Networks and Spatial Economics

, Volume 13, Issue 1, pp 67–106 | Cite as

A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem

  • Hamid Farvaresh
  • Mohammad Mehdi Sepehri


Discrete network design problem (DNDP) is generally formulated as a bi-level programming. Because of non-convexity of bi-level formulation of DNDP which stems from the equilibrium conditions, finding global optimal solutions are very demanding. In this paper, a new branch and bound algorithm being able to find exact solution of the problem is presented. A lower bound for the upper-level objective and its computation method are developed. Numerical experiments show that our algorithm is superior to previous algorithms in terms of both computation time and solution quality. The conducted experiments indicate that in most cases the first incumbent solution which is obtained within a few seconds is superior to the final solution of some of previous algorithms.


Network design problem Bi-level programming Branch and bound Outer approximation 



The authors would like to thank the three anonymous referees for many thoughtful and constructive comments. We also wish to thank Mr. Fouad Behzadpour for his grammatical and lexical revisions and comments. We accept full responsibility for all the remaining errors and shortcomings.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Industrial EngineeringUniversity of KurdistanSanandajIran
  2. 2.Department of Industrial EngineeringTarbiat Modares UniversityTehranIran

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