Electric vehicles (EV) powered by batteries will play a significant role in the road traffic of the future. The unique characteristics of such EVs-limited cruising range, long recharge times, and the ability to regain energy during deceleration-require novel routing algorithms, since the task is now to determine the most economical route rather than just the shortest one. This paper proposes extensions to general shortestpath algorithms that address the problem of energy-optimal routing. Specifically, we (i) formalize energy-efficient routing in the presence of rechargeable batteries as a special case of the constrained shortest path problem (CSP) with hard and soft constraints, and (ii) present an adaption of a general shortest path algorithm (using an energy graph, i.e., a graph with a weight function representing the energy consumption) that respects the given constraints and has a worst case complexity of O(n 3). The presented algorithms have been implemented and evaluated within a prototypic navigation system for energy-efficient routing.

Traditionally routing has focused on finding shortest paths in networks with positive, static edge costs representing the distance between two nodes. Energy-optimal routing for electric vehicles creates novel algorithmic challenges, as simply understanding edge costs as energy values and applying standard algorithms does not work. First, edge costs can be negative due to recuperation, excluding Dijkstra-like algorithms. Second, edge costs may depend on parameters such as vehicle weight only known at query time, ruling out existing preprocessing techniques. Third, considering battery capacity limitations implies that the cost of a path is no longer just the sum of its edge costs. This paper shows how these challenges can be met within the framework of A* search. We show how the specific domain gives rise to a consistent heuristic function yielding an O(n2) routing algorithm. Moreover, we show how battery constraints can be treated by dynamically adapting edge costs and hence can be handled in the same way as parameters given at query time, without increasing run-time complexity. Experimental results with real road networks and vehicle data demonstrate the advantages of our solution.