Finding minimum-cost paths for electric vehicles

Modern route-guidance software for conventional gasoline-powered vehicles does not consider refueling since gasoline stations are ubiquitous and convenient in terms of both accessibility and use. The same technology is insufficient for electric vehicles (EVs), however, as charging stations are much more scarce and a suggested route may be infeasible given an EV´s initial charge level. Recharging decisions may also have significant impacts on the total travel time and longevity of the battery, which can be costly to replace, so they must be considered when planning EV routes. In this paper, the problem of finding a minimum-cost path for an EV when the vehicle must recharge along the way is modeled as a dynamic program. It is proven that the optimal control and state space are discrete under mild assumptions, and two different solution methods are presented.