Range-constrained traffic assignment for electric vehicles under heterogeneous range anxiety

This paper studied the range-constrained traffic assignment problem (RTAP), where heterogeneous range anxiety is considered among the driving population by electric vehicles (EVs). In order not to get stranded en-route, each EV driver is assumed to have his/her own driving range limit for being able to complete the trip. As a result, two types of multi-class RTAP can be defined through discrete or continuous distributed range anxiety. Given path-based side constraint structures, we proposed two variational inequality (VI) formulations for modeling discrete and continuous RTAPs, where the former is finite-dimensional according to a discrete number of user classes and the latter is infinite-dimensional accounting for an infinite number of user classes. We reformulate the continuous RTAP into finite-dimensional by merging adjacent EV drivers into one group. A unified path-based solution framework is developed to solve the two RTAPs, built upon the gradient projection algorithm. We design column generation and dropping schemes to adaptively maintain compact path sets and an inner equilibration strategy to accelerate convergence. Finally, a small network is used to examine the correctness and effectiveness of proposed models, and a large Winnipeg network is adopted to evaluate the impacts of stochastic driving range on network flows and computation costs. Numerical results provide compelling evidence of the outstanding superiority of the proposed algorithm, and show that EV drivers with heightened sensitivity towards range anxiety may contribute to the emergence of critical links experiencing severe congestion.