Optimal Routing of Energy-Aware Vehicles in Transportation Networks With Inhomogeneous Charging Nodes

We study the problem of routing for energy-aware battery-powered vehicles (BPVs) in networks with charging nodes. The objective is to minimize the total elapsed time, including travel and recharging time at charging stations, so that the vehicle reaches its destination without running out of energy. Relaxing the homogeneity of charging stations, and here, we investigate the routing problem for BPVs through a network of “inhomogeneous” charging nodes. We study two versions of the problem: the single-vehicle (user-centric) routing problem and the multiple-vehicle (system-centric) routing problem. For the former, we formulate a mixed-integer nonlinear programming (NLP)problem for obtaining an optimal path and charging policy simultaneously. We then reduce its computational complexity by decomposing it into two linear programming problems. For the latter, we use a similar approach by grouping vehicles into “subflows” and formulating the problem at a subflow-level with the inclusion of traffic congestion effects. We also propose an alternative NLP formulation obtaining near-optimal solutions with orders of magnitude reduction in the computation time. We have applied our optimal routing approach to a subnetwork of the eastern Massachusetts transportation network using actual traffic data provided by the Boston Region Metropolitan Planning Organization. Using these data, we estimate cost (congestion) functions and investigate the optimal solutions obtained under different charging station and energy-aware vehicle loads.