A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad h...

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Bibliographic Details
Published in:European journal of operational research 2010, Vol.200 (1), p.28-35
Main Authors: Obreque, Carlos, Donoso, Macarena, Gutiérrez, Gabriel, Marianov, Vladimir
Format: Article
Language:English
Subjects:
Applied sciences
Branch & bound algorithms
Branch and cut
Cutting planes
Exact sciences and technology
Extensive facility location
Extensive facility location Hierarchical networks Branch and cut Cutting planes
Flows in networks. Combinatorial problems
Graph theory
Hierarchical networks
Logistics
Operational research and scientific management
Operational research. Management science
Optimization techniques
Studies
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Summary:The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2008.12.022