Solving the Pareto-improving toll problem via manifold suboptimization

Transportation Research Part C: Emerging Technologies

Volumn 18, Issue 2, 2010, Pages 234-246

  Lawphongpanich, Siriphong ^a   Yin, Yafeng ^a  

^a University of Florida   (United States)

Author keywords

Complementarity; Congestion pricing; Manifold suboptimization; Pareto improvement; Traffic assignment

Indexed keywords

TRANSPORTATION;

COMPLEMENTARITY; CONGESTION PRICING; MANIFOLD SUBOPTIMIZATION; PARETO IMPROVEMENTS; TRAFFIC ASSIGNMENT;

TRAFFIC CONGESTION;

ALGORITHM; NUMERICAL MODEL; OPTIMIZATION; ROAD PRICING; TRAFFIC CONGESTION;

EID: 75449095252     PISSN: 0968090X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trc.2009.08.006     Document Type: Article

References (49)

1. Ahuja R.K., Magananti T.L., and Orlin J.B. Network Flows: Theory, Algorithms, and Applications (1993), Prentice Hall, Englewood Cliffs, NJ
2. Akiyama T., Mun S.-.I., and Okumshima M. Second-best congestion pricing in urban space. Cordon pricing and its alternatives. Review of Network Economics 3 4 (2004) 401-414
3. Bai L., Hearn D.W., and Lawphongpanich S. Decomposition techniques for the minimum toll revenue problem. Networks 14 2 (2004) 142-150
4. Bard J.F. Practical Bilevel Optimization: Algorithms and Applications (1998), Kluwer Academic Publishers, Dordrecht, The Netherlands
5. Bertsekas D.P. Nonlinear Programming (1995), Athena Scientific, Belmont, MA
6. Brooke, A., Kendrick, D., Meeraus, A., Raman, R., 2003. GAMS: A User's Guide, GAMS Development Corporation, Washington, DC.
7. Chen Y., and Florian M. The nonlinear bi-level programming problem: formulations, regularity and optimality conditions. Optimization 32 (1995) 183-209
8. Daganzo C.F., and Garcia R.C. A Pareto improving strategy for the time-dependent morning commute problem. Transportation Science 34 (2000) 303-311
9. Daganzo C.F. A Pareto optimum congestion reduction scheme. Transportation Research Part B 29 (1995) 139-154
10. Dial R. Minimum revenue congestion pricing part I: a fast algorithm for the single-origin case. Transportation Research Part B 33 3 (1999) 189-202
11. Dial R. Minimum revenue congestion pricing part I: a fast algorithm for the general case. Transportation Research Part B 34 8 (2000) 645-665
12. Drud, A.S., 1995. A System for Large Scale Nonlinear Optimization, Tutorial for CONOPT Subroutine Library, ARKI Consulting and Development A/S, Bagsvaerd, Denmark.
13. Facchinei F., and Pang J.-S. Finite-Dimensional Variational Inequalities and Complementarity Problems vol. I (2003), Springer, New York, NY
14. Ferrari P. Road network toll pricing and social welfare. Transportation Research B 36 5 (2002) 471-483
15. Fletcher R., and Leyffer S. Solving mathematical programs with complementarity constraints as nonlinear programs. Optimization Methods and Software 19 1 (2004) 15
16. Fletcher R., Leyffer S., Ralph D., and Scholtes S. Local convergence of SQP methods for mathematical programs with equilibrium constraints. SIAM Journal of Optimization 17 1 (2006) 259-286
17. Glazer A., and Niskanen E. When users of congested roads may view tolls as unjust. European Transport 31 (2005) 6-14
18. Hearn D.W., and Yildirim M.B. A toll pricing framework for traffic assignment problems with elastic demand. In: Gendreau M., and Marcotte P. (Eds). Current Trends in Transportation and Network Analysis: Miscellanea in Honor of Michael Florian (2001), Kluwer Academic Publishers, Dordrecht, The Netherlands
19. Hearn D.W., and Yildirim M.B. A first-best toll pricing framework for variable demand traffic assignment problems. Transportation Research Part B 39 (2005) 659-678
20. Hearn D.W., and Ramana M.V. Solving congestion toll pricing models. In: Marcotte P., and Nguyen S. (Eds). Equilibrium and Advanced Transportation Modeling (1998), Kluwer Academic Publishers, Nowell, MA 109-124
21. Hearn D.W., and Ribera J. Convergence of the Frank-Wolfe method for certain bounded variable traffic assignment problem. Transportation Research 15B (1981) 437-442
22. Larsson T., and Patriksson M. Side constrained traffic equilibrium models-traffic management through link tolls. In: Marcotte P., and Nguyen S. (Eds). Equilibrium and Advanced Transportation Modelling (1998), Kluwer Academic Publishers, New York 125-151
23. Lawphongpanich S., and Hearn D.W. An MPEC approach to second-best toll pricing. Mathematical Programming, Series B 101 (2004) 33-55
24. Lawphongpanich, S., Yin, Y., 2007. Pareto-improving congestion pricing for general road networks. In: Technical Report, Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, 32611-6595.
25. LeBlanc L.J., Morlok E.K., and Pierskalla W.P. An accurate and efficient approach to equilibrium traffic assignment on congested networks. Transportation Research Record 491, Interactive Graphics and Systems Planning (1974) 12-33
26. Lim, A., 2002. Transportation Network Design Problems: An MPEC Approach, Ph.D. Dissertation, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland.
27. Lindsey R., and Verhoef E. Traffic congestion and congestion pricing. In: Button B.J., and Hensher D.A. (Eds). Handbook of Transport Systems and Traffic Control (2001), Pergamon 77-105
28. Liu, Y., Guo, X., Yang, H., in press. Pareto-improving and revenue-neutral congestion pricing schemes in two-mode traffic networks. Netnomics. doi:10.1007/s11066-008-9018-x.
29. Luo Z.-.Q., Pang J.-.S., and Ralph D. Mathematical Programs with Equilibrium Constraints (1996), Cambridge University Press, New York
30. Maruyama T., and Harata N. Difference between area-based and cordon-based congestion pricing: investigation by trip-chain-based network equilibrium model with non-additive path costs. Transportation Research Record 1964 (2006) 1-8
31. Maruyama T., and Sumalee A. Efficiency and equity comparison of cordon- and area-based road pricing schemes using a trip-chain equilibrium model. Transportation Research Part A 41 (2007) 655-671
32. May, A., Sumalee, A., 2003. One step forward, two step back? An overview of roading pricing application and research outside the United States. In: International Perspectives on Road Pricing, Conference Proceeding 34, Transportation Research Board, Washington, DC, pp. 73-91.
33. Nguyen S., and Dupuis C. An efficient method for computing traffic equilibria in a network with asymmetric transportation costs. Transportation Science 18 (1984) 185-202
34. Outrata J.V., Kocvara M., and Zowe J. Nonsmooth Approach to Optimization Problems with Equilibrium Constraints (1998), Kluwer Academic Publishers, Dordrecht, The Netherlands
35. Patriksson M., and Rockafellar R.T. A mathematical model and descent algorithm for bilevel traffic management. Transportation Science 36 3 (2002) 271-291
36. Pigou A.C. The Economics of Welfare (1920), Macmillan, New York
37. Rosen J.B. An automatic method for finding the greatest or least value of a functions. Computer Journal 3 (1960) 175-184
38. Scheel H., and Scholtes S. Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Mathematics of Operations Research 25 (2000) 1-22
39. Shimizu K., Ishizuka Y., and Bard J.F. Nondifferentiable and Two-Level Mathematical Programming (1997), Kluwer Academic Publishers, Boston
40. Song Z., Yin Y., and Lawphongpanich S. Nonnegative Pareto-improving tolls with multiclass network equilibria. Transportation Research Record 2091 (2009) 70-78
41. Stockholmsförsöket, 2006. Referendum on the Implementation of Congestion Charges in the City of Stockholm. .
42. Sumalee A. Optimal road user charging cordon design: a heuristic optimization approach. Computer-Aided Civil and Infrastructure Engineering 19 (2004) 377-392
43. Ubbels B., and Verhoef E. Acceptability in road pricing and revenue use in the Netherlands. European Transport 32 (2006) 69-94
44. Verhoef E.T. Second-best congestion pricing in general networks: algorithms for finding second-best optimal toll levels and toll points. Transportation Research B 36 8 (2002) 707-729
45. Wu, D., Yin, Y., Lawphongpanich, S., 2009. Pareto-improving congestion pricing on multimodal transportation networks. Working Paper, Department of Civil and Coastal Engineering, University of Florida.
46. Yang, H., Guo, X., 2005. Pareto-improving congestion pricing and revenue refunding schemes in traffic networks. Working Paper, WP-HKUST-YH-2005-08-04, Hong Kong University of Science and Technology.
47. Yang H., and Lam W.H.K. Optimal road tolls under conditions of queuing and congestion. Transportation Research Part A: Policy and Practice 30 5 (1996) 319-332
48. Zangwill W.I. Nonlinear Programming: A Unified Approach (1969), Prentice Hall, Englewood Cliffs, NJ
49. Zhang X., and Yang H. The optimal cordon-based network congestion pricing problem. Transportation Research Part B 38 (2004) 517-537