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Math. Comput. Appl. 2016, 21(4), 50;

Reliable Network Interdiction Models with Multiple Unit Costs

School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236037, China
Author to whom correspondence should be addressed.
Academic Editor: Fazal M. Mahomed
Received: 1 October 2016 / Revised: 24 November 2016 / Accepted: 29 November 2016 / Published: 14 December 2016
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This paper proposes a reliable network interdiction model with multiple unit costs, which maximizes the minimum arrival cost of the invader to the sink by setting obstacles on some arcs with limited resources in the given network. In other words, given a graph with a source and a sink, several arcs will be selected with limited resources such that each path contains as many weights as possible. This model needs to be transferred into a bilevel program because its constraints can hardly be listed explicitly even for a graph with a moderate size, because the number of paths between any two given points increases exponentially according to the size of the graph. This bilevel model is equivalent to an integer model with a low degree number of constraints by converting the inner programming to a shortest path problem. We first prove that this problem is non-deterministic polynomial-time (NP)-hard. Secondly, we reduce the number of constraints to the first power from the exponential degree by using the dual technique. Lastly, the national railway network is used to show the feasibility of our method. View Full-Text
Keywords: bilevel program; dual program; shortest path problems; NP-completeness; knapsack problem bilevel program; dual program; shortest path problems; NP-completeness; knapsack problem

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Zhao, J.; Sun, G. Reliable Network Interdiction Models with Multiple Unit Costs. Math. Comput. Appl. 2016, 21, 50.

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