An Extended Network Interdiction Problem for Optimal Toll Control

Borndörfer, Ralf; Sagnol, Guillaume; Schwartz, Stephan

doi:10.1016/j.endm.2016.03.040

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…Casas et al studied SPNIP for different geographic characteristics [37]. Borndörfer et al introduced the problem of determining the optimal locations for toll control stations considering parallel secondary paths that drivers can avoid from control stations [38]. Sefair and Smith, Cappenera and Scaparra, Sadeghi et al, Lozano and Smith studied trilevel mathematical models for various SPNIPs [8,[39][40][41].…”

Section: Figure 1 the Number Of Spnip Studies By Yearmentioning

confidence: 99%

Providing homeland security strategies against interdictions in the city transportation network: A case study in Turkey

Ayyıldız

Özçelik

Gencer

et al. 2023

Gazi University Journal of Science

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This paper defines a capacitated multiple-source multiple-sink shortest path problem and introduces its extension, called the capacitated multiple-source multiple-sink shortest path network interdiction problem (CMSSNIP). CMSSNIP examines the actions of attackers who attempt to maximize the total shortest path of network users trying to reach the crime locations for the aid process after causing an incident in certain regions to provide strategic information for the defense systems of the government. In this context, the exact mathematical model ensuring useful information about safe routes to network users is proposed. In this manner, to the best knowledge of authors, the CMSSNIP consisting of multiple-source nodes and multiple-sink nodes and considering capacity-demand relations between security units and crime locations is studied for the first time. Accordingly, a set of scenarios is considered based on the interdiction budget levels and the number of crime locations through a real case application to show the applicability of the model. Furthermore, computational experiments are performed to evaluate the model performance on different-sized networks. It is realized that especially the model provides resilient strategies versus interdictions in terms of obtaining the safe shortest paths at the operational level within seconds in the real case application.

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Section: Figure 1 the Number Of Spnip Studies By Yearmentioning

confidence: 99%

Providing homeland security strategies against interdictions in the city transportation network: A case study in Turkey

Ayyıldız

Özçelik

Gencer

et al. 2023

Gazi University Journal of Science

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“…These instances stem from a research project on optimal truck toll control with the German Federal Office for Goods Transport (cf. [9,10]). In order to have more instances, that can also be made publicly available, we generate two types of random transit networks with artificial traffic volume that resemble the real-world instances: random trees, and random networks based on Voronoi diagrams.…”

Section: Setting and Test Instancesmentioning

confidence: 99%

Vertex covering with capacitated trees

2022

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The covering of a graph with (possibly disjoint) connected subgraphs is a fundamental problem in graph theory. In this paper, we study a version to cover a graph's vertices by connected subgraphs subject to lower and upper weight bounds, and propose a column generation approach to dynamically generate feasible and promising subgraphs. Our focus is on the solution of the pricing problem which turns out to be a variant of the NP-hard Maximum Weight Connected Subgraph Problem. We compare different formulations to handle connectivity, and find that a single-commodity flow formulation performs best. This is notable since the respective literature seems to have widely dismissed this formulation. We improve it to a new coarse-to-fine flow formulation that is theoretically and computationally superior, especially for large instances with many vertices of degree 2 like highway networks, where it provides a speed-up factor of 5 over the non-flow-based formulations. We also propose a preprocessing method that exploits a median property of weight-constrained subgraphs, a primal heuristic, and a local search heuristic. In an extensive computational study we evaluate the presented connectivity formulations on different classes of instances, and demonstrate the effectiveness of the proposed enhancements. Their speed-ups essentially multiply to an overall factor of well over 10. Overall, our approach allows the reliable solution of instances with several hundreds of vertices in a few minutes. These findings are further corroborated in a comparison to existing districting models on a set of test instances from the literature.

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