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    An outer approximation method for the road network design problem

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    Author
    Bagloee, SA; Sarvi, M
    Date
    2018-03-28
    Source Title
    PLoS One
    Publisher
    PUBLIC LIBRARY SCIENCE
    University of Melbourne Author/s
    Asadi Bagloee, Saeed; Sarvi, Majid
    Affiliation
    Infrastructure Engineering
    Metadata
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    Document Type
    Journal Article
    Citations
    Bagloee, S. A. & Sarvi, M. (2018). An outer approximation method for the road network design problem. PLOS ONE, 13 (3), https://doi.org/10.1371/journal.pone.0192454.
    Access Status
    Open Access
    URI
    http://hdl.handle.net/11343/254736
    DOI
    10.1371/journal.pone.0192454
    Abstract
    Best investment in the road infrastructure or the network design is perceived as a fundamental and benchmark problem in transportation. Given a set of candidate road projects with associated costs, finding the best subset with respect to a limited budget is known as a bilevel Discrete Network Design Problem (DNDP) of NP-hard computationally complexity. We engage with the complexity with a hybrid exact-heuristic methodology based on a two-stage relaxation as follows: (i) the bilevel feature is relaxed to a single-level problem by taking the network performance function of the upper level into the user equilibrium traffic assignment problem (UE-TAP) in the lower level as a constraint. It results in a mixed-integer nonlinear programming (MINLP) problem which is then solved using the Outer Approximation (OA) algorithm (ii) we further relax the multi-commodity UE-TAP to a single-commodity MILP problem, that is, the multiple OD pairs are aggregated to a single OD pair. This methodology has two main advantages: (i) the method is proven to be highly efficient to solve the DNDP for a large-sized network of Winnipeg, Canada. The results suggest that within a limited number of iterations (as termination criterion), global optimum solutions are quickly reached in most of the cases; otherwise, good solutions (close to global optimum solutions) are found in early iterations. Comparative analysis of the networks of Gao and Sioux-Falls shows that for such a non-exact method the global optimum solutions are found in fewer iterations than those found in some analytically exact algorithms in the literature. (ii) Integration of the objective function among the constraints provides a commensurate capability to tackle the multi-objective (or multi-criteria) DNDP as well.

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