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

Abstract

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.INDEX TERMS Linear program, second-order cone program, traffic assignment, user equilibrium.

Spatial and temporal modelling of coupled power and transportation systems: A comprehensive review

“…Detailed models can be found in [51, 52]. Both are optimization models that can be solved by either a numerical optimization method [53] or a metaheuristic algorithm [54]. In certain cases, the UE can also be extended to stochastic user equilibrium by importing the user decision uncertainty [52, 55].…”

A Traffic Assignment Approach for Multi-Modal Transportation Networks Considering Capacity Constraints and Route Correlations

“…Liu et al [40] and Meng et al [41] prove that MSWA converges faster than MSA in dealing with SUE problems. In addition, when facing with largescale systems, we can use the second-order cone program to meet accuracy and efficiency requirements simultaneously [42].…”