Optimal routing of electric vehicles in networks with charging nodes: A dynamic programming approach

Motivated by the significant role of recharging in battery-powered vehicles, we study the routing problem for vehicles with limited energy through a network of charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We have studied the case of homogeneous charging nodes in [1] and generalized it to inhomogeneous charging nodes in [2] by formulating and solving a Mixed Integer Non-Linear Programming problem (MINLP) for a single-vehicle. In this paper, we solve the same problem using Dynamic Programming (DP), resulting in optimal solutions with lower computational complexity compared to [2]. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into “subflows” and propose a DP formulation. Our numerical results show that DP becomes prohibitively slow as the number of subflows increases. As in [1] and [2] we resort to an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss of accuracy.