Volume 52, Number 4-5, October–December 2018
|Page(s)||1107 - 1121|
|Published online||22 November 2018|
Reverse maximum flow problem under the weighted Chebyshev distance
Department of Industrial Engineering, Birjand University of Technology,
2 Department of Mathematics, Faculty of sciences, Imam Ali University, Tehran, Iran.
* Corresponding author: email@example.com
Accepted: 30 November 2017
Given a network G(V, A, u) with two specific nodes, a source node s and a sink node t, the reverse maximum flow problem is to increase the capacity of some arcs (i, j) as little as possible under bound constraints on the modifications so that the maximum flow value from s to t in the modified network is lower bounded by a prescribed value v0. In this paper, we study the reverse maximum flow problem when the capacity modifications are measured by the weighted Chebyshev distance. We present an efficient algorithm to solve the problem in two phases. The first phase applies the binary search technique to find an interval containing the optimal value. The second phase uses the discrete type Newton method to obtain exactly the optimal value. Finally, some computational experiments are conducted to observe the performance of the proposed algorithm.
Mathematics Subject Classification: 90C35 / 90B10 / 05C21
Key words: Maximum flow problem / reverse problem / Chebyshev distance / network design / Newton method / binary search
© EDP Sciences, ROADEF, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.