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

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Amal Benhamiche , A. Ridha Mahjoub , Nancy Perrot , Eduardo Uchoa ·

YOU? · · 2017 · Open Access · · DOI: https://doi.org/10.1590/0101-7438.2017.037.03.0545

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 AND (ii) each capacity (subband) is assigned a route in the physical layer. The traffic demands cannot be splitted along several paths (nor even several capacities installed on the same link), which makes the problem even more difficult. In this paper, we present new non-compact ILP formulations to model the problem and provide column generation procedures, based on different Dantzig-Wolfe decomposition schemes to solve it. More precisely, an arc-flow formulation is given for the problem and used to derive two different paths formulations: non-aggregated and aggregated. The former contains two families of path variables and requires a double column generation procedure to solve it, while the latter relies on a single path variable with a specific structure. These alternative modeling approaches induce two Branch-and-Price algorithms that allow to solve the problem efficiently for several classes of instances.

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Column generation Computer science Column (typography) Mathematical optimization Path (computing) Variable (mathematics) Layer (electronics) Set (abstract data type) Flow (mathematics) Network planning and design Decomposition Algorithm Flow network Mathematics Computer network Biology Organic chemistry Programming language Geometry Mathematical analysis Ecology Chemistry Frame (networking)

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Type: article
Language: en
Landing Page: https://doi.org/10.1590/0101-7438.2017.037.03.0545
PDF: http://www.scielo.br/pdf/pope/v37n3/1678-5142-pope-37-03-545.pdf
OA Status: diamond
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DOI: https://doi.org/10.1590/0101-7438.2017.037.03.0545

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

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Language: en

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Publication year: 2017

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Publication date: 2017-09-01

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Authors: Amal Benhamiche, A. Ridha Mahjoub, Nancy Perrot, Eduardo Uchoa

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Landing page: https://doi.org/10.1590/0101-7438.2017.037.03.0545

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Concepts: Column generation, Computer science, Column (typography), Mathematical optimization, Path (computing), Variable (mathematics), Layer (electronics), Set (abstract data type), Flow (mathematics), Network planning and design, Decomposition, Algorithm, Flow network, Mathematics, Computer network, Biology, Organic chemistry, Programming language, Geometry, Mathematical analysis, Ecology, Chemistry, Frame (networking)

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Cited by: 1

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