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**Harvard**

Bagloee, S., Sarvi, M. och Patriksson, M. (2016) *A hybrid branch-and-bound and Benders decomposition algorithm for the network design problem*.

** BibTeX **

@article{

Bagloee2016,

author={Bagloee, Saeed Asadi and Sarvi, Majid and Patriksson, Michael},

title={A hybrid branch-and-bound and Benders decomposition algorithm for the network design problem},

journal={Computer-Aided Civil and Infrastructure Engineering},

issn={1467-8667},

volume={32},

issue={4},

pages={319-343},

abstract={Given a set of candidate road projects associated with costs, finding the best subset with respect to a limited budget is known as the network design problem (NDP). The NDP is often cast in a bilevel programming problem which is known to be NP-hard. In this study, we tackle a special case of the NDP where the decision variables are integers. A variety of exact solutions has been proposed for the discrete NDP, but due to the combinatorial complexity, the literature has yet to address the problem for large-size networks, and accounting for the multimodal and multiclass traffic flows. To this end, the bilevel problem is solved by branch-and-bound. At each node of the search tree, a valid lower bound based on system optimal (SO) traffic flow is calculated. The SO traffic flow is formulated as a mixed integer, non-linear programming (MINLP) problem for which the Benders decomposition method is used. The algorithm is coded on a hybrid and synchronized platform consisting of MATLAB (optimization engine), EMME 3 (transport planning module), MS Access (database), and MS Excel (user interface). The proposed methodology is applied to three examples including Gao's network, the Sioux-Falls network, and a real size network representing the city of Winnipeg, Canada. Numerical tests on the network of Winnipeg at various budget levels have shown promising results.},

year={2016},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 237540

A1 Bagloee, Saeed Asadi

A1 Sarvi, Majid

A1 Patriksson, Michael

T1 A hybrid branch-and-bound and Benders decomposition algorithm for the network design problem

YR 2016

JF Computer-Aided Civil and Infrastructure Engineering

SN 1467-8667

VO 32

IS 4

SP 319

OP 343

AB Given a set of candidate road projects associated with costs, finding the best subset with respect to a limited budget is known as the network design problem (NDP). The NDP is often cast in a bilevel programming problem which is known to be NP-hard. In this study, we tackle a special case of the NDP where the decision variables are integers. A variety of exact solutions has been proposed for the discrete NDP, but due to the combinatorial complexity, the literature has yet to address the problem for large-size networks, and accounting for the multimodal and multiclass traffic flows. To this end, the bilevel problem is solved by branch-and-bound. At each node of the search tree, a valid lower bound based on system optimal (SO) traffic flow is calculated. The SO traffic flow is formulated as a mixed integer, non-linear programming (MINLP) problem for which the Benders decomposition method is used. The algorithm is coded on a hybrid and synchronized platform consisting of MATLAB (optimization engine), EMME 3 (transport planning module), MS Access (database), and MS Excel (user interface). The proposed methodology is applied to three examples including Gao's network, the Sioux-Falls network, and a real size network representing the city of Winnipeg, Canada. Numerical tests on the network of Winnipeg at various budget levels have shown promising results.

LA eng

DO 10.1111/mice.12224

LK http://dx.doi.org/10.1111/mice.12224

OL 30