Robust Wardrop's User Equilibrium Under Uncertainty

Traffic equilibrium problems have been widely studied for years, which possess profound value and meaning in the field of traffic and transportation assignment and management. The Wardrop user equilibrium principle is a behavioral axiom that postu-lates the route choice of the network users. Specially, the principle stipulates that users of the traffic network will choose the minimum cost path between each OD pair, and through this process the paths that are used will have equal costs; moreover, paths with costs higher than the minimum will have no flow.This paper focuses on the traffic network considering uncertainties in both demand and supply sides to propose a best worst-case model for robust Wardrop user equilib-rium based on the robust optimization.This model is essentially a nonlinear comple-mentarity problem, however the function we consider mostly in the deeply-exploited nonlinear complementarity problem is smooth while here the one with maximum oper-ator is non-smooth, which becomes a barrier in our model. We then establish the exis-tence and discuss the uniqueness results for an equilibrium solution of this model under relatively weaker condition. In addition, we employ aggregation function to smooth the maximum operator. We then solve the best worst-case model with semi-smooth Newton's method and smoothing technique. Numerical experiments are carried out in the traffic framework to illustrate the robustness of the model and the validity of the approach.