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An Algorithm for the Mixed Transportation Network Design Problem

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  • Xinyu Liu
  • Qun Chen

Abstract

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.

Suggested Citation

  • Xinyu Liu & Qun Chen, 2016. "An Algorithm for the Mixed Transportation Network Design Problem," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-18, September.
  • Handle: RePEc:plo:pone00:0162618
    DOI: 10.1371/journal.pone.0162618
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    Cited by:

    1. Behbahani, Hamid & Nazari, Sobhan & Jafari Kang, Masood & Litman, Todd, 2019. "A conceptual framework to formulate transportation network design problem considering social equity criteria," Transportation Research Part A: Policy and Practice, Elsevier, vol. 125(C), pages 171-183.
    2. Mohsen Momenitabar & Jeremy Mattson, 2021. "A Multi-Objective Meta-Heuristic Approach to Improve the Bus Transit Network: A Case Study of Fargo-Moorhead Area," Sustainability, MDPI, vol. 13(19), pages 1-25, September.
    3. Najmi, Ali & Waller, Travis & Rashidi, Taha H., 2023. "Equity in network design and pricing: A discretely-constrained MPEC problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 176(C).

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