A sensitivity analysis–based heuristic is proposed for application to solving the continuous equilibrium network design problem. The heuristic uses a minimum distance approach to generate sensitivity information and release the nondegeneracy assumption. The trip maker’s behavior is then represented by a linear approximation of the reaction function that is generated from the sensitivity information. Two numerical examples are given.
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References
1.
DafermosS. C.Traffic Equilibrium and Variational Inequalities. Transportation Science, Vol. 14, 1980, pp. 42–54.
2.
SmithM. J.The Existence, Uniqueness and Stability of Traffic Equilibria. Transportation Research, Vol. 13B, 1979, pp. 295–304.
3.
WardropJ. G.Some Theoretical Aspects of Road Traffic Research. Proc., Institute of Civil Engineers, Part 2, 1952, pp. 325–378.
4.
FrieszT. L., and HarkerP. T.. Properties of the Iterative Optimization Equilibrium Algorithm. Civil Engineering System, Vol. 2, 1985, pp. 142–154.
5.
TobinR. L.Sensitivity Analysis for Variational Inequalities. Journal of Optimization Theory and Applications, Vol. 48, 1986, pp. 191–204.
6.
TobinR. L., and FrieszT. L.. Sensitivity Analysis for Equilibrium Network Flow. Transportation Science, Vol. 22, No. 4, 1988, pp. 242–250.
7.
YangH., and YagarS.. Traffic Assignment and Traffic Control in General Freeway-Arterial Corridor Systems. Transportation Research, Vol. 28B, 1994, pp. 463–486.
8.
YangH., and YagarS.. Traffic Assignment and Signal Control in Saturated Road Networks. Transportation Research, Vol. 29A, 1995, pp. 125–139.
9.
YangH., and LamW. H. K.. Optimal Road Tolls Under Conditions of Queuing and Congestion. Transportation Research, Vol. 30A, 1996, pp. 319–332.
10.
ChoH.-J., and LeeJ.-H.. Solving Bilevel Network Design Problem Using Sensitivity Information Without Nondegeneracy Assumption. International Journal of Operations and Quantitative Management(forthcoming).
11.
ChoH.-J., SmithT., and FrieszT. L.. A Reduction Method for Local Sensitivity Analyses of Network Equilibrium Arc Flows. Transportation Research B (forthcoming).
12.
DafermosS. C., and NagurneyA.. On Some Traffic Equilibrium Theory Paradoxes. Transportation Research, Vol. 18B, 1984, pp. 101–110.
13.
ChoH.-J., and LoS.-C.. A Study of Estimating Nonnegative Path Flow by the Properties of Generalized Inverse Matrix. Journal of the Chinese Institute of Transportation(in Chinese) (forthcoming).
14.
AbdulaalM., and LeBlancL. J.. Continuous Equilibrium Network Design Models. Transportation Research, Vol. 13B, 1979, pp. 19–32.
15.
SteenbrinkP. A.Optimization of Transport Network. John Wiley and Sons, New York, 1974.
16.
SuwansirikulC., FreiszT. L., and TobinR. L.. Equilibrium Decomposed Optimization: A Heuristic for the Continuous Equilibrium Network Design Problem. Transportation Science, Vol. 21, 1987, pp. 254–263.
17.
HarkerP. T., and FrieszT. L.. Bounding the Solution of the Continuous Equilibrium Network Design Problem. Proc., 9th International Symposium on Transportation and Traffic Theory, VNU Science Press, Utrecht, the Netherlands, 1984, pp. 233–252.
18.
FrieszT. L., TobinR. L., ChoH.-J., and MehtaN.. Sensitivity Analysis Based Heuristic Algorithm for Mathematical Programs with Variational Inequality Constraints. Mathematical Programming, Vol. 48, 1990, pp. 265–284.
