Mathematical Programming Algorithms for Two-Path Routing Problems with Reliability Considerations

Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality, introducing nonlinear, nonconvex constraints. We examine the robust t...

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Bibliographic Details
Published in:INFORMS journal on computing Vol. 20; no. 4; pp. 553 - 564
Main Authors: Andreas, April K, Smith, J. Cole
Format: Journal Article
Language:English
Published: Linthicum INFORMS 22.09.2008
Institute for Operations Research and the Management Sciences
Subjects:
Advantages
Algorithms
Analysis
branch and bound
Branch and bound algorithms
Graph theory
graphs
integer
Mathematical optimization
Mathematical programming
networks
nonlinear
programming
Routing
Studies
theory
United States
ISSN:1091-9856, 1526-5528, 1091-9856
Online Access:Get full text
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Summary:Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality, introducing nonlinear, nonconvex constraints. We examine the robust two-path problem, which seeks to establish two paths between a source and destination node wherein at least one path must remain fully operable with some threshold probability. We consider the case where both paths must be arc disjoint and the case where arcs can be shared between the paths. We examine various strategies for solving the resulting nonlinear integer program, including pruning, coefficient tightening, lifting, and branch-and-bound partitioning schemes. We discuss the advantages and disadvantages of these methods and conclude with computational results.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1080.0266