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Cone projection versus half-space projection for the bilevel optimisation of transportation networks

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  • Clegg, J.
  • Smith, M. J.

Abstract

This paper describes the half-space projection method and cone-projection methods of optimising an urban transportation model. The paper then compares these two methods as applied to seek optimal capacity changes within a very simple example network model. The optimisation has, in each of the cases, a bilevel character since it is performed on two functions; the equilibrium function E (which must have value zero for equilibrium) and the objective function Z which is minimised subject to the constraint that E is zero. Thus E=0 (or 'small') always has priority.

Suggested Citation

  • Clegg, J. & Smith, M. J., 2001. "Cone projection versus half-space projection for the bilevel optimisation of transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 71-82, January.
    • Handle: RePEc:eee:transb:v:35:y:2001:i:1:p:71-82
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    References listed on IDEAS

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    1. Marcotte, Patrice, 1988. "A note on a bilevel programming algorithm by Leblanc and Boyce," Transportation Research Part B: Methodological, Elsevier, vol. 22(3), pages 233-236, June.
    2. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
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    Cited by:

    1. Shen, Yueqing & Qian, Tong & Li, Weiwei & Zhao, Wei & Tang, Wenhu & Chen, Xingyu & Yu, Zeyuan, 2023. "Mobile energy storage systems with spatial–temporal flexibility for post-disaster recovery of power distribution systems: A bilevel optimization approach," Energy, Elsevier, vol. 282(C).
    2. Takebayashi, Mikio, 2021. "Workability of a multiple-gateway airport system with a high-speed rail network," Transport Policy, Elsevier, vol. 107(C), pages 61-71.
    3. Cohen, Guy & Quadrat, Jean-Pierre & Wynter, Laura, 2002. "On the convergence of the algorithm for bilevel programming problems by Clegg and Smith," Transportation Research Part B: Methodological, Elsevier, vol. 36(10), pages 939-944, December.
    4. Takebayashi, Mikio & Yamaguchi, Hiromichi, 2022. "Managing a multiple-gateway airport system with super high-speed rail," Journal of Air Transport Management, Elsevier, vol. 99(C).

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