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Methodological aspects of ring network design

  • Claudio Arbib
  • Ugo Mocci
  • Caterina Scoglio
II Mathematical Programming II.2 Discrete Optimization
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)

Abstract

We analyse ring network design problems, with the aim of satisfying at a minimum cost a given demand matrix. The network model considers link capacities ranging over a discrete set of values, and both fixed and linear costs, which pose severe limitations to the possibility of finding global optimum solutions. An approximated version of the problem — which neglects the discrete nature of link capacities — is here formulated as a multicommodity flow problem with linear cost function and fixed costs on a hypergraph. Such a problem is NP-hard. A greedy algorithm, which extends the one proposed by Minoux, is devised. A more general solution approach is also developed, which consists of a decomposition of the general problem into two major steps. Aim of the first is to design a partial network which satisfies a given percentage of the overall demand. This task is formulated as a pure combinatorial problem, in terms of 0–1 linear programming. The second step consists of finding a completion of the partial network, and can be formulated as a classical multicommodity graph-flow problem with fixed costs. Prior to both approaches, effective cluster analysis techniques are suggested for reducing the input size, according to demand, and/or to geographical, logical, and economic criteria.

Keywords

Link Capacity Network Design Problem Internal Demand Partial Network Linear Cost Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Claudio Arbib
    • 1
  • Ugo Mocci
    • 2
  • Caterina Scoglio
    • 2
  1. 1.Dip. di Ingegneria ElettronicaUniv. Roma "Tor Vergata"RomaItaly
  2. 2.Fondazione "Ugo Bordoni"RomaItaly

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