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A Branch-and-Bound Algorithm to Solve a Multi-level Network Optimization Problem

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Journal of Mathematical Modelling and Algorithms

Abstract

Multi-level network optimization problems arise in many contexts such as telecommunication, transportation, and electric power systems. A model for multi-level network design is formulated as a mixed-integer program. The approach is innovative because it integrates in the same model aspects of discrete facility location, topological network design, and dimensioning. We propose a branch-and-bound algorithm based on Lagrangian relaxation to solve the model. Computational results for randomly generated problems are presented showing the quality of our approach. We also present and discuss a real world problem of designing a two-level local access urban telecommunication network and solving it with the proposed methodology.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de Minas Gerais, 31270-901 –, Belo Horizonte – MG, Brazil

    F. R. B. Cruz

  2. Departamento de Ciência da Computação, Universidade Federal de Minas Gerais, 31270-901 –, Belo Horizonte – MG, Brazil

    G. R. Mateus

  3. Department of Mechanical & Industrial Engineering, University of Massachusetts, Amherst, MA, 01003, U.S.A

    J. MacGregor Smith

Authors
  1. F. R. B. Cruz
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  2. G. R. Mateus
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  3. J. MacGregor Smith
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Cruz, F.R.B., Mateus, G.R. & MacGregor Smith, J. A Branch-and-Bound Algorithm to Solve a Multi-level Network Optimization Problem. Journal of Mathematical Modelling and Algorithms 2, 37–56 (2003). https://doi.org/10.1023/A:1023670814370

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