An effective bilevel programming approach for the evasive flow capturing location problem.

*(English)*Zbl 07257985Summary: This paper addresses the problem of locating weigh-in-motion (WIM) sensors on a road transportation network to effectively detect and intercept overloaded trucks assuming that truckers quickly find out the locations of WIM facilities, and make an attempt to avoid them by deviating from their predefined shortest paths. We formulate the problem as a bi-level programming (BLP) model and propose two approaches to find its optimal solution: The first approach utilizes the Karush-Kuhn-Tucker (KKT) conditions to provide a single-level reformulation of the BLP model. However, the second one is an exact decomposition-based algorithm that is superior to the KKT-based reformulation in terms of the computational time. The algorithm starts with a relaxed version of the BLP model and adds a family of cuts on the fly, the optimum is obtained within a few iterations. The idea behind our cut generation is novel and it is based on the knowledge of the underlying problem structure. Computational experiments on some randomly generated instances confirm the efficiency of the algorithm.

##### Keywords:

evasive flow capturing problem; weigh-in-motion; vehicle inspection stations; bi-level program; KKT-based reformulation; exact decomposition-based algorithm
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\textit{F. Hooshmand} and \textit{S. A. MirHassani}, Netw. Spat. Econ. 18, No. 4, 909--935 (2018; Zbl 07257985)

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