{"id":"https://openalex.org/W3092752072","doi":"https://doi.org/10.1093/imamci/dnaa023","title":"Solving multiobjective optimal control problems using an improved scalarization method","display_name":"Solving multiobjective optimal control problems using an improved scalarization method","publication_year":2020,"publication_date":"2020-10-07","ids":{"openalex":"https://openalex.org/W3092752072","doi":"https://doi.org/10.1093/imamci/dnaa023","mag":"3092752072"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnaa023","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnaa023","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"},"type":"article","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/A5045747796","display_name":"Gholam Hosein Askarirobati","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139126","display_name":"University of Science and Technology of Mazandaran","ror":"https://ror.org/04jf6jw55","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210139126"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Gholam Hosein Askarirobati","raw_affiliation_strings":["Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr 48518-78195, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr 48518-78195, Iran","institution_ids":["https://openalex.org/I4210139126"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079877663","display_name":"Akbar Hashemi Borzabadi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139126","display_name":"University of Science and Technology of Mazandaran","ror":"https://ror.org/04jf6jw55","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210139126"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Akbar Hashemi Borzabadi","raw_affiliation_strings":["Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr 48518-78195, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr 48518-78195, Iran","institution_ids":["https://openalex.org/I4210139126"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062052016","display_name":"Aghileh Heydari","orcid":"https://orcid.org/0000-0002-8740-2621"},"institutions":[{"id":"https://openalex.org/I55547365","display_name":"Payame Noor University","ror":"https://ror.org/031699d98","country_code":"IR","type":"education","lineage":["https://openalex.org/I55547365"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Aghileh Heydari","raw_affiliation_strings":["Department of Mathematics, Payame Noor University, Tehran 19395-36971, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Payame Noor University, Tehran 19395-36971, Iran","institution_ids":["https://openalex.org/I55547365"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045747796"],"corresponding_institution_ids":["https://openalex.org/I4210139126"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":0.1407,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.53601513,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"37","issue":"4","first_page":"1524","last_page":"1547"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9980000257492065,"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/T10969","display_name":"Water resources management and optimization","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/pareto-principle","display_name":"Pareto principle","score":0.7727043628692627},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7427597045898438},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5796509385108948},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5646790266036987},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.537979245185852},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5291809439659119},{"id":"https://openalex.org/keywords/pareto-optimal","display_name":"Pareto optimal","score":0.45803478360176086},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4325731694698334},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4164867401123047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3758346736431122},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06894397735595703}],"concepts":[{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.7727043628692627},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7427597045898438},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5796509385108948},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5646790266036987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.537979245185852},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5291809439659119},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.45803478360176086},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4325731694698334},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4164867401123047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3758346736431122},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06894397735595703},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnaa023","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnaa023","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W641771830","https://openalex.org/W803972901","https://openalex.org/W1483431698","https://openalex.org/W1543403517","https://openalex.org/W1595498733","https://openalex.org/W1966864823","https://openalex.org/W1969813241","https://openalex.org/W1989731402","https://openalex.org/W2019338521","https://openalex.org/W2020622546","https://openalex.org/W2022098233","https://openalex.org/W2023979785","https://openalex.org/W2024008934","https://openalex.org/W2051752778","https://openalex.org/W2064079650","https://openalex.org/W2072620509","https://openalex.org/W2076432546","https://openalex.org/W2085262389","https://openalex.org/W2091716471","https://openalex.org/W2095486619","https://openalex.org/W2114201868","https://openalex.org/W2115800158","https://openalex.org/W2123808725","https://openalex.org/W2123871098","https://openalex.org/W2150046657","https://openalex.org/W2593781315","https://openalex.org/W2786741601","https://openalex.org/W2798500587","https://openalex.org/W2974160637","https://openalex.org/W3178101160","https://openalex.org/W4233757421","https://openalex.org/W4236400251","https://openalex.org/W6630252409","https://openalex.org/W6678577751","https://openalex.org/W6683588596","https://openalex.org/W6767070002"],"related_works":["https://openalex.org/W2337862504","https://openalex.org/W2084351816","https://openalex.org/W3165698115","https://openalex.org/W4312397206","https://openalex.org/W2492127985","https://openalex.org/W4245126131","https://openalex.org/W2088468004","https://openalex.org/W1555536861","https://openalex.org/W2619137665","https://openalex.org/W1995277538"],"abstract_inverted_index":{"Abstract":[0],"Detecting":[1],"the":[2,7,13,80,97,102,105,114,125,130,139,142,145,164,178,182],"Pareto":[3,8,33,76,81,93,98,118,135,179],"optimal":[4,19,65,77,94,127,136],"points":[5],"on":[6,79,96,177],"frontier":[9,34,99,180],"is":[10,50,68,85,108,122,133,148,167],"one":[11],"of":[12,35,58,62,75,92,104,120,129,138,144,175],"most":[14],"important":[15],"topics":[16],"in":[17,111],"multiobjective":[18],"control":[20,66],"problems":[21,67],"(MOCPs).":[22],"This":[23],"paper":[24],"presents":[25],"a":[26,56,60,72,88,134,186],"scalarization":[27,44],"technique":[28],"to":[29,70,86,113],"construct":[30],"an":[31,38],"approximate":[32],"MOCPs,":[36],"using":[37,55,155],"improved":[39],"normal":[40,190],"boundary":[41],"intersection":[42],"(NBI)":[43],"strategy.":[45],"For":[46],"this":[47],"purpose,":[48],"MOCP":[49],"first":[51],"discretized":[52],"and":[53,100,150,170,192],"then":[54],"grid":[57],"weights,":[59],"sequence":[61],"single":[63],"objective":[64],"solved":[69],"achieve":[71,87],"uniform":[73,173],"distribution":[74,91,174],"solutions":[78,95,121,176],"frontier.":[82],"The":[83,159],"aim":[84],"more":[89,168,172],"even":[90],"improve":[101],"efficiency":[103],"algorithm.":[106],"It":[107],"shown":[109],"that":[110,163],"contrast":[112],"NBI":[115],"method,":[116],"where":[117],"optimality":[119],"not":[123],"guaranteed,":[124],"obtained":[126],"solution":[128,137],"scalarized":[131],"problem":[132],"MOCP.":[140],"Finally,":[141],"ability":[143],"proposed":[146,165],"method":[147,166],"evaluated":[149],"compared":[151],"with":[152],"other":[153,183],"approaches":[154],"several":[156],"practical":[157],"MOCPs.":[158],"numerical":[160],"results":[161],"indicate":[162],"efficient":[169],"provides":[171],"than":[181],"methods,":[184],"such":[185],"weighted":[187],"sum,":[188],"normalized":[189],"constraint":[191],"NBI.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}