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

Date
2010
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Source Title
Computers and Operations Research
Print ISSN
0305-0548
Electronic ISSN
Publisher
Elsevier
Volume
38
Issue
1
Pages
277 - 286
Language
English
Type
Article
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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.

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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
Citation
Published Version (Please cite this version)