Efficient Computation of User Optimal Traffic Assignment via Second-Order Cone and Linear Programming Techniques

Static traffic assignment aims to disclose the spatial distribution of vehicular flow over a transportation network subject to given traffic demands, and plays an essential role in transportation engineering. User-optimal pattern adheres the individual rationality of motorists, in which everyone chooses a route that minimizes his own travel cost, while considering congestion effects influenced by the aggregated movement of vehicles. User optimal traffic assignment, which is also known as the user equilibrium, entails solving an optimization problem with a strictly convex objective function and linear constraints. However, the performances of general-purpose solvers are quite disappointing. This paper proposes two highly efficient computation models for the user equilibrium problem. The first one exploits the second-order cone reformulation of a convex power function, resulting in a second-order cone program, and no approximation is incurred. The second one approximates the convex objective function using a piece-wise linear function, and comes down to a linear program. An adaptive path generation oracle is devised in order to circumvent path enumeration in problem setup. Case studies demonstrate that the proposed method can deal with large-scale transportation systems, and outperforms the most popular iterative algorithm in the literature.