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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Vydané v:INFORMS journal on computing Ročník 20; číslo 4; s. 553 - 564
Hlavní autori: Andreas, April K, Smith, J. Cole
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Linthicum INFORMS 22.09.2008
Institute for Operations Research and the Management Sciences
Predmet:
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
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Abstract 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.
AbstractList 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.
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. [PUBLICATION ABSTRACT]
Audience Academic
Author Andreas, April K
Smith, J. Cole
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SubjectTerms Advantages
Algorithms
Analysis
branch and bound
Branch and bound algorithms
Graph theory
graphs
integer
Mathematical optimization
Mathematical programming
networks
nonlinear
programming
Routing
Studies
theory
Title Mathematical Programming Algorithms for Two-Path Routing Problems with Reliability Considerations
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