Solving stochastic transportation network protection problems using the progressive hedging-based method

Networks and Spatial Economics

Volumn 10, Issue 2, 2010, Pages 193-208

  Fan, Yueyue ^a   Liu, Changzheng ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Decomposition method; Disaster mitigation; Equilibrium constraints; Networks; Stochastic programming

Indexed keywords

COMPLEMENTARY CONSTRAINTS; DECOMPOSITION METHODS; DISASTER MITIGATION; EQUILIBRIUM CONSTRAINT; STOCHASTIC NETWORK OPTIMIZATIONS; STOCHASTIC TRANSPORTATION; TRANSPORTATION NETWORK; TWO-STAGE STOCHASTIC PROGRAMMING;

NETWORKS (CIRCUITS); STOCHASTIC PROGRAMMING; STOCHASTIC SYSTEMS;

DISASTERS;

EID: 77955049199     PISSN: 1566113X     EISSN: 15729427     Source Type: Journal    
DOI: 10.1007/s11067-008-9062-y     Document Type: Article

References (28)

1. Ban J, Liu H, Ferris MC, Ran B (2006) A general MPCC model and its solution algorithm for continuous network design problem. Math Comput Model 43: 493-505.
2. Bell M, Iida Y (1997) Transportation network analysis. Wiley, Hoboken.
3. Cho S, Fan Y, Moore J (2003) Modeling transportation network flows as a simultaneous function of travel demand, network damage, and network level of service. Proceedings of the ASCE Technical Council on Lifeline Earthquake Engineering (TCLEE) Sixth U. S. Conference and Workshop on Lifeline Earthquake Engineering, August 10-13, 2003, Long Beach, CA, pp 868-877.
4. Dafermos S, Nagurney A (1984) On some traffic equilibrium theory paradoxes. Transp Res B 18: 101-110.
5. Dantzig GB (1955) Linear programming under uncertainty. Manage Sci 1: 197-206.
6. Ferris MC et al (2002) Mathematical programs with equilibrium constraints: automatic reformulation and solution via constrained optimization. Oxford University Computing Laboratory. http://citeseer. ist. psu. edu/633625. html.
7. Hagstrom JN, Abram RA (2001) Characterizing Braess's Paradox for traffic networks, 2001 IEEE Intelligent Transportation Systems Conference Proceedings, Oakland, California. IEEE, Los Alamitos August.
8. Harker TL, Friesz TL (1984) Bounding the solution of the continuous equilibrium network design problem, Proceedings of the Ninth International Symposium on Transportation and Traffic Theory, Netherlands.
9. Jonsbraten TW, Wets RJ-B, Woodruff DL (1997) A class of stochastic programs with decision dependent random elements, Technical Report. University of California Davis, Davis August.
10. Leblanc LJ, Morlok EK, Pierskalla WP (1975) An efficient approach to solving the road network equilibrium traffic assignment problem. Transp Res 9: 309-318 Data available at http://www. bgu. ac. il/~bargera/tntp/.
11. Liu CZ, Fan YY (2007) A two-stage stochastic programming model for transportation network protection, Proceedings of Transportation Research Board Annual Meeting. TRB, Washington, D. C.
12. Lokketangen A, Woodruff D (1996) Progressive hedging and tabu search applied to mixed integer (0, 1) multi-stage stochastic programming. J Heuristics 2: 111-128.
13. Luo ZQ, Pang JS, Ralph D (1996) Mathematical programs with equilibrium constraints. Cambridge University Press, Cambridge, UK.
14. Magnanti TL, Wong RT (1984) Network design and transportation planning: models and algorithms. Transp Sci 18: 1-55.
15. Marcotte P, Zhu DL (1996) Exact and inexact penalty methods for the generalized bilevel problem. Math Program 74: 141-157.
16. Mulvey JM, Vladimirou H (1991) Applying the progressive hedging algorithm to stochastic generalized networks. Ann Oper Res 31: 399-424.
17. Mulvey JM, Vladimirou H (1992) Stochastic network programming for financial planning problems. Manage Sci 38(11): 1642-1664.
18. Patil G, Ukkusuri S (2007) Stochastic system optimal network design problem. Proceedings of Transportation Research Board Annual Meeting. TRB, Washington, D. C.
19. Patriksson M, Rockafellar RT (2002) A mathematical model and descent algorithm for bilevel traffic management. Transp Sci 36: 271-291.
20. Ralph D, Wright SJ (2004) Some properties of regularization and penalization schemes for MPECs. Optim Methods Softw 19: 527-556.
21. Rockafellar RT, Wets RJ-B (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16: 119-147.
22. Ruszczynski A (1997) Decomposition methods in stochastic programming. Math Program 79: 333-353.
23. van Slyke RM, Wets RJB (1969) L-shaped programs with applications to optimal control and stochastic linear programming. SIAM J Appl Math 17: 638-663.
24. Viswanath K, Peeta S, Salman FS (2004) Investing in the links of stochastic network to minimize expected shortest path length, working paper. Purdue University, Lafayette.
25. Wets RJB (1966) Programming under uncertainty: The equivalent convex program. SIAM J Appl Math 14(1): 89-105.
26. Wets RJB (1974) Stochastic programs with fixed recourse: the equivalent deterministic program. SIAM Rev 16: 309-339.
27. Woodruff D (2003) Network interdiction and stochastic programming. Kluwer Academic, New York.
28. Yang H, Bell MGH (1998) Models and algorithms for road network design: a review and some new developments. Transp Rev 18: 257-278.