A path-based gradient projection algorithm for the cost-based system optimum problem in networks with continuously distributed value of time

The cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form,which cannot be solved by the frank-wolfe algorithm. in light of magnitude improvement in the availability of computer memory in recent years,path-based algorithms have been regarded as a viable approach for traffic assignment problems with reasonably large network sizes. we develop a path-based gradient projection algorithm for solving the cost-based system optimum model,based on goldstein-levitin-polyak method which has been successfully applied to solve standard user equilibrium and system optimum problems. the sioux falls network tested is used to verify the effectiveness of the algorithm. © 2014 wen-xiang wu and hai-jun huang.