{"id":"https://openalex.org/W1990375985","doi":"https://doi.org/10.1109/icca.2013.6565151","title":"A novel probabilistic approximate subgradient method in Lagrangian Relaxation for flow-shop scheduling problems","display_name":"A novel probabilistic approximate subgradient method in Lagrangian Relaxation for flow-shop scheduling problems","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W1990375985","doi":"https://doi.org/10.1109/icca.2013.6565151","mag":"1990375985"},"language":"en","primary_location":{"id":"doi:10.1109/icca.2013.6565151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2013.6565151","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 10th IEEE International Conference on Control and Automation (ICCA)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110581374","display_name":"Lei Shi","orcid":"https://orcid.org/0000-0001-5201-4082"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Shi","raw_affiliation_strings":["Department of Automation, Tsinghua University, Beijing, China","Tsinghua National Laboratory for Information Science and Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua National Laboratory for Information Science and Technology, Beijing, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103989643","display_name":"Yongheng Jiang","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongheng Jiang","raw_affiliation_strings":["Department of Automation, Tsinghua University, Beijing, China","Tsinghua National Laboratory for Information Science and Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua National Laboratory for Information Science and Technology, Beijing, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040580297","display_name":"Dexian Huang","orcid":"https://orcid.org/0000-0001-7743-0023"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dexian Huang","raw_affiliation_strings":["Department of Automation, Tsinghua University, Beijing, China","Tsinghua National Laboratory for Information Science and Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Tsinghua National Laboratory for Information Science and Technology, Beijing, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10479689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"152","issue":null,"first_page":"693","last_page":"698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","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/T10551","display_name":"Scheduling and Optimization Algorithms","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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9933000206947327,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.9238278865814209},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.8848456144332886},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.741062343120575},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6791194677352905},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6157819032669067},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5903887748718262},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5674558877944946},{"id":"https://openalex.org/keywords/flow-shop-scheduling","display_name":"Flow shop scheduling","score":0.5344618558883667},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.5004186630249023},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.46560126543045044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28714412450790405},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19863209128379822},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.17204639315605164},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07233062386512756}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.9238278865814209},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.8848456144332886},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.741062343120575},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6791194677352905},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6157819032669067},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5903887748718262},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5674558877944946},{"id":"https://openalex.org/C158336966","wikidata":"https://www.wikidata.org/wiki/Q3074426","display_name":"Flow shop scheduling","level":4,"score":0.5344618558883667},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.5004186630249023},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.46560126543045044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28714412450790405},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19863209128379822},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.17204639315605164},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07233062386512756},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icca.2013.6565151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2013.6565151","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 10th IEEE International Conference on Control and Automation (ICCA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.5,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1501934796","https://openalex.org/W1984909291","https://openalex.org/W1989626574","https://openalex.org/W1995083096","https://openalex.org/W2009367875","https://openalex.org/W2071660494","https://openalex.org/W2082862030","https://openalex.org/W2116152588","https://openalex.org/W2150473588","https://openalex.org/W2158023072","https://openalex.org/W2164802608","https://openalex.org/W2576116471","https://openalex.org/W4254313632"],"related_works":["https://openalex.org/W2037613239","https://openalex.org/W3183857959","https://openalex.org/W4243844638","https://openalex.org/W2894990380","https://openalex.org/W195910675","https://openalex.org/W2363143319","https://openalex.org/W2351035339","https://openalex.org/W1980006501","https://openalex.org/W3032916910","https://openalex.org/W2899851694"],"abstract_inverted_index":{"It":[0],"is":[1,26,48,66,98,119,173],"widely":[2],"accepted":[3],"that":[4,102],"scheduling":[5,24,43],"plays":[6],"a":[7,27,81,99,112],"key":[8,100],"role":[9],"in":[10,148],"enterprise":[11],"manufacturing":[12],"systems":[13],"as":[14,68],"it":[15,47],"greatly":[16],"improves":[17],"the":[18,41,78,103,133,153,158,170],"efficiency":[19],"and":[20,144,181],"competitiveness.":[21],"The":[22,136,167],"flow-shop":[23,42],"problem":[25,31,83],"kind":[28],"of":[29,37,49,160,169],"typical":[30],"which":[32,71,91],"relates":[33],"to":[34,52,94,127,131,165],"many":[35],"kinds":[36],"practical":[38,50],"problems.":[39,76,183],"Since":[40],"problems":[44],"are":[45,92,125],"NP-hard,":[46],"value":[51],"obtain":[53,128],"satisfying":[54,146],"solutions":[55],"within":[56],"short":[57],"CPU":[58],"time":[59,142,155],"for":[60,179],"large-scale":[61,74,180],"cases.":[62],"Lagrangian":[63,104,134],"Relaxation":[64],"(LR)":[65],"known":[67],"an":[69],"approach":[70],"can":[72,84,139],"handle":[73],"separable":[75],"By":[77],"LR":[79],"approach,":[80],"complex":[82],"be":[85],"separated":[86],"into":[87],"several":[88],"small":[89],"subproblems":[90],"easier":[93],"solve.":[95],"However,":[96],"there":[97],"challenge":[101],"multipliers":[105],"may":[106],"converge":[107],"slowly.":[108],"In":[109],"this":[110],"paper,":[111],"novel":[113],"probability":[114,159],"approximate":[115],"subgradient":[116],"(PASG)":[117],"method":[118,138,172],"developed,":[120],"where":[121],"intelligent":[122],"optimization":[123],"algorithms":[124],"used":[126],"proper":[129],"directions":[130],"improve":[132],"multipliers.":[135],"PASG":[137,171],"allocate":[140],"computation":[141,150,154],"reasonably":[143],"get":[145],"schedules":[147],"limited":[149],"time.":[151],"As":[152],"goes":[156],"on,":[157],"obtaining":[161],"optimal":[162],"solution":[163],"converges":[164],"1.":[166],"effectiveness":[168],"demonstrated":[174],"by":[175],"numerical":[176],"testing":[177],"results":[178],"long-time-horizon":[182]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
