{"id":"https://openalex.org/W2944319505","doi":"https://doi.org/10.1109/access.2019.2915597","title":"An ${\\ell}_{0}$ -Norm Minimization for Energy-Efficient Timetabling in Subway Systems","display_name":"An ${\\ell}_{0}$ -Norm Minimization for Energy-Efficient Timetabling in Subway Systems","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2944319505","doi":"https://doi.org/10.1109/access.2019.2915597","mag":"2944319505"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2915597","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2915597","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08709796.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08709796.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071190011","display_name":"Ziyan Luo","orcid":"https://orcid.org/0000-0002-4926-5929"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziyan Luo","raw_affiliation_strings":["State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-4926-5929","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101801974","display_name":"Xiaotong Yu","orcid":"https://orcid.org/0000-0002-0795-3846"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaotong Yu","raw_affiliation_strings":["State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-0795-3846","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100449171","display_name":"Xiaoyu Li","orcid":"https://orcid.org/0000-0003-0735-5560"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyu Li","raw_affiliation_strings":["Department of Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.9327,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79863496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"7","issue":null,"first_page":"59422","last_page":"59436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11568","display_name":"Railway Systems and Energy Efficiency","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11568","display_name":"Railway Systems and Energy Efficiency","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10842","display_name":"Railway Engineering and Dynamics","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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":0.9855999946594238,"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":0.6624299883842468},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5468388199806213},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4733704924583435},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.43939611315727234},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4341297745704651},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.43151354789733887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.357143759727478},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14205941557884216}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6624299883842468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5468388199806213},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4733704924583435},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.43939611315727234},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4341297745704651},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.43151354789733887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.357143759727478},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14205941557884216},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2915597","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2915597","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08709796.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:43aa25c28e0645599b7ab5132be0e55d","is_oa":true,"landing_page_url":"https://doaj.org/article/43aa25c28e0645599b7ab5132be0e55d","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":"IEEE Access, Vol 7, Pp 59422-59436 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2915597","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2915597","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08709796.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8999999761581421,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G5892020810","display_name":null,"funder_award_id":"2019JBM078","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2944319505.pdf","grobid_xml":"https://content.openalex.org/works/W2944319505.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W345883418","https://openalex.org/W398786567","https://openalex.org/W1592169525","https://openalex.org/W1601741115","https://openalex.org/W1781051676","https://openalex.org/W1852135537","https://openalex.org/W1969403566","https://openalex.org/W1977520307","https://openalex.org/W1980454827","https://openalex.org/W1988381049","https://openalex.org/W1998893746","https://openalex.org/W1999174140","https://openalex.org/W2008911998","https://openalex.org/W2056201402","https://openalex.org/W2068360796","https://openalex.org/W2090786169","https://openalex.org/W2106743447","https://openalex.org/W2107528688","https://openalex.org/W2117699623","https://openalex.org/W2119017405","https://openalex.org/W2126607811","https://openalex.org/W2129131372","https://openalex.org/W2147424320","https://openalex.org/W2164452299","https://openalex.org/W2294449466","https://openalex.org/W2340487166","https://openalex.org/W2345655518","https://openalex.org/W2505379252","https://openalex.org/W2526006345","https://openalex.org/W2608351549","https://openalex.org/W2738939536","https://openalex.org/W2775019217","https://openalex.org/W2782296524","https://openalex.org/W2803796690","https://openalex.org/W2804954685","https://openalex.org/W2809565161","https://openalex.org/W2899057210","https://openalex.org/W2908211935","https://openalex.org/W2962853966","https://openalex.org/W2963292690","https://openalex.org/W2963351303","https://openalex.org/W4249667877","https://openalex.org/W4250955649","https://openalex.org/W6736781110"],"related_works":["https://openalex.org/W2155858901","https://openalex.org/W4382519099","https://openalex.org/W2491194410","https://openalex.org/W2917933030","https://openalex.org/W1515727993","https://openalex.org/W2037179686","https://openalex.org/W2120257557","https://openalex.org/W2920493340","https://openalex.org/W4319661813","https://openalex.org/W2892063770"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,52,106],"sparse":[4,41],"optimization":[5,42,81],"model":[6,99,142],"with":[7],"\u21130-norm":[8],"and":[9,83,129,149],"the":[10,14,29,39,45,63,72,77,85,89,94,101,116,130,138,150],"squared":[11],"\u21132-norm":[12],"as":[13],"objective":[15],"function":[16],"is":[17,36,48,127],"proposed":[18,40,78,98,117,154],"for":[19,38,71,76,100,114],"energy-efficient":[20,102],"timetabling":[21],"in":[22,143,156],"subway":[23],"systems":[24],"by":[25],"means":[26],"of":[27,96,112,140,145,152,158],"improving":[28],"regenerative":[30],"braking":[31],"energy":[32,146],"utilization.":[33],"Optimality":[34],"analysis":[35],"addressed":[37],"problem.":[43],"Specifically,":[44],"local":[46],"minimizer":[47],"shown":[49],"to":[50,132],"be":[51],"KKT":[53],"point":[54],"without":[55],"any":[56],"additional":[57],"constraint":[58],"qualification.":[59],"Moreover,":[60],"based":[61,108],"on":[62,122],"hard-thresholding":[64,107],"operator,":[65],"we":[66,104],"yield":[67],"an":[68],"explicit":[69],"formula":[70],"Lagrangian":[73],"dual":[74],"problem":[75,82],"non-convex":[79],"discontinuous":[80],"achieve":[84],"strong":[86],"duality":[87],"under":[88],"stationarity":[90],"condition.":[91],"To":[92],"evaluate":[93],"effectiveness":[95,139],"our":[97,141,153],"timetabling,":[103],"design":[105],"alternating":[109],"direction":[110],"method":[111],"multipliers":[113],"solving":[115],"model.":[118],"The":[119],"case":[120],"study":[121],"Beijing":[123],"Metro":[124],"Yizhuang":[125],"Line":[126],"conducted":[128],"comparison":[131],"some":[133],"recent":[134],"existing":[135],"approaches":[136],"illustrates":[137],"terms":[144,157],"saving":[147],"rate":[148],"efficiency":[151],"algorithm":[155],"computation":[159],"time.":[160]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
