New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller-Tucker-Zemlin constraints
Author(s)
Date
2010Source Title
Computers and Operations Research
Print ISSN
0305-0548
Publisher
Elsevier
Volume
38
Issue
1
Pages
277 - 286
Language
English
Type
ArticleItem Usage Stats
142
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488
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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 constraintsInteger 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
Permalink
http://hdl.handle.net/11693/28420Published Version (Please cite this version)
http://dx.doi.org/10.1016/j.cor.2010.05.003Collections
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