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Energy-Optimal Routes for Battery Electric Vehicles

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Abstract

We study the problem of computing paths that minimize energy consumption of a battery electric vehicle. For that, we must cope with specific properties, such as regenerative braking and constraints imposed by the battery capacity. These restrictions can be captured by profiles, which are a functional representation of optimal energy consumption between two locations, subject to initial state of charge. Efficient computation of profiles is a relevant problem on its own, but also a fundamental ingredient to many route planning approaches for battery electric vehicles. In this work, we prove that profiles have linear complexity. We examine different variants of Dijkstra’s algorithm to compute energy-optimal paths or profiles. Further, we derive a polynomial-time algorithm for the problem of finding an energy-optimal path between two locations that allows stops at charging stations. We also discuss a heuristic variant that is easy to implement, and carefully integrate it with the well-known Contraction Hierarchies algorithm and A* search. Finally, we propose a practical approach that enables computation of energy-optimal routes within milliseconds after fast (metric-dependent) preprocessing of the whole network. This enables flexible updates due to, e. g., weather forecasts or refinements of the consumption model. Practicality of our approaches is demonstrated in a comprehensive experimental study on realistic, large-scale road networks.

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Notes

  1. Formally, energy consumption does not define a metric on the input graph due to negative costs and the lack of symmetry. Nevertheless, we stick to the term as it is commonly used in the literature.

  2. http://www.ptvgroup.com.

  3. http://srtm.csi.cgiar.org.

  4. http://www.chargemap.com.

  5. http://www.openstreetmap.org.

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Acknowledgements

We would like to thank Raphael Luz for providing the consumption data [38, 66], Renato Werneck for running PUNCH [21], Moritz Kobitzsch for interesting discussions, and Christian Schulz and Dennis Luxen for providing Buffoon [53] and OSRM [48], respectively, which we used in our preliminary experiments. We thank Sabine Storandt for making Jap-OSM available, and Konstantinos Demestichas for providing sample data on energy consumption of EVs.

Funding

Funding was provided by Deutsche Forschungsgemeinschaft (Grant No. WA 654/23-1).

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  1. Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Moritz Baum, Jonas Sauer, Dorothea Wagner & Tobias Zündorf

  2. Sunnyvale, USA

    Julian Dibbelt & Thomas Pajor

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  1. Moritz Baum
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Preliminary versions of this manuscript have appeared in the proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems [10] and the 16th International Symposium on Experimental Algorithms [13]. It is based on the thesis of one of the authors [7]. Tobias Zündorf acknowledges support by DFG Research Grant WA 654/23-1.

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Baum, M., Dibbelt, J., Pajor, T. et al. Energy-Optimal Routes for Battery Electric Vehicles. Algorithmica 82, 1490–1546 (2020). https://doi.org/10.1007/s00453-019-00655-9

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