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...harging is significant. A recent thread of research has tackled the problem of finding the most energy-efficient path in a network for EVs. In [8], the authors model the problem as a shortest path problem with constraints on the charge level of the vehicle, such that the charge level can never be negative and cannot exceed the maximum charge level of the battery. Edge weights are permitted to be negative to represent energy recapturing from regenerative braking, but no negative cycles exist. A simple algorithm for solving the problem is provided, and more efficient algorithms are presented in [9] and [10]. It is shown in [9] that the battery capacity constraints can be modeled as cost functions on the edges, and a transformation of the edge cost functions permits the application of Dijkstra’s algorithm. The approach described in [10] avoids the use of preprocessing techniques so that edge costs can be calculated dynamically, and it achieves an order of magnitude reduction in the time complexity of the algorithm from [8]. However, none of these methods consider recharging decisions at nodes. III. MODEL Let G = (N, A) be a directed, acyclic network with recharging capability at every no...

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...utonomous vehicle applications [141], whereas others augmentedsOSM route network data with Shuttle Radar Topography Mission (SRTM) height information toscompute the optimal path for electric vehicles =-=[142]-=-.sThe open approach to data contributions in OSM allows for the development of a plethora ofsapplications, online or printable maps tailored to particular needs, such as hiking, biking, skiing orspubl...

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...emestichas et al. [14] use machine learning to obtain consumption data from real electric vehicles in field tests. However, their work does not focus on routing algorithms. In contrast, Eisner et al. =-=[18, 34]-=- use a relatively simple consumption model based on distance and height difference. For route planning they go beyond potential shifting, and integrate battery constraints into the arc costs by modeli...

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...l articles addressed the MCPP-CV in the literature (Lin et al. 2007, Khuller et al. 2007, Lin 2008a,b, 2012, Suzuki 2008, 2009, 2012, Adler et al. 2013). Mixed Integer Programming (MIP) formulations, heuristic techniques and lineartime algorithms with dynamic programming approach are proposed as solution methodologies for both fixed and non-fixed path assumptions. 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. Kobayashi et al. (2011) and Siddiqi et al. (2011) further include battery recharging stations in their models and propose heuristic techniques as solution methodologies. Schneider et al. (2014) also consider time windows beside recharging stations. Note that assuming the electricity as a commodity similar to gasoline, the algorithms mentioned above for MCPPCV can also be used as solution methodologies for MCPP-EV. In such a case, we also need to assume that the EV...

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...ver, this algorithm is not appropriate in the case of electric vehicles, since some road segments have negative consumption cost. In fact, electric vehicles regenerate the energy when they decelerate (e.g. in downhill). [3] [4] aim to find the shortest path for an electric vehicle, using Johnson algorithm [5] or an adaptation of Bellman Ford algorithm [6] to calculate the shortest path. Those latter allow having some negative edges between source and destination. The authors consider only vehicle weight, air friction and road elevation to determine the most economic path. Green Navigation [7] [8] is a prototypical system for forecasting and calculating energyoptimal routes for electrical vehicles. It uses OpenStreetMap [9] and SRTM (NASA Shuttle Radar Topographic Mission) to calculate the shortest path with four generic shortest path algorithms (Dijkstra, FiFO, expand, expand-distance), those latter being adapted to consider negative charging cost of EV. Though, all previous solutions may help to find best itinerary. However, in case of battery drop, the driver has to leave the already planned route to find an electric charging station. Other applications like CarStations [10] or Char...

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...* algorithm is an extension of A* search [16] to the multicriteria case [20], where vertex potentials help reducing the number of label scans. This approach was also applied to road networks [19] and later parallelized [24, 10]. For the case that the metric is a linear combination of two or more criteria, practical algorithms are available as well [14, 12]. For electric vehicles, most papers have focused on the integration of battery capacity constraints and negative edge weights (a result of recuperation) into classical single-criterion route planning algorithms optimizing energy consumption [9, 23, 4]. However, such routes may have disproportionate detours: driving slower saves energy at the cost of greatly longer travel time. Storandt [25] therefore optimizes energy consumption, but bounding the amount by which travel time may increase. Instead, we would like to present users a reasonably-sized set of routes that differently trade energy consumption and driving time, enabling them to adequately pick the one most suitable to them. Moreover, all known approaches assume a fixed driving speed per road segment, neglecting attractive solutions that still use major roads (such as freeways) but s...

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...egative to represent energy recapturing from regenerative braking, yet no negative cycles exist. A simple algorithm for solving the problem is provided, and more efficient algorithms are presented in =-=[4]-=- and [19]. It is shown in [4] that the battery capacity constraints can be modeled as cost functions on the edges, and a transformation of the edge cost functions permits the application of Dijkstra’s...