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Global optimization method for network design problem with stochastic user equilibrium

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  • Liu, Haoxiang
  • Wang, David Z.W.

Abstract

In this paper, we consider the continuous road network design problem with stochastic user equilibrium constraint that aims to optimize the network performance via road capacity expansion. The network flow pattern is subject to stochastic user equilibrium, specifically, the logit route choice model. The resulting formulation, a nonlinear nonconvex programming problem, is firstly transformed into a nonlinear program with only logarithmic functions as nonlinear terms, for which a tight linear programming relaxation is derived by using an outer-approximation technique. The linear programming relaxation is then embedded within a global optimization solution algorithm based on range reduction technique, and the proposed approach is proved to converge to a global optimum.

Suggested Citation

  • Liu, Haoxiang & Wang, David Z.W., 2015. "Global optimization method for network design problem with stochastic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 20-39.
    • Handle: RePEc:eee:transb:v:72:y:2015:i:c:p:20-39
    DOI: 10.1016/j.trb.2014.10.009
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    1. Luathep, Paramet & Sumalee, Agachai & Lam, William H.K. & Li, Zhi-Chun & Lo, Hong K., 2011. "Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 808-827, June.
    2. Wang, Shuaian & Meng, Qiang & Yang, Hai, 2013. "Global optimization methods for the discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 42-60.
    3. Yang, Hai & Yagar, Sam, 1995. "Traffic assignment and signal control in saturated road networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 125-139, March.
    4. Han-Lin Li & Hao-Chun Lu, 2009. "Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables," Operations Research, INFORMS, vol. 57(3), pages 701-713, June.
    5. 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.
    6. Juan Pablo Vielma & Shabbir Ahmed & George Nemhauser, 2010. "Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions," Operations Research, INFORMS, vol. 58(2), pages 303-315, April.
    7. 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.
    8. Davis, Gary A., 1994. "Exact local solution of the continuous network design problem via stochastic user equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 28(1), pages 61-75, February.
    9. Larry J. Leblanc, 1975. "An Algorithm for the Discrete Network Design Problem," Transportation Science, INFORMS, vol. 9(3), pages 183-199, August.
    10. Chaisak Suwansirikul & Terry L. Friesz & Roger L. Tobin, 1987. "Equilibrium Decomposed Optimization: A Heuristic for the Continuous Equilibrium Network Design Problem," Transportation Science, INFORMS, vol. 21(4), pages 254-263, November.
    11. 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.
    12. Terry L. Friesz & Hsun-Jung Cho & Nihal J. Mehta & Roger L. Tobin & G. Anandalingam, 1992. "A Simulated Annealing Approach to the Network Design Problem with Variational Inequality Constraints," Transportation Science, INFORMS, vol. 26(1), pages 18-26, February.
    13. Fontaine, Pirmin & Minner, Stefan, 2014. "Benders Decomposition for Discrete–Continuous Linear Bilevel Problems with application to traffic network design," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 163-172.
    14. Kang, Jee Eun & Chow, Joseph Y.J. & Recker, Will W., 2013. "On activity-based network design problems," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 398-418.
    15. Wang, David Z.W. & Lo, Hong K., 2010. "Global optimum of the linearized network design problem with equilibrium flows," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 482-492, May.
    16. Abdulaal, Mustafa & LeBlanc, Larry J., 1979. "Continuous equilibrium network design models," Transportation Research Part B: Methodological, Elsevier, vol. 13(1), pages 19-32, March.
    17. 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.
    18. Yang, Hai, 1997. "Sensitivity analysis for the elastic-demand network equilibrium problem with applications," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 55-70, February.
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