{"id":"https://openalex.org/W3085950292","doi":"https://doi.org/10.1155/2020/2845426","title":"The Biobjective Bike-Sharing Rebalancing Problem with Balance Intervals: A Multistart Multiobjective Particle Swarm Optimization Algorithm","display_name":"The Biobjective Bike-Sharing Rebalancing Problem with Balance Intervals: A Multistart Multiobjective Particle Swarm Optimization Algorithm","publication_year":2020,"publication_date":"2020-09-17","ids":{"openalex":"https://openalex.org/W3085950292","doi":"https://doi.org/10.1155/2020/2845426","mag":"3085950292"},"language":"en","primary_location":{"id":"doi:10.1155/2020/2845426","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/2845426","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/2845426.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/2845426.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100725714","display_name":"YongJi Jia","orcid":"https://orcid.org/0000-0002-0195-6042"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongji Jia","raw_affiliation_strings":["Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China"],"raw_orcid":"https://orcid.org/0000-0002-0195-6042","affiliations":[{"raw_affiliation_string":"Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China","institution_ids":["https://openalex.org/I181326427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100704963","display_name":"Yuanyuan Xu","orcid":"https://orcid.org/0000-0001-7147-4498"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanyuan Xu","raw_affiliation_strings":["Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China","institution_ids":["https://openalex.org/I181326427"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033239008","display_name":"Dong Yang","orcid":"https://orcid.org/0000-0003-4530-1934"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong Yang","raw_affiliation_strings":["Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China","institution_ids":["https://openalex.org/I181326427"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102859755","display_name":"Jia Li","orcid":"https://orcid.org/0000-0003-4411-6614"},"institutions":[{"id":"https://openalex.org/I181326427","display_name":"Donghua University","ror":"https://ror.org/035psfh38","country_code":"CN","type":"education","lineage":["https://openalex.org/I181326427"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia Li","raw_affiliation_strings":["Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China","institution_ids":["https://openalex.org/I181326427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100725714"],"corresponding_institution_ids":["https://openalex.org/I181326427"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.6049,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80072197,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10298","display_name":"Urban Transport and Accessibility","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10298","display_name":"Urban Transport and Accessibility","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10768","display_name":"Electric Vehicles and Infrastructure","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7145617008209229},{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.6883289217948914},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5840455293655396},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.5436018109321594},{"id":"https://openalex.org/keywords/crossover","display_name":"Crossover","score":0.536882758140564},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5305047035217285},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5131769776344299},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4730837941169739},{"id":"https://openalex.org/keywords/bike-sharing","display_name":"Bike sharing","score":0.46426984667778015},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2524116039276123},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.14637205004692078},{"id":"https://openalex.org/keywords/transport-engineering","display_name":"Transport engineering","score":0.11953604221343994},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08401277661323547}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7145617008209229},{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.6883289217948914},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5840455293655396},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.5436018109321594},{"id":"https://openalex.org/C122507166","wikidata":"https://www.wikidata.org/wiki/Q628906","display_name":"Crossover","level":2,"score":0.536882758140564},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5305047035217285},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5131769776344299},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4730837941169739},{"id":"https://openalex.org/C2994001137","wikidata":"https://www.wikidata.org/wiki/Q1358919","display_name":"Bike sharing","level":2,"score":0.46426984667778015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2524116039276123},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14637205004692078},{"id":"https://openalex.org/C22212356","wikidata":"https://www.wikidata.org/wiki/Q775325","display_name":"Transport engineering","level":1,"score":0.11953604221343994},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08401277661323547},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/2845426","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/2845426","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/2845426.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:2845426","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/2845426.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:8c152154880f493cb1e1d77352a210b2","is_oa":true,"landing_page_url":"https://doaj.org/article/8c152154880f493cb1e1d77352a210b2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/2845426","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/2845426","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/2845426.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5784864056","display_name":null,"funder_award_id":"2018BGL018","funder_id":"https://openalex.org/F4320328759","funder_display_name":"Shanghai Office of Philosophy and Social Science"}],"funders":[{"id":"https://openalex.org/F4320328759","display_name":"Shanghai Office of Philosophy and Social Science","ror":"https://ror.org/05pjsqp06"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3085950292.pdf","grobid_xml":"https://content.openalex.org/works/W3085950292.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1970180010","https://openalex.org/W1984698666","https://openalex.org/W1989913148","https://openalex.org/W2032251915","https://openalex.org/W2040282510","https://openalex.org/W2052997156","https://openalex.org/W2065031863","https://openalex.org/W2066178369","https://openalex.org/W2074069971","https://openalex.org/W2143381319","https://openalex.org/W2165171393","https://openalex.org/W2176511201","https://openalex.org/W2265976659","https://openalex.org/W2402961903","https://openalex.org/W2416372015","https://openalex.org/W2552201582","https://openalex.org/W2565567774","https://openalex.org/W2596000220","https://openalex.org/W2610175547","https://openalex.org/W2610909953","https://openalex.org/W2626391197","https://openalex.org/W2783226629","https://openalex.org/W2792879906","https://openalex.org/W2807281108","https://openalex.org/W2862315792","https://openalex.org/W2890678740","https://openalex.org/W2892611519","https://openalex.org/W2896778286","https://openalex.org/W2900803712","https://openalex.org/W2901472204","https://openalex.org/W2904850496","https://openalex.org/W2905631454","https://openalex.org/W2936269421","https://openalex.org/W2944053197","https://openalex.org/W2957361684","https://openalex.org/W2963578052","https://openalex.org/W2963614565"],"related_works":["https://openalex.org/W2090178682","https://openalex.org/W4241467429","https://openalex.org/W2001591765","https://openalex.org/W2073147994","https://openalex.org/W2384474142","https://openalex.org/W3083133203","https://openalex.org/W1588199609","https://openalex.org/W2744462909","https://openalex.org/W1971520370","https://openalex.org/W1550055091"],"abstract_inverted_index":{"The":[0,171],"bike-sharing":[1,70,84],"system":[2],"(BSS),":[3],"as":[4,112],"a":[5,79,97,102,113,129,148],"sustainable":[6],"way":[7],"to":[8,31,45,51,54,158,183],"deal":[9,67],"with":[10,68,73,118,176,189,207],"the":[11,28,34,69,82,90,106,110,119,124,134,142,160,164,194],"\u201clast":[12],"mile\u201d":[13],"problem":[14,72],"of":[15,36,61,81,92,101,121,145],"mass":[16],"transit":[17],"systems,":[18],"is":[19,78,94,156,174],"increasingly":[20],"popular":[21],"in":[22,105],"recent":[23],"years.":[24],"Despite":[25],"its":[26,185],"success,":[27],"BSS":[29,42],"tends":[30],"suffer":[32],"from":[33,48],"mismatch":[35],"bike":[37],"supply":[38],"and":[39,133,179,192],"user":[40],"demand.":[41],"operators":[43],"have":[44],"transfer":[46],"bikes":[47],"surplus":[49],"stations":[50,53,58],"deficit":[52],"redistribute":[55],"them":[56],"among":[57],"by":[59,96],"means":[60],"trucks.":[62],"In":[63,87],"this":[64,88],"paper,":[65],"we":[66],"rebalancing":[71,85],"balance":[74,98,103],"intervals":[75],"(BRP-BIs),":[76],"which":[77],"variant":[80],"static":[83],"problem.":[86],"problem,":[89],"equilibrium":[91],"station":[93],"characterized":[95],"interval":[99],"instead":[100],"point":[104],"literature.":[107],"We":[108],"formulate":[109],"BRP-BI":[111],"biobjective":[114],"mixed-integer":[115],"programming":[116],"model":[117,161],"aim":[120],"determining":[122],"both":[123],"minimum":[125],"cost":[126],"route":[127],"for":[128,141],"single":[130],"capacitated":[131],"vehicle":[132],"maximum":[135],"average":[136],"rebalance":[137],"utility,":[138],"an":[139],"index":[140],"balanced":[143],"degree":[144],"station.":[146],"Then,":[147],"multistart":[149],"multiobjective":[150],"particle":[151],"swarm":[152],"optimization":[153],"(MS-MOPSO)":[154],"algorithm":[155,173],"proposed":[157,172],"solve":[159],"such":[162],"that":[163,199],"Pareto":[165,204],"optimal":[166,205],"solutions":[167,206],"can":[168,202],"be":[169],"derived.":[170],"extended":[175],"crossover":[177],"operator":[178],"variable":[180],"neighbourhood":[181],"search":[182],"enhance":[184],"exploratory":[186],"capability.":[187],"Compared":[188],"Hybrid":[190],"NSGA-II":[191],"MOPSO,":[193],"computational":[195],"experimental":[196],"results":[197],"demonstrate":[198],"our":[200],"MS-MOPSO":[201],"obtain":[203],"higher":[208],"quality.":[209]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}