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The equivalence of transfer and generalized benders decomposition methods for traffic assignment

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  • Barton, Russell R.
  • Hearn, Donald W.
  • Lawphongpanich, Siriphong

Abstract

In prior work we have given an intuitive development of Transfer Decomposition, a decomposition of the traffic assignment problem into two traffic assignment problems. The intent of this paper is to provide a rigorous basis for this technique by establishing that it is a generalized Benders decomposition. As an illustration of the result, we give a decomposition algorithm that is based on the familiar Frank-Wolfe method.

Suggested Citation

  • Barton, Russell R. & Hearn, Donald W. & Lawphongpanich, Siriphong, 1989. "The equivalence of transfer and generalized benders decomposition methods for traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 23(1), pages 61-73, February.
    • Handle: RePEc:eee:transb:v:23:y:1989:i:1:p:61-73
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    Cited by:

    1. Jafari, Ehsan & Pandey, Venktesh & Boyles, Stephen D., 2017. "A decomposition approach to the static traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 270-296.
    2. 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.
    3. J. Fuller & William Chung, 2005. "Dantzig—Wolfe Decomposition of Variational Inequalities," Computational Economics, Springer;Society for Computational Economics, vol. 25(4), pages 303-326, June.
    4. W. Chung & J. Fuller & Y. Wu, 2003. "A New Demand-Supply Decomposition Method for a Class of Economic Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 231-243, June.
    5. Shen, Siqian & Chen, Zhihao, 2013. "Optimization models for differentiating quality of service levels in probabilistic network capacity design problems," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 71-91.
    6. Fuller, J. David & Chung, William, 2008. "Benders decomposition for a class of variational inequalities," European Journal of Operational Research, Elsevier, vol. 185(1), pages 76-91, February.
    7. William Chung & J. D. Fuller & Y. June Wu, 2006. "A New Decomposition Method for Multiregional Economic Equilibrium Models," Operations Research, INFORMS, vol. 54(4), pages 643-655, August.
    8. Xin, Yong-Lin & Sun, Qing-Han & Zhao, Tian & Li, Xia & Chen, Qun, 2023. "A categorized and decomposed algorithm for thermal system simulation based on generalized benders decomposition," Energy, Elsevier, vol. 282(C).

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