System optimal relaxation and Benders decomposition algorithm for the large-sized road network design problem
by Saeed Asadi Bagloee; Majid Sarvi; Abbas Rajabifard; Russell George Thompson
International Journal of Logistics Systems and Management (IJLSM), Vol. 34, No. 4, 2019

Abstract: Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as the discrete network design problem (DNDP). The DNDP is often characterised as a bilevel programming problem which is known to be NP-hard. Despite a plethora of research, due to the combinatorial complexity, the literature addressing this problem for large-sized networks is scarce. To this end, we first transform the bilevel problem into a single-level problem by relaxing it to a system-optimal traffic flow. As such, the problem turns to be a mixed integer nonlinear programming (MINLP) problem. Secondly, we develop an efficient Benders decomposition algorithm to solve the ensuing MINLP problem. The proposed methodology is applied to three examples, a pedagogical network, Sioux Falls and a real-size network representing the City of Winnipeg, Canada. Numerical tests on the network of Winnipeg at various budget levels demonstrate promising results.

Online publication date: Mon, 04-Nov-2019

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