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Efficient Algorithms for Solving Elastic Demand Traffic Assignment Problems and Mode Split-Assignment Problems

Author

Listed:
  • Larry J. LeBlanc

    (Vanderbilt University, Nashville, Tennessee)

  • Keyvan Farhangian

    (Southern Methodist University, Dallas, Texas)

Abstract

Different algorithms for solving elastic demand traffic assignment problems and mode split-assignment problems are discussed. We note that there are different ways to implement the Frank-Wolfe technique to solve these problems and give the most efficient implementation. We then discuss Evans' procedure and compare it with the Frank-Wolfe technique. Computational results indicate that the Frank-Wolfe algorithm is unstable for the elastic assignment problem---its rate of convergence is very sensitive to values used for upper bounds on trips, which are purely artificial “tuning parameters.” Evans' algorithm is found to be more robust and to converge consistently faster than the Frank-Wolfe technique for both classes of problems studied.

Suggested Citation

  • Larry J. LeBlanc & Keyvan Farhangian, 1981. "Efficient Algorithms for Solving Elastic Demand Traffic Assignment Problems and Mode Split-Assignment Problems," Transportation Science, INFORMS, vol. 15(4), pages 306-317, November.
    • Handle: RePEc:inm:ortrsc:v:15:y:1981:i:4:p:306-317
    DOI: 10.1287/trsc.15.4.306
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    Cited by:

    1. W Rothengatter, 1986. "Scheduling of Interstate Road and Railway Investments," Environment and Planning A, , vol. 18(4), pages 465-483, April.
    2. D E Boyce & K S Chon & Y J Lee & K T Lin & L J LeBlanc, 1983. "Implementation and Computational Issues for Combined Models of Location, Destination, Mode, and Route Choice," Environment and Planning A, , vol. 15(9), pages 1219-1230, September.
    3. Codina, Esteve & Barcelo, Jaume, 2004. "Adjustment of O-D trip matrices from observed volumes: An algorithmic approach based on conjugate directions," European Journal of Operational Research, Elsevier, vol. 155(3), pages 535-557, June.
    4. Kitthamkesorn, Songyot & Chen, Anthony, 2017. "Alternate weibit-based model for assessing green transport systems with combined mode and route travel choices," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 291-310.
    5. Lam, William H. K. & Tam, M. L., 1997. "Why standard modelling and evaluation procedures are inadequate for assessing traffic congestion measures," Transport Policy, Elsevier, vol. 4(4), pages 217-223, October.
    6. 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.
    7. Mori, Kentaro & Miwa, Tomio & Abe, Ryosuke & Morikawa, Takayuki, 2022. "Equilibrium analysis of trip demand for autonomous taxi services in Nagoya, Japan," Transportation Research Part A: Policy and Practice, Elsevier, vol. 166(C), pages 476-498.
    8. D E Boyce, 1984. "Urban Transportation Network-Equilibrium and Design Models: Recent Achievements and Future Prospects," Environment and Planning A, , vol. 16(11), pages 1445-1474, November.
    9. 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.
    10. David Boyce, 2007. "Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models," Networks and Spatial Economics, Springer, vol. 7(2), pages 99-128, June.
    11. Chen, Anthony & Choi, Keechoo, 2017. "Solving the combined modal split and traffic assignment problem with two types of transit impedance functionAuthor-Name: Ryu, Seungkyu," European Journal of Operational Research, Elsevier, vol. 257(3), pages 870-880.
    12. Jian Wang & Muqing Du & Lili Lu & Xiaozheng He, 2018. "Maximizing Network Throughput under Stochastic User Equilibrium with Elastic Demand," Networks and Spatial Economics, Springer, vol. 18(1), pages 115-143, March.
    13. Xu, Meng & Chen, Anthony & Gao, Ziyou, 2008. "An improved origin-based algorithm for solving the combined distribution and assignment problem," European Journal of Operational Research, Elsevier, vol. 188(2), pages 354-369, July.

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