{"id":"https://openalex.org/W2070900830","doi":"https://doi.org/10.1051/ro/2010011","title":"Extended VIKOR as a new method for solving Multiple Objective Large-Scale Nonlinear Programming problems","display_name":"Extended VIKOR as a new method for solving Multiple Objective Large-Scale Nonlinear Programming problems","publication_year":2010,"publication_date":"2010-04-01","ids":{"openalex":"https://openalex.org/W2070900830","doi":"https://doi.org/10.1051/ro/2010011","mag":"2070900830"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2010011","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2010011","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.numdam.org/item/10.1051/ro/2010011.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054873265","display_name":"Majeed Heydari","orcid":"https://orcid.org/0000-0003-2306-5379"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Majeed Heydari","raw_affiliation_strings":["Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir","Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060338969","display_name":"Mohammad Kazem Sayadi","orcid":null},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Kazem Sayadi","raw_affiliation_strings":["Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir","Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054075175","display_name":"Kamran Shahanaghi","orcid":"https://orcid.org/0000-0003-0947-0773"},"institutions":[{"id":"https://openalex.org/I67009956","display_name":"Iran University of Science and Technology","ror":"https://ror.org/01jw2p796","country_code":"IR","type":"education","lineage":["https://openalex.org/I67009956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Kamran Shahanaghi","raw_affiliation_strings":["Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir","Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir","institution_ids":["https://openalex.org/I67009956"]},{"raw_affiliation_string":"Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran","institution_ids":["https://openalex.org/I67009956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054873265"],"corresponding_institution_ids":["https://openalex.org/I67009956"],"apc_list":null,"apc_paid":null,"fwci":0.4045,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.69993337,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"44","issue":"2","first_page":"139","last_page":"152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9779000282287598,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vikor-method","display_name":"VIKOR method","score":0.7894419431686401},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.727329432964325},{"id":"https://openalex.org/keywords/closeness","display_name":"Closeness","score":0.7162133455276489},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.6758320927619934},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6165090799331665},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5564090013504028},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5363413691520691},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47393590211868286},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.47155997157096863},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.46705758571624756},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.44003307819366455},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37593668699264526},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.37041062116622925},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3229556083679199},{"id":"https://openalex.org/keywords/multiple-criteria-decision-analysis","display_name":"Multiple-criteria decision analysis","score":0.2884201407432556},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.19962474703788757},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1412907838821411},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09894382953643799}],"concepts":[{"id":"https://openalex.org/C172438850","wikidata":"https://www.wikidata.org/wiki/Q7907019","display_name":"VIKOR method","level":3,"score":0.7894419431686401},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.727329432964325},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.7162133455276489},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.6758320927619934},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6165090799331665},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5564090013504028},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5363413691520691},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47393590211868286},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.47155997157096863},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.46705758571624756},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.44003307819366455},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37593668699264526},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.37041062116622925},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3229556083679199},{"id":"https://openalex.org/C11105738","wikidata":"https://www.wikidata.org/wiki/Q1895805","display_name":"Multiple-criteria decision analysis","level":2,"score":0.2884201407432556},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.19962474703788757},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1412907838821411},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09894382953643799},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2010011","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2010011","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2010__44_2_139_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ro/2010011/","pdf_url":"https://www.numdam.org/item/10.1051/ro/2010011.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"}],"best_oa_location":{"id":"pmh:oai:numdam.org:RO_2010__44_2_139_0","is_oa":true,"landing_page_url":"http://www.numdam.org/articles/10.1051/ro/2010011/","pdf_url":"https://www.numdam.org/item/10.1051/ro/2010011.pdf","source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"},"sustainable_development_goals":[{"score":0.7599999904632568,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2070900830.pdf","grobid_xml":"https://content.openalex.org/works/W2070900830.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1481747975","https://openalex.org/W1554018745","https://openalex.org/W1983743030","https://openalex.org/W1986813400","https://openalex.org/W2001043894","https://openalex.org/W2002217366","https://openalex.org/W2020291596","https://openalex.org/W2035278750","https://openalex.org/W2041546765","https://openalex.org/W2053190248","https://openalex.org/W2065109455","https://openalex.org/W2092452692","https://openalex.org/W2097850690","https://openalex.org/W2116163370","https://openalex.org/W2122222032","https://openalex.org/W2127470768","https://openalex.org/W2406037574","https://openalex.org/W2503096983"],"related_works":["https://openalex.org/W1611569871","https://openalex.org/W3095911504","https://openalex.org/W2041546765","https://openalex.org/W2809251074","https://openalex.org/W2000323899","https://openalex.org/W2340170180","https://openalex.org/W3108882786","https://openalex.org/W335496838","https://openalex.org/W4251720609","https://openalex.org/W2032560733"],"abstract_inverted_index":{"The":[0,45],"VIKOR":[1,71,114],"method":[2,11,23,72,115],"was":[3],"introduced":[4],"as":[5,58,107,109],"a":[6,30,63,98,122],"Multi-Attribute":[7],"Decision":[8],"Making":[9],"(MADM)":[10],"to":[12,41,75,127],"solve":[13,76],"discrete":[14],"decision-making":[15,117],"problems":[16,82],"with":[17,83],"incommensurable":[18],"and":[19,27,129],"conflicting":[20],"criteria.":[21],"This":[22],"focuses":[24],"on":[25,35],"ranking":[26,50],"selecting":[28],"from":[29,53],"set":[31],"of":[32,39,113],"alternatives":[33],"based":[34],"the":[36,42,54,70,88,91,103,111,131],"particular":[37],"measure":[38,47],"\u201ccloseness\u201d":[40],"\u201cideal\u201d":[43],"solution.":[44],"multi-criteria":[46],"for":[48,116],"compromise":[49,64],"is":[51,73,95,125],"developed":[52,134],"l\u2013p":[55],"metric":[56],"used":[57],"an":[59],"aggregating":[60],"function":[61],"in":[62,118,135],"programming":[65],"method.":[66],"In":[67,87],"this":[68,136],"paper,":[69],"extended":[74],"Multi-Objective":[77],"Large-Scale":[78],"Non-Linear":[79],"Programming":[80],"(MOLSNLP)":[81],"block":[84],"angular":[85],"structure.":[86],"proposed":[89],"approach,":[90],"Y-dimensional":[92],"objective":[93],"space":[94,100],"reduced":[96],"into":[97],"one-dimensional":[99],"by":[101],"applying":[102],"Dantzig-Wolfe":[104],"decomposition":[105],"algorithm":[106],"well":[108],"extending":[110],"concepts":[112],"continues":[119],"environment.":[120],"Finally,":[121],"numerical":[123],"example":[124],"given":[126],"illustrate":[128],"clarify":[130],"main":[132],"results":[133],"paper.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
