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Comparative tests of multimodal traffic equilibrium methods

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  • Nagurney, Anna B.

Abstract

In this study we proceeded to test the relative efficiencies of the two main computational techniques now available for calculating the traffic equilibrium in multimodal networks, namely, the relaxation and projection methods. Since both of these methods solve at each step a mathematical programming problem, we first set out to test the Frank-Wolfe algorithm and the Dafermos-Sparrow algorithm and found the latter to be the more efficient algorithm. As expected, this was also the case when these algorithms were used to solve the mathematical programming problem at each step of the relaxation method. We then investigated how different versions of the projection method enhance its performance. Subsequently, we proceeded to our main goal to compare the best projection method with the relaxation method. We tested multimodal networks with three different classes of monotone travel cost functions and found that the form of the travel cost functions affects the performance of the two basic techniques available for computing the multimodal equilibrium.

Suggested Citation

  • Nagurney, Anna B., 1984. "Comparative tests of multimodal traffic equilibrium methods," Transportation Research Part B: Methodological, Elsevier, vol. 18(6), pages 469-485, December.
    • Handle: RePEc:eee:transb:v:18:y:1984:i:6:p:469-485
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    Cited by:

    1. García, Ricardo & Marín, Angel, 2005. "Network equilibrium with combined modes: models and solution algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 39(3), pages 223-254, March.
    2. Elnaz Miandoabchi & Reza Farahani & W. Szeto, 2012. "Bi-objective bimodal urban road network design using hybrid metaheuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 583-621, December.
    3. Louis de Grange & Juan Carlos Muñoz, 2007. "An equivalent optimization formulation for the traffic assignment problem with asymmetric linear costs," Transportation Planning and Technology, Taylor & Francis Journals, vol. 32(1), pages 1-25, March.
    4. Andrew Ensor & Felipe Lillo, 2016. "Colored-Edge Graph Approach for the Modeling of Multimodal Transportation Systems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-21, February.
    5. Jayakrishnan, R. & Tsai, Wei T. & Prashker, Joseph N. & Rajadhyaksha, Subodh, 1994. "A Faster Path-Based Algorithm for Traffic Assignment," University of California Transportation Center, Working Papers qt2hf4541x, University of California Transportation Center.
    6. Anna Nagurney & Patrizia Daniele & Ladimer S. Nagurney, 2020. "Refugee migration networks and regulations: a multiclass, multipath variational inequality framework," Journal of Global Optimization, Springer, vol. 78(3), pages 627-649, November.
    7. Liu, Tian-Liang & Huang, Hai-Jun & Yang, Hai & Zhang, Xiaoning, 2009. "Continuum modeling of park-and-ride services in a linear monocentric city with deterministic mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 692-707, July.
    8. Chen, Yuh-Wen & Tzeng, Gwo-Hshiung, 2001. "Using fuzzy integral for evaluating subjectively perceived travel costs in a traffic assignment model," European Journal of Operational Research, Elsevier, vol. 130(3), pages 653-664, May.
    9. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    10. Walter C. Labys & Chin-wei Yang, 1991. "Advances in the Spatial Equilibrium Modeling of Mineral and Energy Issues," International Regional Science Review, , vol. 14(1), pages 61-94, April.
    11. Meneguzzer, Claudio, 1995. "An equilibrium route choice model with explicit treatment of the effect of intersections," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 329-356, October.
    12. Cantarella, Giulio Erberto & Cartenì, Armando & de Luca, Stefano, 2015. "Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues," European Journal of Operational Research, Elsevier, vol. 241(2), pages 330-347.
    13. D. Zhang & A. Nagurney, 1997. "Formulation, Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 417-444, May.
    14. Xiang Zhang & David Rey & S. Travis Waller & Nathan Chen, 2019. "Range-Constrained Traffic Assignment with Multi-Modal Recharge for Electric Vehicles," Networks and Spatial Economics, Springer, vol. 19(2), pages 633-668, June.
    15. Tao Zhang & Yang Yang & Gang Cheng & Minjie Jin, 2020. "A Practical Traffic Assignment Model for Multimodal Transport System Considering Low-Mobility Groups," Mathematics, MDPI, vol. 8(3), pages 1-19, March.

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