{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:11:55Z","timestamp":1760148715142,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,24]],"date-time":"2023-05-24T00:00:00Z","timestamp":1684886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Finding the optimal speed profile of an autonomous electric vehicle (AEV) for a given route (eco-driving) can lead to a reduction in energy consumption. This energy reduction is even more noticeable when the regenerative braking (RB) capability of AEVs is carefully considered in obtaining the speed profile. In this paper, a new approach for calculating the optimum eco-driving profile of an AEV is formulated using mixed-integer linear programming (MILP) while carefully integrating the RB capability and its limitations in the process of obtaining a driving profile with minimum energy consumption. One of the most important limitations of RB which has been neglected in previous studies is operation below the low-speed boundary (LSB) of electric motors, which impairs the energy extraction capability of RB. The novelty of this work is finding the optimal speed profile given this limitation, leading to a much more realistic eco-driving profile. Python is used to code the MILP problem, and CPLEX is employed as the solver. To verify the results, the eco-driving problem is applied to two scenarios to show the significance of considering a dynamic LSB. It is shown that for the route under study, up to 27% more energy can be harvested by employing the proposed approach.<\/jats:p>","DOI":"10.3390\/a16060262","type":"journal-article","created":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T02:00:55Z","timestamp":1684980055000},"page":"262","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Autonomous Electric Vehicle Route Optimization Considering Regenerative Braking Dynamic Low-Speed Boundary"],"prefix":"10.3390","volume":"16","author":[{"given":"Masoud","family":"Mohammadi","sequence":"first","affiliation":[{"name":"Department of Electrical and Biomedical Engineering, University of Nevada Reno, Reno, NV 89557, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2812-5994","authenticated-orcid":false,"given":"Poria","family":"Fajri","sequence":"additional","affiliation":[{"name":"Department of Electrical and Biomedical Engineering, University of Nevada Reno, Reno, NV 89557, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0875-8433","authenticated-orcid":false,"given":"Reza","family":"Sabzehgar","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, San Diego State University, San Diego, CA 92182, USA"}]},{"given":"Farshad","family":"Harirchi","sequence":"additional","affiliation":[{"name":"Amazon Web Service, Seattle, WA 98109, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2491","DOI":"10.1109\/TITS.2014.2319812","article-title":"Cloud-Based Velocity Profile Optimization for Everyday Driving: A Dynamic-Programming-Based Solution","volume":"15","author":"Ozatay","year":"2014","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1016\/j.rser.2016.11.122","article-title":"Study of the environmental Kuznets curve for transport carbon dioxide emissions in Saudi Arabia","volume":"75","author":"Alshehry","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1109\/TITS.2018.2839102","article-title":"Energy aware driving: Optimal electric vehicle speed profiles for sustainability in transportation","volume":"20","author":"Yi","year":"2019","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.trc.2018.02.018","article-title":"Energy impact evaluation for eco-routing and charging of autonomous electric vehicle fleet: Ambient temperature consideration","volume":"89","author":"Yi","year":"2018","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.tra.2016.08.020","article-title":"Operations of a shared, autonomous, electric vehicle fleet: Implications of vehicle & charging infrastructure decisions","volume":"94","author":"Chen","year":"2016","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Lima, P.F., Trincavelli, M., M\u00e5rtensson, J., and Wahlberg, B. (2015, January 15\u201318). Clothoid-based speed profiler and control for autonomous driving. Proceedings of the 2015 IEEE 18th International Conference on Intelligent Transportation Systems, Gran Canaria, Spain.","DOI":"10.1109\/ITSC.2015.354"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1061\/(ASCE)0733-947X(2005)131:3(173)","article-title":"Vehicle Speed Profiles to Minimize Work and Fuel Consumption","volume":"131","author":"Chang","year":"2005","journal-title":"J. Transp. Eng."},{"key":"ref_8","unstructured":"Vomlel, J., and Kratochv\u00edl, V. (2015, January 16\u201319). Influence diagrams for speed profile optimization: Computational issues. Proceedings of the 10th Workshop Uncertainty Process (WUPES), Mon\u00ednec, Czech Republic."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhu, Z., Gupta, S., Pivaro, N., Deshpande, S.R., and Canova, M. (July, January 29). A GPU Implementation of a Look-Ahead Optimal Controller for Eco-Driving Based on Dynamic Programming. Proceedings of the 2021 European Control Conference (ECC), Delft, The Netherlands.","DOI":"10.23919\/ECC54610.2021.9655197"},{"key":"ref_10","unstructured":"Bin, Y., Li, Y., Gong, Q., and Peng, Z.-R. (2009, January 10\u201312). Multi-information integrated trip specific optimal power management for plug-in hybrid electric vehicles. Proceedings of the 2009 American Control Conference, St. Louis, MO, USA."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Katsargyri, G.-E., Kolmanovsky, I.V., Michelini, J., Kuang, M.L., Phillips, A.M., Rinehart, M., and Dahleh, M.A. (2009, January 10\u201312). Optimally controlling Hybrid Electric Vehicles using path forecasting. Proceedings of the 2009 American Control Conference, St. Louis, MO, USA.","DOI":"10.1109\/ACC.2009.5160504"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bae, S., Choi, Y., Kim, Y., Guanetti, J., Borrelli, F., and Moura, S. (2019, January 11\u201313). Real-time Ecological Velocity Planning for Plug-in Hybrid Vehicles with Partial Communication to Traffic Lights. Proceedings of the 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France.","DOI":"10.1109\/CDC40024.2019.9030166"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1109\/TITS.2016.2634019","article-title":"Optimal Energy Management for HEVs in Eco-Driving Applications Using Bi-Level MPC","volume":"18","author":"Guo","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mohammadi, M., Heydari, S., Fajri, P., Harirchi, F., and Yi, Z. (2022, January 15\u201317). Energy-Aware Driving Profile of Autonomous Electric Vehicles Considering Regenerative Braking Limitations. Proceedings of the 2022 IEEE Transportation Electrification Conference & Expo (ITEC), Anaheim, CA, USA.","DOI":"10.1109\/ITEC53557.2022.9813916"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1109\/TIE.2009.2015356","article-title":"A Cost-Effective Method of Electric Brake with Energy Regeneration for Electric Vehicles","volume":"56","author":"Yang","year":"2009","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chu, L., Yao, L., Chen, J., Chao, L., Guo, J., Zhang, Y., and Liu, M. (2011, January 6\u20139). Integrative braking control system for electric vehicles. Proceedings of the IEEE Vehicle Power and Propulsion Conference (VPPC), Chicago, IL, USA.","DOI":"10.1109\/VPPC.2011.6042995"},{"key":"ref_17","unstructured":"Suntharalingam, P. (2011). Kinetic Energy Recovery and Power Management for Hybrid Electric Vehicles. [Ph.D. Thesis, Cranfield University]."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4264","DOI":"10.1109\/TVT.2015.2504363","article-title":"Modeling and Integration of Electric Vehicle Regenerative and Friction Braking for Motor\/Dynamometer Test Bench Emulation","volume":"65","author":"Fajri","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"350","DOI":"10.4271\/2013-01-1473","article-title":"Analysis of input power, energy availability, and efficiency during deceleration for X-EV vehicles","volume":"2","author":"Rask","year":"2013","journal-title":"SAE J. Altern. Powertrains"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1678","DOI":"10.1109\/TIA.2013.2257976","article-title":"Configure Methodology of Onboard Supercapacitor Array for Recycling Regenerative Braking Energy of URT Vehicles","volume":"49","author":"Shen","year":"2013","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1806","DOI":"10.1109\/TEC.2020.2994520","article-title":"Optimal Brake Allocation in Electric Vehicles for Maximizing Energy Harvesting During Braking","volume":"35","author":"Heydari","year":"2020","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_22","unstructured":"(2022, March 20). Simplex Optimizers in the CPLEX Callable Library (C API) Reference Manual. Available online: https:\/\/www.ibm.com\/docs\/en\/icos\/22.1.0?topic=cclcarm-simplex-optimizers-in-cplex-callable-library-c-api-reference-manual."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/6\/262\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:41:10Z","timestamp":1760125270000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/6\/262"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,24]]},"references-count":22,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["a16060262"],"URL":"https:\/\/doi.org\/10.3390\/a16060262","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2023,5,24]]}}}