Abstract
In this paper we develop an algorithm for solving a version of the (static) traffic equilibrium problem in which the cost incurred on each path is not simply the sum of the costs on the arcs that constitute that path. The method we describe is based on the recent NE/SQP algorithm, a fast and robust technique for solving nonlinear complementarity problems. Finally, we present an example that illustrates both the importance of using nonadditive costs and the effectiveness of the NE/SQP method.
While Dr. Gabriel was a member of the the Mathematics and Computer Science Division of Argonne National Laboratory (ANL), this work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H.Z. Aashtiani, The Multi-Model Assignment Problem, Ph.D. Thesis, Sloan School of Management, Massachusetts Institute of Technology (1979)
H.Z. Aashtiani and T. Magnanti, “Equilibria on a Congested Transportation Network,” SIAM Journal on Algebraic and Discrete Methods 2 (1981) 213–226
D. Bernstein and T.E. Smith, “Network Equilibria with Lower Semicontinuous Costs: With an Application to Congestion Pricing,” Transportation Science 28 (1984) 221–235
D.P. Bertsekas and E.M. Gafni, “Projection Methods for Variational Inequalities with Applications to the Traffic Assignment Problem,” Mathematical Programming Study 17 (1982) 139–159
R.W. Cottle, J.S. Pang, and R. E. Stone, The Linear Complementarity Problem, Academic Press, Inc., Boston (1992)
M. Florian and H. Spiess, “The Convergence of Diagonalization Algorithms for Network Equilibrium Problems,” Transportation Research B 16B (1982) 447–483
M. Frank and P. Wolfe, “An Algorithm for Quadratic Programming,” Naval Research Logistics Quarterly 3 (1956) 95–110
S.A. Gabriel and D.H. Bernstein, “The Traffic Equilibrium Problem with Non-additive Path Costs,” Transportation Science, (1996), forthcoming
S.A. Gabriel and J.S. Pang, “An Inexact NE/SQP Method for Solving the Nonlinear Complementarity Problem,” Computational Optimization and Applications 1 (1992) 67–91
T. Larsson, and M. Patricksson, “Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem,” Transportation Science 26 (1992) 4–17
S. Lawphonpanich and D.W. Hearn, “Simplicial Decomposition of the Asymmetric Traffic Assignment Problem,” Transportation Research B 18B (1984) 123–133
L.J. LeBlanc, E.K. Morlok, and W. Pierskalla, “An Efficient Approach to Solving the Road Network Equilibrium Traffic Assignment Problem,” Transportation Research 9 (1975) 309–318
T. Leventhal, G. Nemhauser and L. Trotter, Jr., “A Column Generation Algorithm for Optimal Traffic Assignment,” Transportation Science 7 (1973) 168–176
P. Marcotte and J. Guélat, “Adaptation of a Modified Newton Method for Solving the Asymmetric Traffic Equilibrium Problem,” Transportation Science 22 (1988) 112–124
A. Nagurney, “Comparative Tests of Multimodal Traffic Equilibrium Methods,” Transportation Research B 18B (1984) 469–485
S. Nguyen, “A Unified Approach to Equilibrium methods for Traffic Assignment,” in M. Florian (ed.) Traffic Equilibrium Methods, Springer-Verlag (1974)
J. S. Pang and S. A. Gabriel, “NE/SQP: A Robust Algorithm for the Nonlinear Complementarity Problem,” Mathematical Programming 60 (1993) 295–337
J. S. Pang and C. S. Yu, “Linearized Simplicial Decomposition Methods for Computing Traffic Equlibria on Networks,” Networks 14 (1984) 427–438
M.J. Smith, “The existence and calculation of traffic equilibria,” Transportation Research B 17B (1983) 291–303
M. J. Smith, “An Algorithm for Solving Asymmetric Equilibrium Problems with a Continuous Cost-Flow Function,” Transportation Research B 17B (1983) 365–371
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bernstein, D., Gabriel, S.A. (1997). Solving the Nonadditive Traffic Equilibrium Problem. In: Pardalos, P.M., Hearn, D.W., Hager, W.W. (eds) Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59179-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-59179-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62541-4
Online ISBN: 978-3-642-59179-2
eBook Packages: Springer Book Archive