The Shortest Path Problem Revisited: Optimal Routing for Electric Vehicles

Abstract

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.

Energy-optimal routes for electric vehicles

“…Regarding electric vehicles, Artmeier at al. [1] observe that using energy consumption as metric may result in negative cost values for some arcs (though, physical constraints prohibit negative cycles). They use a simplistic energy consumption model and handle negative costs by variants of…”

Minimum cost path problem for Plug-in Hybrid Electric Vehicles

“…Lin (2012) provides interesting complexity results about several variants of MCPP-CV. On the EV side, the problem of energy efficient routing of EVs has been addressed in the literature by considering limited cruising range and regenerative breaking capabilities of EVs (Artmeier et al, 2010;Sachenbacher et al, 2011;Eisner et al, 2011) and polynomial time algorithms have been developed. These problems only consider routing in a network without charging facilities.…”

Energy-Efficient Routing: Taking Speed into Account

“…There is a fundamental disadvantage of this approach, though: it only aims at minimizing the energy consumption not taking into account travel time or length of the respective route. In particular, since the models in [2] and [3] always assume that road segments are used with their typical maximum speed (e.g. residential roads at 30 km/h, inner city roads 50 km/h, country roads 100 km/h, autobahns 130 km/h), applying these approaches often leads to routes which excessively use residential and inner city roads since at these lower speeds the energy consumption is minimal -routes of this type are hardly useful in practice.…”

“…Artmeier et al in [2] formalized one variant of energy-constrained route planning, taking into account special characteristics of EVs like energy recuperation. They essentially use a variant of the Bellman-Ford algorithm to compute the most energy-efficient route for an EV.…”