A modified gradient projection algorithm for solving the elastic demand traffic assignment problem

• Adapt GP algorithm for solving elastic demand traffic assignment.
• Make use of excess-demand reformulation and network representation.
• Demonstrate efficiency with real transportation networks.
• Conduct sensitivity analysis on scaling parameter to examine computational efforts.
• Show modified GP is as efficient as original GP for fixed demand.

This paper develops a path-based traffic assignment algorithm for solving the elastic demand traffic assignment problem (EDTAP). A modified path-based gradient projection (GP) method combined with a column generation is suggested for solving the equivalent excess-demand reformulation of the problem in which the elastic demand problem is reformulated as a fixed demand problem through an appropriate modification of network representation. Numerical results using a set of real transportation networks are provided to demonstrate the efficiency of the modified GP algorithm for solving the excess-demand formulation of the EDTAP. In addition, a sensitivity analysis is conducted to examine the effects of the scaling parameter used in the elastic demand function on the estimated total demand, number of generated paths, number of used paths, and computational efforts of the modified GP algorithm.