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Network Optimization with Continuous Control Parameters

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  • Patrice Marcotte

    (Université de Montréal, Montréal, Quebec)

Abstract

In this paper we consider two network optimization problems which have the following characteristics: control parameters vary continuously and network users behave according to War-drop's first principle of traffic equilibrium (“user-optimization”). For each problem, we study an exact algorithm based on constraint accumulation and a heuristic algorithm previously proposed in the literature.

Suggested Citation

  • Patrice Marcotte, 1983. "Network Optimization with Continuous Control Parameters," Transportation Science, INFORMS, vol. 17(2), pages 181-197, May.
    • Handle: RePEc:inm:ortrsc:v:17:y:1983:i:2:p:181-197
    DOI: 10.1287/trsc.17.2.181
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    Cited by:

    1. Enrique Fernández L., J. & de Cea Ch., Joaquin & Malbran, R. Henry, 2008. "Demand responsive urban public transport system design: Methodology and application," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(7), pages 951-972, August.
    2. Li, Changmin & Yang, Hai & Zhu, Daoli & Meng, Qiang, 2012. "A global optimization method for continuous network design problems," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1144-1158.
    3. Meng, Qiang & Yang, Hai, 2002. "Benefit distribution and equity in road network design," Transportation Research Part B: Methodological, Elsevier, vol. 36(1), pages 19-35, January.
    4. 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.
    5. Gallo, Mariano & D'Acierno, Luca & Montella, Bruno, 2010. "A meta-heuristic approach for solving the Urban Network Design Problem," European Journal of Operational Research, Elsevier, vol. 201(1), pages 144-157, February.
    6. D’Acierno, Luca & Gallo, Mariano & Montella, Bruno, 2012. "An Ant Colony Optimisation algorithm for solving the asymmetric traffic assignment problem," European Journal of Operational Research, Elsevier, vol. 217(2), pages 459-469.
    7. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    8. Chu, James C. & Korsesthakarn, Kanticha & Hsu, Yu-Ting & Wu, Hua-Yen, 2019. "Models and a solution algorithm for planning transfer synchronization of bus timetables," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 247-266.
    9. Garcia-Rodenas, Ricardo & Verastegui-Rayo, Doroteo, 2008. "A column generation algorithm for the estimation of origin-destination matrices in congested traffic networks," European Journal of Operational Research, Elsevier, vol. 184(3), pages 860-878, February.
    10. Cipriani, Ernesto & Fusco, Gaetano, 2004. "Combined signal setting design and traffic assignment problem," European Journal of Operational Research, Elsevier, vol. 155(3), pages 569-583, June.
    11. Yang, Hai & Bell, Michael G. H., 2001. "Transport bilevel programming problems: recent methodological advances," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 1-4, January.
    12. Evers, Ruth & Proost, Stef, 2015. "Optimizing intersections," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 100-119.
    13. Chiou, Suh-Wen, 2005. "Bilevel programming for the continuous transport network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(4), pages 361-383, May.
    14. Meng, Q. & Yang, H. & Bell, M. G. H., 2001. "An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 83-105, January.
    15. 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.
    16. Mishra, Savita, 2007. "Weighting method for bi-level linear fractional programming problems," European Journal of Operational Research, Elsevier, vol. 183(1), pages 296-302, November.
    17. Mathur, Kanchan & Puri, M. C., 1995. "A bilevel bottleneck programming problem," European Journal of Operational Research, Elsevier, vol. 86(2), pages 337-344, October.
    18. Guo, Jianhua & Kong, Ye & Li, Zongzhi & Huang, Wei & Cao, Jinde & Wei, Yun, 2019. "A model and genetic algorithm for area-wide intersection signal optimization under user equilibrium traffic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 92-104.
    19. Zvi Drezner & Said Salhi, 2002. "Using hybrid metaheuristics for the one‐way and two‐way network design problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(5), pages 449-463, August.
    20. Andrew Koh & Simon Shepherd & Agachai Sumalee, 2009. "Second best toll and capacity optimisation in networks: solution algorithm and policy implications," Transportation, Springer, vol. 36(2), pages 147-165, March.

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