqowxtm

k-splittable delay constrained routing problem: A branch and price approach

Jerome Truffot, Christophe Duhamel, Philippe Mahey
2007 2007 6th International Workshop on Design and Reliable Communication Networks  
We analyze here 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?  ... 
doi:10.1109/drcn.2007.4762284 fatcat:f3hzlm2zmrfa7lqxhgj67yv46e

k-Splittable delay constrained routing problem: A branch-and-price approach

Jérôme Truffot, Christophe Duhamel, Philippe Mahey
2009 Networks  
We analyze here 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?  ... 
doi:10.1002/net.20311 fatcat:i3nbifgrsbc5ncsulr3h3ygrxm

Models and algorithms for network design problems

Michael Poss
2011 4OR  
Multi-layer 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  ... 
doi:10.1007/s10288-011-0174-8 fatcat:j4iuucjoqvcuxccma5wkfxmkom

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 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.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Minimum color‐degree perfect b ‐matchings

Mariia Anapolska, Christina Büsing, Martin Comis, Tabea Krabs
2020 Networks  
The last speaker of the session will chair the session, with two exceptions 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.  ... 
doi:10.1002/net.21974 fatcat:4qgtutmxrrcy7anvxks4fivcii
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