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A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem

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  • Hamid Farvaresh
  • Mohammad Sepehri

Abstract

Discrete network design problem (DNDP) is generally formulated as a bi-level programming. Because of non-convexity of bi-level formulation of DNDP which stems from the equilibrium conditions, finding global optimal solutions are very demanding. In this paper, a new branch and bound algorithm being able to find exact solution of the problem is presented. A lower bound for the upper-level objective and its computation method are developed. Numerical experiments show that our algorithm is superior to previous algorithms in terms of both computation time and solution quality. The conducted experiments indicate that in most cases the first incumbent solution which is obtained within a few seconds is superior to the final solution of some of previous algorithms. Copyright Springer Science+Business Media, LLC 2013

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  • Hamid Farvaresh & Mohammad Sepehri, 2013. "A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem," Networks and Spatial Economics, Springer, vol. 13(1), pages 67-106, March.
  • Handle: RePEc:kap:netspa:v:13:y:2013:i:1:p:67-106
    DOI: 10.1007/s11067-012-9173-3
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    1. Dung-Ying Lin & Ampol Karoonsoontawong & S. Waller, 2011. "A Dantzig-Wolfe Decomposition Based Heuristic Scheme for Bi-level Dynamic Network Design Problem," Networks and Spatial Economics, Springer, vol. 11(1), pages 101-126, March.
    2. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    3. Karakostas, George & Kim, Taeyon & Viglas, Anastasios & Xia, Hao, 2011. "On the degradation of performance for traffic networks with oblivious users," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 364-371, February.
    4. Hossain Poorzahedy & Farhad Abulghasemi, 2005. "Application of Ant System to network design problem," Transportation, Springer, vol. 32(3), pages 251-273, May.
    5. Byung Kim & Wonkyu Kim, 2006. "An equilibrium network design model with a social cost function for multimodal networks," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 40(3), pages 473-491, August.
    6. Kaj Holmberg & Johan Hellstrand, 1998. "Solving the Uncapacitated Network Design Problem by a Lagrangean Heuristic and Branch-and-Bound," Operations Research, INFORMS, vol. 46(2), pages 247-259, April.
    7. Gao, Ziyou & Wu, Jianjun & Sun, Huijun, 2005. "Solution algorithm for the bi-level discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(6), pages 479-495, July.
    8. LeBlanc, Larry J. & Boyce, David E., 1986. "A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows," Transportation Research Part B: Methodological, Elsevier, vol. 20(3), pages 259-265, June.
    9. Nie, Yu (Marco), 2010. "A class of bush-based algorithms for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 73-89, January.
    10. Poorzahedy, Hossain & Turnquist, Mark A., 1982. "Approximate algorithms for the discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 16(1), pages 45-55, February.
    11. 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.
    12. Lihui Zhang & Siriphong Lawphongpanich & Yafeng Yin, 2009. "An Active-set Algorithm for Discrete Network Design Problems," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 283-300, Springer.
    13. D E Boyce & A Farhi & R Weischedel, 1973. "Optimal Network Problem: A Branch-and-Bound Algorithm," Environment and Planning A, , vol. 5(4), pages 519-533, August.
    14. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    15. 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.
    16. Larry J. Leblanc, 1975. "An Algorithm for the Discrete Network Design Problem," Transportation Science, INFORMS, vol. 9(3), pages 183-199, August.
    17. 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.
    18. Farvaresh, Hamid & Sepehri, Mohammad Mehdi, 2011. "A single-level mixed integer linear formulation for a bi-level discrete network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 623-640, September.
    19. Byung Chung & Tao Yao & Chi Xie & Andreas Thorsen, 2011. "Robust Optimization Model for a Dynamic Network Design Problem Under Demand Uncertainty," Networks and Spatial Economics, Springer, vol. 11(2), pages 371-389, June.
    20. Poorzahedy, Hossain & Rouhani, Omid M., 2007. "Hybrid meta-heuristic algorithms for solving network design problem," European Journal of Operational Research, Elsevier, vol. 182(2), pages 578-596, October.
    21. 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.
    22. Dantzig, George B. & Harvey, Roy P. & Lansdowne, Zachary F. & Robinson, David W. & Maier, Steven F., 1979. "Formulating and solving the network design problem by decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 13(1), pages 5-17, March.
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