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      New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller-Tucker-Zemlin constraints

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      Author(s)
      Akgün, İbrahim
      Date
      2010
      Source Title
      Computers and Operations Research
      Print ISSN
      0305-0548
      Publisher
      Elsevier
      Volume
      38
      Issue
      1
      Pages
      277 - 286
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      Given an undirected network with positive edge costs and a natural number p, the hop-constrained minimum spanning tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, the new models based on the Miller-Tucker-Zemlin (MTZ) subtour elimination constraints are developed and computational results together with comparisons against MTZ-based, flow-based, and hop-indexed formulations are reported. The first model is obtained by adapting the MTZ-based Asymmetric Traveling Salesman Problem formulation of Sherali and Driscoll [18] and the other two models are obtained by combining topology-enforcing and MTZ-related constraints offered by Akgün and Tansel (submitted for publication) [20] for HMST with the first model appropriately. Computational studies show that the best LP bounds of the MTZ-based models in the literature are improved by the proposed models. The best solution times of the MTZ-based models are not improved for optimally solved instances. However, the results for the harder, large-size instances imply that the proposed models are likely to produce better solution times. The proposed models do not dominate the flow-based and hop-indexed formulations with respect to LP bounds. However, good feasible solutions can be obtained in a reasonable amount of time for problems for which even the LP relaxations of the flow-based and hop-indexed formulations can be solved in about 2 days. © 2010 Elsevier Ltd. All rights reserved.
      Keywords
      Hop constraints
      Integer programming
      Miller-Tucker-Zemlin constraints
      Network flows
      Spanning trees
      Asymmetric traveling salesman problem
      Computational results
      Computational studies
      Constrained minimum spanning tree
      Feasible solution
      Hop-constraints
      Hop-indexed formulations
      Large sizes
      LP relaxation
      Miller-Tucker-Zemlin constraints
      Natural number
      Network flows
      New model
      Root nodes
      Spanning tree
      Total costs
      Undirected network
      Integer programming
      Parallel architectures
      Query processing
      Telecommunication networks
      Topology
      Traveling salesman problem
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      http://hdl.handle.net/11693/28420
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.cor.2010.05.003
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