Finding Most Vital Links over Time in a Flow Network

This paper deals with finding most vital links of a network which carries flows over time (also called ”dynamic flows”). Given a network and a time horizon T, Single Most Vital Link Over Time (SMVLOT) problem looks for a link whose removal results in greatest decrease in the value of maximum flow ov...

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Bibliographic Details
Published in:An international journal of optimization and control Vol. 2; no. 2; pp. 173 - 186
Main Authors: MOROWATI-SHALILVAND, Shahram, MEHRI-TEKMEH, Javad
Format: Journal Article
Language:English
Published: Balikesir Balikesir University, Faculty of Engineering Department of Industrial Engineering 01.01.2012
Subjects:
Algorithms
Benders decomposition
Combinatorial analysis
Integer programming
Linear programming
Links
Mathematical programming
ISSN:2146-0957, 2146-5703
Online Access:Get full text
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Summary:This paper deals with finding most vital links of a network which carries flows over time (also called ”dynamic flows”). Given a network and a time horizon T, Single Most Vital Link Over Time (SMVLOT) problem looks for a link whose removal results in greatest decrease in the value of maximum flow over time (dynamic maximum flow) up to time horizon T between two terminal nodes. SMVLOT problem is formulated as a mixed binary linear programming problem. This formulation is extended to a general case called k-Most Vital Links Over Time (KMVLOT) problem, in which we look for finding those k links whose removal makes greatest decrease in the value of maximum flow over time. A Benders decomposition algorithm is proposed for solving SMVLOT and KMVLOT problems. For the case of SMVLOT problem, the proposed algorithm is improved to a fully combinatorial algorithm by adopting an iterative method for solving existing integer programming problem. However, our experimental results showed the superiority of proposed methods.
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ISSN:2146-0957
2146-5703
DOI:10.11121/ijocta.01.2012.0098