An Active-set Algorithm for Discrete Network Design Problems

  • Lihui Zhang
  • Siriphong Lawphongpanich
  • Yafeng Yin


In this paper, we formulate a discrete network design problem as a mathematical program with complementarity constraints and propose an active set algorithm to solve the problem. Each complementarity constraint requires the product of a pair of nonnegative variables to be zero. Instead of dealing with this type of constraints directly, the proposed algorithm assigns one of the nonnegative variables in each pair a value of zero. Doing so reduces the design problem to a regular nonlinear program. Using the multipliers associated with the constraints forcing nonnegative variables to be zero, the algorithm then constructs and solves binary knapsack problems to make changes to the zero-value assignments in order to improve the system delay. Numerical experiments with data from networks in the literature indicate that the algorithm is effective and has the potential for solving larger network design problems.


System Delay Network Design Problem User Equilibrium Complementarity Constraint Transportation Research Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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This research is supported in part by grants from National Science Foundation (CMMI-0653804) and the Center for Multimodal Solutions for Congestion Mitigation at the University of Florida.


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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  • Lihui Zhang
    • 1
  • Siriphong Lawphongpanich
    • 1
  • Yafeng Yin
    • 1
  1. 1.University of FloridaCaliforniaU.S.A

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