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Main Authors: Klyuchikov, Artyom, Hildebrand, Roland, Protasov, Sergei, Rogozin, Alexander, Chernov, Alexei
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2504.17031
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author Klyuchikov, Artyom
Hildebrand, Roland
Protasov, Sergei
Rogozin, Alexander
Chernov, Alexei
author_facet Klyuchikov, Artyom
Hildebrand, Roland
Protasov, Sergei
Rogozin, Alexander
Chernov, Alexei
contents We consider the robust version of a multi-commodity network flow problem. The robustness is defined with respect to the deletion, or failure, of edges. While the flow problem itself is a polynomially-sized linear program, its robust version is a saddle-point problem with discrete variables. We present two approaches for the solution of the robust network flow problem. One way is to formulate the problem as a bigger linear program. The other is to solve a multi-level optimization problem, where the linear programs appearing at the lower level can be solved by the dual simplex method with a warm start. We then consider the problem of robustifying the network. This is accomplished by optimally using a fixed budget for strengthening certain edges, i.e., increasing their capacity. This problem is solved by a sequence of linear programs at the upper level, while at the lower levels the mentioned dual simplex algorithm is employed.
format Preprint
id arxiv_https___arxiv_org_abs_2504_17031
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Robustifying networks for flow problems against edge failure
Klyuchikov, Artyom
Hildebrand, Roland
Protasov, Sergei
Rogozin, Alexander
Chernov, Alexei
Optimization and Control
We consider the robust version of a multi-commodity network flow problem. The robustness is defined with respect to the deletion, or failure, of edges. While the flow problem itself is a polynomially-sized linear program, its robust version is a saddle-point problem with discrete variables. We present two approaches for the solution of the robust network flow problem. One way is to formulate the problem as a bigger linear program. The other is to solve a multi-level optimization problem, where the linear programs appearing at the lower level can be solved by the dual simplex method with a warm start. We then consider the problem of robustifying the network. This is accomplished by optimally using a fixed budget for strengthening certain edges, i.e., increasing their capacity. This problem is solved by a sequence of linear programs at the upper level, while at the lower levels the mentioned dual simplex algorithm is employed.
title Robustifying networks for flow problems against edge failure
topic Optimization and Control
url https://arxiv.org/abs/2504.17031