Simultaneous Convexification of Bilinear Functions over Polytopes with Application to Network Interdiction

2017 ◽  
Vol 27 (3) ◽  
pp. 1801-1833 ◽  
Author(s):  
Danial Davarnia ◽  
Jean-Philippe P. Richard ◽  
Mohit Tawarmalani
Keyword(s):  
Network Interdiction ◽  
Bilinear Functions

Symmetric bilinear functions

1967 ◽  
pp. 244-278
Author(s):  
W. H. Greub
Keyword(s):  
Bilinear Functions

The Bicriterion Maximum Flow Network Interdiction Problem in s-t-Planar Graphs

2020 ◽  
pp. 133-139
Author(s):  
Luca E. Schäfer ◽  
Tobias Dietz ◽  
Marco V. Natale ◽  
Stefan Ruzika ◽  
Sven O. Krumke ◽  
...  
Keyword(s):  
Planar Graphs ◽  
Maximum Flow ◽  
Network Interdiction ◽  
Flow Network

scholarly journals A Decomposition Approach for Stochastic Shortest-Path Network Interdiction with Goal Threshold

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 237 ◽  
Author(s):  
Xiangyu Wei ◽  
Kai Xu ◽  
Peng Jiao ◽  
Quanjun Yin ◽  
Yabing Zha
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Benders Decomposition ◽  
Research Problem ◽  
Resource Consumption ◽  
Network Interdiction ◽  
Master Problem ◽  
Decomposition Approach ◽  
Stochastic Shortest Path ◽  
T Path

Shortest-path network interdiction, where a defender strategically allocates interdiction resource on the arcs or nodes in a network and an attacker traverses the capacitated network along a shortest s-t path from a source to a terminus, is an important research problem with potential real-world impact. In this paper, based on game-theoretic methodologies, we consider a novel stochastic extension of the shortest-path network interdiction problem with goal threshold, abbreviated as SSPIT. The attacker attempts to minimize the length of the shortest path, while the defender attempts to force it to exceed a specific threshold with the least resource consumption. In our model, threshold constraint is introduced as a trade-off between utility maximization and resource consumption, and stochastic cases with some known probability p of successful interdiction are considered. Existing algorithms do not perform well when dealing with threshold and stochastic constraints. To address the NP-hard problem, SSPIT-D, a decomposition approach based on Benders decomposition, was adopted. To optimize the master problem and subproblem iteration, an efficient dual subgraph interdiction algorithm SSPIT-S and a local research based better-response algorithm SSPIT-DL were designed, adding to the SSPIT-D. Numerical experiments on networks of different sizes and attributes were used to illustrate and validate the decomposition approach. The results showed that the dual subgraph and better-response procedure can significantly improve the efficiency and scalability of the decomposition algorithm. In addition, the improved enhancement algorithms are less sensitive and robust to parameters. Furthermore, the application in a real-world road network demonstrates the scalability of our decomposition approach.

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