Risk-Aware Optimization of Charging Time and Route Selection for Electric Vehicles Under Uncertainty
##plugins.themes.bootstrap3.article.main##
##plugins.themes.bootstrap3.article.sidebar##
Abstract
Effective decision-making during fast-charging sessions is becoming increasingly critical as Electric Vehicles (EVs) are deployed at scale. Drivers must make operational decisions under uncertainty arising from charging-time requirements, travel constraints, and the risk of battery depletion before destination. Moreover, from the EV driver's point of view, the reality of popular EV charging stations is far from ideal: charging station billing schemes, charging power decreases over time, and the applicable charging protocol depends on both the charger and the vehicle. In this setting, a driver charging at a given station who intends to reach a predefined destination faces two key operational questions: how long to charge the vehicle and which route to take, given that multiple feasible routes may be available. Accordingly, the driver must determine the required charging time to reach the destination, accounting for uncertainty in the estimated State of Charge (SoC) and stochasticity in route-dependent energy demand, while ensuring that the route can be completed without violating a voltage-based feasibility condition associated with power cut-off. Against this backdrop, we formulate the charging decision as a probabilistic optimization problem that captures the trade-off between charging time, travel time, and the probability of energy shortfall under a user-defined level of risk tolerance. The problem is centered on estimating the likelihood of an End-of-Power-Availability (EPA) event, thereby enabling route-aware range prediction under uncertainty. We conduct experiments using real charging curves, time-based tariffs, and two alternative routes in Costa Rica. Results show a clear trade-off between charging duration and EPA probability and consistent improvements over simple heuristics such as charging to full capacity or targeting a fixed SoC threshold. These results position the proposed approach as a practical decision-support tool for EV users, enabling charging and routing decisions to be made explicitly under uncertainty and user-defined risk preferences.
How to Cite
##plugins.themes.bootstrap3.article.details##
Electric vehicles, Fast charging, Charging time optimization, Route selection, Risk-aware decision-making, Uncertainty quantification, Maximum Driving Range, End-of-Power-Availability, Chance-constrained optimization
Autoridad Reguladora de los Servicios Públicos (ARESEP). (2023). RE-0020-IE-2023: Fijación de oficio de la tarifa aplicable en los centros de recarga rápida para vehículos eléctricos (T-VE) por tiempo de uso (Tech. Rep.). Intendencia de Energía, ARESEP. Retrieved from https://asomove.org/redirect/legislacion/fc1e3 (Accessed: 2026-01-22)
Baptista, M. L., Mishra, M., Henriques, E., & Prendinger, H. (2024). Using explainable artificial intelligence to interpret remaining useful life estimation with gated recurrent unit. In Annual Conference of the PHM Society (Vol. 16). doi: 10.36001/phmconf.2024.v16i1.4124
Biresselioglu, M. E., Kaplan, M. D., & Yilmaz, B. K. (2018, March). Electric mobility in Europe: A comprehensive review of motivators and barriers in decision making processes. Transportation Research Part A: Policy and Practice, 109, 1–13. doi: 10.1016/j.tra.2018.01.017
Brown, A., Cappellucci, J., Gaus, M., & Buleje, H. (2024, November). Electric vehicle charging infrastructure trends from the alternative fueling station locator: Second quarter 2024 (Tech. Rep.). National Renewable Energy Laboratory (NREL). doi: 10.2172/2478445
Burgos-Mellado, C., Orchard, M. E., Kazerani, M., Cárdenas, R., & Sáez, D. (2016, January). Particle-filtering-based estimation of maximum available power state in lithium-ion batteries. Applied Energy, 161, 349–363. doi: 10.1016/j.apenergy.2015.09.092
Bustos, J. E., Baeza, C., Schiele, B. B., Rivera, V., Masserano, B., Orchard, M. E., . . . Perez, A. (2025, February). A novel data-driven framework for driving range prognostics in electric vehicles. Engineering Applications of Artificial Intelligence, 142, 109925. doi: 10.1016/j.engappai.2024.109925
Bustos, J. E. G., Schiele, B. B., Masserano, B., Salas-Espiñeira, R., Troncoso-Kurtovic, D., Acuña-Ureta, D. E., ... Perez, A. (2026, June). Enabling online maximum driving range prognostics in electric vehicles via uncertain event likelihood functions. Engineering Applications of Artificial Intelligence, 173, 114449. doi: 10.1016/j.engappai.2026.114449
Chen, J., Jing, H., Chang, Y., & Liu, Q. (2019). Gated recurrent unit based recurrent neural network for remaining useful life prediction of nonlinear deterioration process. Reliability Engineering & System Safety, 185, 372–382. doi: 10.1016/j.ress.2019.01.006
Clar-Garcia, D., Fabra-Rodriguez, M., Campello-Vicente, H., & Velasco-Sanchez, E. (2025, October). Optimal DC fast-charging strategies for battery electric vehicles during long-distance trips. Batteries, 11, 394. doi: 10.3390/batteries11110394
Egbue, O., & Long, S. (2012, September). Barriers to widespread adoption of electric vehicles: An analysis of consumer attitudes and perceptions. Energy Policy, 48, 717–729. doi: 10.1016/j.enpol.2012.06.009
Gnann, T., Funke, S., Jakobsson, N., Plötz, P., Sprei, F., & Bennehag, A. (2018, July). Fast charging infrastructure for electric vehicles: Today’s situation and future needs. Transportation Research Part D: Transport and Environment, 62, 314–329. doi: 10.1016/j.trd.2018.03.004
gridX. (2025). European EV charging report 2025. Retrieved 2026-01-22, from [www.gridx.ai/resources/european-ev-charging-report-2025](http://www.gridx.ai/resources/european-ev-charging-report-2025) (gridX GmbH, Aachen/Munich, Germany)
Hanig, L., Ledna, C., Nock, D., Harper, C. D., Yip, A., Wood, E., & Spurlock, C. A. (2025, January). Finding gaps in the national electric vehicle charging station coverage of the United States. Nature Communications, 16, 561. doi: 10.1038/s41467-024-55696-8
Hoen, F. S., Díez-Gutiérrez, M., Babri, S., Hess, S., & Tørset, T. (2023, September). Charging electric vehicles on long trips and the willingness to pay to reduce waiting for charging: Stated preference survey in Norway. Transportation Research Part A: Policy and Practice, 175, 103774. doi: 10.1016/j.tra.2023.103774
Huang, C. H., Soto, M., Ortiz, J., Arguello, A., & Perez, A. (2024, November). A quick overview of how electric vehicles are rapidly charged. In 2024 IEEE PES Generation, Transmission and Distribution Latin America Conference and Industrial Exposition (GTDLA) (pp. 1–5). IEEE. doi: 10.1109/GTDLA61236.2024.10913612
International Energy Agency (IEA). (2025, May). Global EV outlook 2025 (Tech. Rep.). Paris: International Energy Agency. Retrieved 2026-01-22, from [www.iea.org/reports/global-ev-outlook-2025](http://www.iea.org/reports/global-ev-outlook-2025) (Published 14 May 2025. Licence: CC BY 4.0)
Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W., ... Liu, T.-Y. (2017). LightGBM: A highly efficient gradient boosting decision tree. In Proceedings of the 31st International Conference on Neural Information Processing Systems (pp. 3149–3157). Red Hook, NY, USA: Curran Associates Inc.
Liu, H., Xiao, Q., Jin, Y., Mu, Y., Meng, J., Zhang, T., . . . Teodorescu, R. (2022). Improved LightGBM-based framework for electric vehicle lithium-ion battery remaining useful life prediction using multi health indicators. Symmetry, 14(8), 1584. doi: 10.3390/sym14081584
Liu, R., He, G., Wang, X., Mallapragada, D., Zhao, H., Shao-Horn, Y., & Jiang, B. (2024, January). A cross-scale framework for evaluating flexibility values of battery and fuel cell electric vehicles. Nature Communications, 15, 280. doi: 10.1038/s41467-023-43884-x
Löbel, F., Borndörfer, R., & Weider, S. (2023). Non-linear charge functions for electric vehicle scheduling with dynamic recharge rates. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) (Vol. 115, pp. 15:1–15:6). Schloss Dagstuhl – Leibniz-Zentrum für Informatik. doi: 10.4230/OASIcs.ATMOS.2023.15
Nemirovski, A., & Shapiro, A. (2007, January). Convex approximations of chance constrained programs. SIAM Journal on Optimization, 17, 969–996. doi: 10.1137/050622328
Noel, L., de Rubens, G. Z., Kester, J., & Sovacool, B. K. (2020, March). Understanding the socio-technical nexus of Nordic electric vehicle (EV) barriers: A qualitative discussion of range, price, charging and knowledge. Energy Policy, 138, 111292. doi: 10.1016/j.enpol.2020.111292
Perez, A., Jaramillo, F., Baeza, C., Valderrama, M., Quintero, V., & Orchard, M. (2021, November). A particle-swarm-optimization-based approach for the state-of-charge estimation of an electric vehicle when driven under real conditions. Annual Conference of the PHM Society, 13. doi: 10.36001/phmconf.2021.v13i1.3013
Sohil, F., Sohali, M. U., & Shabbir, J. (2022, January). An introduction to statistical learning with applications in R. Statistical Theory and Related Fields, 6, 87–87. doi: 10.1080/24754269.2021.1980261
Tomaszewska, A., Chu, Z., Feng, X., O’Kane, S., Liu, X., Chen, J., ... Wu, B. (2019, August). Lithium-ion battery fast charging: A review. eTransportation, 1, 100011. doi: 10.1016/j.etran.2019.100011
Unterluggauer, T., Rich, J., Andersen, P. B., & Hashemi, S. (2022, May). Electric vehicle charging infrastructure planning for integrated transportation and power distribution networks: A review. eTransportation, 12, 100163. doi: 10.1016/j.etran.2022.100163
Zhan, W., Liao, Y., Deng, J., Wang, Z., & Yeh, S. (2025, March). Large-scale empirical study of electric vehicle usage patterns and charging infrastructure needs. npj Sustainable Mobility and Transport, 2, 9. doi: 10.1038/s44333-024-00023-3
Zhang, H., & Chow, M.-Y. (2010, November). On-line PHEV battery hysteresis effect dynamics modeling. In IECON 2010 36th Annual Conference on IEEE Industrial Electronics Society (pp. 1844–1849). IEEE. doi: 10.1109/IECON.2010.5675395
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
The Prognostic and Health Management Society advocates open-access to scientific data and uses a Creative Commons license for publishing and distributing any papers. A Creative Commons license does not relinquish the author’s copyright; rather it allows them to share some of their rights with any member of the public under certain conditions whilst enjoying full legal protection. By submitting an article to the International Conference of the Prognostics and Health Management Society, the authors agree to be bound by the associated terms and conditions including the following:
As the author, you retain the copyright to your Work. By submitting your Work, you are granting anybody the right to copy, distribute and transmit your Work and to adapt your Work with proper attribution under the terms of the Creative Commons Attribution 3.0 United States license. You assign rights to the Prognostics and Health Management Society to publish and disseminate your Work through electronic and print media if it is accepted for publication. A license note citing the Creative Commons Attribution 3.0 United States License as shown below needs to be placed in the footnote on the first page of the article.
First Author et al. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 United States License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.