{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T14:49:44Z","timestamp":1774968584128,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T00:00:00Z","timestamp":1707868800000},"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>Electric scooter sharing mobility services have recently spread in major cities all around the world. However, the bad parking behavior of users has become a major source of issues, provoking accidents and compromising urban decorum of public areas. Reducing wild parking habits can be pursued by setting reserved parking spaces. In this work, we consider the problem faced by a municipality that hosts e-scooter sharing services and must choose which locations in its territory may be rented as reserved parking lots to sharing companies, with the aim of maximizing a return on renting and while taking into account spatial consideration and parking needs of local residents. Since this problem may result difficult to solve even for a state-of-the-art optimization software, we propose a hybrid metaheuristic solution algorithm combining a quantum-inspired ant colony optimization algorithm with an exact large neighborhood search. Results of computational tests considering realistic instances referring to the Italian capital city of Rome show the superior performance of the proposed hybrid metaheuristic.<\/jats:p>","DOI":"10.3390\/a17020080","type":"journal-article","created":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T06:59:26Z","timestamp":1707893966000},"page":"80","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Quantum-Inspired Ant Colony Optimization Algorithm for Parking Lot Rental to Shared E-Scooter Services"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6505-1720","authenticated-orcid":false,"given":"Antonella","family":"Nardin","sequence":"first","affiliation":[{"name":"Department of Engineering, Universit\u00e0 degli Studi Roma Tre, Via Vito Volterra 62, 00146 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0872-3636","authenticated-orcid":false,"given":"Fabio","family":"D\u2019Andreagiovanni","sequence":"additional","affiliation":[{"name":"Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via Giovanni Amendola 2, 42122 Reggio Emilia, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,14]]},"reference":[{"key":"ref_1","unstructured":"Federal Highway Administration United States Department of Transportation (2023, December 31). Shared Mobility: Current Practices and Guiding Principles, Available online: https:\/\/ops.fhwa.dot.gov\/publications\/fhwahop16022\/fhwahop16022.pdf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.tra.2016.12.001","article-title":"Getting smart about urban mobility-aligning the paradigms of smart and sustainable","volume":"115","author":"Lyons","year":"2018","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1080\/15568318.2012.660103","article-title":"Carsharing and personal vehicle services: Worldwide market developments and emerging trends","volume":"7","author":"Shaheen","year":"2013","journal-title":"Int. J. Sustain. Transp."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.trd.2018.08.003","article-title":"Measuring the car ownership impact of free-floating car-sharing\u2014A case study in Basel, Switzerland","volume":"65","author":"Becker","year":"2018","journal-title":"Transport. Res. D"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Turo\u0144, K., Kubik, A., and Chen, F. (2021). When, What and How to Teach about Electric Mobility? An Innovative Teaching Concept for All Stages of Education: Lessons from Poland. Energies, 14.","DOI":"10.3390\/en14196440"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1080\/15568318.2022.2054390","article-title":"A comprehensive review of shared mobility for sustainable transportation systems","volume":"17","author":"Zhu","year":"2023","journal-title":"Int. J. Sustain. Transp."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102874","DOI":"10.1016\/j.jtrangeo.2020.102874","article-title":"Survey of E-scooter users in Vienna: Who they are and how they ride","volume":"89","author":"Laa","year":"2020","journal-title":"J. Transp. Geogr."},{"key":"ref_8","first-page":"217","article-title":"To scoot or not to scoot: Findings from a recent survey about the benefits and barriers of using E-scooters for riders and non-riders","volume":"139","author":"Sanders","year":"2020","journal-title":"Transp. Part A"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Turo\u0144, K., Kubik, A., Folega, P., and Chen, F. (2023). Perception of Shared Electric Scooters: A Case Study from Poland. Sustainability, 15.","DOI":"10.3390\/su151612596"},{"key":"ref_10","first-page":"1","article-title":"Integrating e-scooters in urban transportation: Problems, policies, and the prospect of system change","volume":"79","year":"2020","journal-title":"Transp. Res. Part D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1080\/15568318.2022.2044097","article-title":"Dockless electric scooters: A review of a growing micromobility mode","volume":"17","author":"Llerena","year":"2023","journal-title":"Int. J. Sustain. Transp."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1080\/15389588.2022.2030057","article-title":"Modeling factors contributing to dockless e-scooter injury accidents in Austin, Texas","volume":"23","author":"Azimian","year":"2022","journal-title":"Traffic Inj. Prev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"104313","DOI":"10.1016\/j.scs.2022.104313","article-title":"Electric scooter safety: An integrative review of evidence from transport and medical research domains","volume":"89","author":"Kazemzadeh","year":"2023","journal-title":"Sustain. Cities Soc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"103037","DOI":"10.1016\/j.trd.2021.103037","article-title":"Planning for e-scooter use in metropolitan cities: A case study for Paris","volume":"100","author":"Latinopoulos","year":"2021","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_15","unstructured":"CNN (2023, December 31). E-Scooters Suddenly Appeared Everywhere, but Now They\u2019re Riding into Serious Trouble. Available online: https:\/\/edition.cnn.com\/travel\/article\/electric-scooter-bans-world\/index.html."},{"key":"ref_16","unstructured":"The Guardian (2023, December 31). Rented E-Scooters Cleared from Paris Streets on Eve of Ban. Available online: https:\/\/www.theguardian.com\/world\/2023\/aug\/31\/rented-e-scooters-cleared-from-paris-streets-on-eve-of-ban."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103149","DOI":"10.1016\/j.trd.2021.103149","article-title":"Geofence planning for electric scooters","volume":"102","author":"Liazos","year":"2022","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1016\/j.trpro.2021.12.058","article-title":"Developing micromobility in urban areas: Network planning criteria for e-scooters and electric micromobility devices","volume":"60","author":"Ignaccolo","year":"2022","journal-title":"Transp. Res. Procedia"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tranpol.2023.02.009","article-title":"Regulation of shared electric kick scooters in urban areas: Key drivers from expert stakeholders","volume":"134","author":"Sobrino","year":"2023","journal-title":"Transp. Policy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1016\/j.trpro.2021.01.069","article-title":"A Beautiful Fleet: Optimal Repositioning in E-scooter Sharing Systems for Urban Decorum","volume":"52","author":"Carrese","year":"2021","journal-title":"Transp. Res. Procedia"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Carrese, S., D\u2019Andreagiovanni, F., Giacchetti, T., Nardin, A., and Zamberlan, L. (2021, January 16\u201317). Seek & Beautify: Integrating UAVs in the optimal beautification of e-scooter sharing fleets. Proceedings of the 7th International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS), Heraklion, Greece.","DOI":"10.1109\/MT-ITS49943.2021.9529312"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"104426","DOI":"10.1016\/j.scs.2023.104426","article-title":"Sustainable E-scooter parking operation in urban areas using fuzzy Dombi based RAFSI model","volume":"91","author":"Deveci","year":"2023","journal-title":"Sustain. Cities Soc."},{"key":"ref_23","first-page":"100368","article-title":"Data driven methods for effective micromobility parking","volume":"10","author":"Sandoval","year":"2021","journal-title":"Transp. Res. Interdiscip. Perspect."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"103082","DOI":"10.1016\/j.trd.2021.103082","article-title":"Micromobility implementation challenges and opportunities: Analysis of e-scooter parking and high-use corridors","volume":"101","author":"Zakhem","year":"2021","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.trpro.2020.03.064","article-title":"An optimization model for renting public parking slots to carsharing services","volume":"45","author":"Carrese","year":"2020","journal-title":"Transp. Res. Procedia"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"100962","DOI":"10.1016\/j.retrec.2020.100962","article-title":"An optimization model and genetic-based matheuristic for parking slot rent optimization to carsharing","volume":"85","author":"Carrese","year":"2021","journal-title":"Res. Transp. Econ."},{"key":"ref_27","unstructured":"(2023, December 31). City of Rome-DGC225. (In Italian)."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1002\/nav.21520","article-title":"The knapsack problem with a minimum filling constraint","volume":"60","author":"Xu","year":"2013","journal-title":"Nav. Res. Logist."},{"key":"ref_29","unstructured":"(2023, December 31). IBM ILOG CPLEX. Available online: http:\/\/www-01.ibm.com\/software."},{"key":"ref_30","unstructured":"(2023, December 31). GNU Linear Programming Kit. Available online: https:\/\/www.gnu.org\/software\/glpk\/."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"101248","DOI":"10.1016\/j.swevo.2023.101248","article-title":"Performance assessment and exhaustive listing of 500+ nature-inspired metaheuristic algorithms","volume":"77","author":"Ma","year":"2023","journal-title":"Swarm Evol. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1007\/s12559-020-09730-8","article-title":"Comprehensive Taxonomies of Nature- and Bio-inspired Optimization: Inspiration Versus Algorithmic Behavior, Critical Analysis Recommendations","volume":"12","author":"Molina","year":"2020","journal-title":"Cogn. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1016\/j.ejor.2022.06.009","article-title":"Stochastic stability analysis of particle swarm optimization with pseudo random number assignment strategy","volume":"305","author":"Chih","year":"2023","journal-title":"Eur. J. Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.ins.2013.03.005","article-title":"Credit portfolio management using two-level particle swarm optimization","volume":"237","author":"Lu","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"17011","DOI":"10.1007\/s00500-023-08378-4","article-title":"4PL routing problem using hybrid beetle swarm optimization","volume":"27","author":"Lu","year":"2023","journal-title":"Soft Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"6567","DOI":"10.1007\/s11227-021-04127-2","article-title":"Colony search optimization algorithm using global optimization","volume":"78","author":"Wen","year":"2022","journal-title":"J. Supercomput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/3477.484436","article-title":"Ant system: Optimization by a colony of cooperating agents","volume":"26","author":"Dorigo","year":"1996","journal-title":"IEEE Trans. Syst. Man Cybernet.-Part B"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1016\/j.asoc.2011.02.032","article-title":"Hybrid metaheuristics in combinatorial optimization: A survey","volume":"11","author":"Blum","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.tcs.2005.05.020","article-title":"Ant colony optimization theory: A survey","volume":"344","author":"Dorigo","year":"2005","journal-title":"Theor. Comput. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"8831746","DOI":"10.1155\/2020\/8831746","article-title":"The Fourth-Party Logistics Routing Problem Using Ant Colony System-Improved Grey Wolf Optimization","volume":"2020","author":"Lu","year":"2020","journal-title":"J. Adv. Transp."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Dehuri, S. (2020). Biologically Inspired Techniques in Many-Criteria Decision Making, Springer. BITMDM 2019; Learning and Analytics in Intelligent Systems.","DOI":"10.1007\/978-3-030-39033-4"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Mavrovouniotis, M., Anastasiadou, M.N., and Hadjimitsis, D. (2023). Measuring the Performance of Ant Colony Optimization Algorithms for the Dynamic Traveling Salesman Problem. Algorithms, 16.","DOI":"10.3390\/a16120545"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"101816","DOI":"10.1016\/j.aei.2022.101816","article-title":"A Quantum-inspired Ant Colony Optimization for solving a sustainable four-dimensional traveling salesman problem under type-2 fuzzy variable","volume":"55","author":"Das","year":"2023","journal-title":"Adv. Eng. Inform."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.asoc.2014.10.016","article-title":"A fast hybrid primal heuristic for multiband robust capacitated network design with multiple time periods","volume":"26","author":"Krolikowski","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_45","unstructured":"Di Caro, G., and Theraulaz, G. (2020). Bio-Inspired Models of Network, Information, and Computing Systems, Springer. BIONETICS 2012; Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1287\/ijoc.11.4.358","article-title":"Exact and Approximate Nondeterministic Tree-Search Procedures for the Quadratic Assignment Problem","volume":"11","author":"Maniezzo","year":"1999","journal-title":"INFORMS J. Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s10107-004-0518-7","article-title":"Exploring relaxation induced neighborhoods to improve MIP solutions","volume":"102","author":"Danna","year":"2005","journal-title":"Math. Progr."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1016\/j.ejor.2012.02.038","article-title":"Coupling ant colony systems with strong local searches","volume":"220","author":"Gambardella","year":"2012","journal-title":"Eur. J. Oper. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.cosrev.2018.11.002","article-title":"A Survey on quantum computing technology","volume":"31","author":"Gyongyosi","year":"2019","journal-title":"Comput. Sci. Rev."},{"key":"ref_50","unstructured":"(2023, December 31). City of Rome-DGC136. (In Italian)."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.trpro.2021.12.057","article-title":"An Analysis of the Service Coverage and Regulation of E-Scooter Sharing in Rome (Italy)","volume":"60","author":"Nardin","year":"2022","journal-title":"Transp. Res. Procedia"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/2\/80\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:59:38Z","timestamp":1760104778000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/2\/80"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,14]]},"references-count":51,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["a17020080"],"URL":"https:\/\/doi.org\/10.3390\/a17020080","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,14]]}}}