Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios

We consider the design of a multicommodity flow network, in which point-to-point demands are routed across the network subject to link capacity restrictions. Such a design must build enough capacity and diverse routing paths through the network to ensure that feasible multicommodity flows continue t...

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Veröffentlicht in:Omega (Oxford) Jg. 36; H. 6; S. 1057 - 1071
Hauptverfasser: Garg, Manish, Smith, J. Cole
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Exeter Elsevier Ltd 01.12.2008
Elsevier
Elsevier Science Publishers
Pergamon Press Inc
Schriftenreihe:Omega
Schlagworte:
Algorithms
Analysis
Applied sciences
Computing
Design and construction
Exact sciences and technology
Flows in networks. Combinatorial problems
Integer programming
Integer programming Routing Optimization Computing
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Routing
Studies
Telecommunication systems
United States
Integer programming
Routing
Computing
Optimization
Script
Channel capacity
Network flow
Partition method
Optimal algorithm
Rupture
Mixed integer programming
Failures
Modeling
Multicommodity flow problem
Graph connectivity
Inequality constraint
ISSN:0305-0483, 1873-5274
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Zusammenfassung:We consider the design of a multicommodity flow network, in which point-to-point demands are routed across the network subject to link capacity restrictions. Such a design must build enough capacity and diverse routing paths through the network to ensure that feasible multicommodity flows continue to exist, even when components of the network fail. In this paper, we examine several methodologies to optimally design a minimum-cost survivable network that continues to support a multicommodity flow under any of a given set of failure scenarios, where each failure scenario consists of the simultaneous failure of multiple arcs. We begin by providing a single extensive form mixed-integer programming formulation for this problem, along with a Benders decomposition algorithm as an alternative to the extensive form approach. We next investigate strategies to improve the performance of the algorithm by augmenting the master problem with several valid inequalities such as cover constraints, connectivity constraints, and path constraints. For the smallest instances (eight nodes, 10 origin–destination pairs, and 10 failure scenarios), the Benders implementation consumes only 10% of the time required by the mixed-integer programming formulation, and our best augmentation strategy reduces the solution time by another 50%. For medium- and large-sized instances, the extensive form problem fails to terminate within 2 h on any instance, while our decomposition algorithms provide optimal solutions on all but two problem instances.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0305-0483
1873-5274
DOI:10.1016/j.omega.2006.05.006