{"id":"https://openalex.org/W4401698331","doi":"https://doi.org/10.3390/eng5030104","title":"A Review on Multi-Objective Mixed-Integer Non-Linear Optimization Programming Methods","display_name":"A Review on Multi-Objective Mixed-Integer Non-Linear Optimization Programming Methods","publication_year":2024,"publication_date":"2024-08-17","ids":{"openalex":"https://openalex.org/W4401698331","doi":"https://doi.org/10.3390/eng5030104"},"language":"en","primary_location":{"id":"doi:10.3390/eng5030104","doi":"https://doi.org/10.3390/eng5030104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/eng5030104","pdf_url":"https://www.mdpi.com/2673-4117/5/3/104/pdf?version=1723899950","source":{"id":"https://openalex.org/S4210179454","display_name":"Eng\u2014Advances in Engineering","issn_l":"2673-4117","issn":["2673-4117"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Eng","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4401698331"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2673-4117/5/3/104/pdf?version=1723899950","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074242979","display_name":"Ahmed Jaber","orcid":"https://orcid.org/0000-0001-5508-1299","observed_orcids":["https://orcid.org/0000-0001-5508-1299"]},"institutions":[{"id":"https://openalex.org/I140494188","display_name":"Universit\u00e9 de Technologie de Troyes","ror":"https://ror.org/01qhqcj41","country_code":"FR","type":"education","lineage":["https://openalex.org/I140494188"]},{"id":"https://openalex.org/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]},{"id":"https://openalex.org/I4210137107","display_name":"Laboratoire des Syst\u00e8mes M\u00e9caniques et d'Ing\u00e9nierie Simultan\u00e9e","ror":"https://ror.org/04damed73","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I140494188","https://openalex.org/I4210110412","https://openalex.org/I4210137107","https://openalex.org/I4210139971"]}],"countries":["FR","LB"],"is_corresponding":true,"raw_author_name":"Ahmed Jaber","raw_affiliation_strings":["Faculty of Engineering, Lebanese University, Beirut 1003, Lebanon","LASMIS Lab, Mechanics Materials Optics and Nanotechnology (M2ON) Department, University of Technology of Troyes, 10010 Troyes, France"],"raw_orcid":"https://orcid.org/0000-0001-5508-1299","affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Lebanese University, Beirut 1003, Lebanon","institution_ids":["https://openalex.org/I160368002"]},{"raw_affiliation_string":"LASMIS Lab, Mechanics Materials Optics and Nanotechnology (M2ON) Department, University of Technology of Troyes, 10010 Troyes, France","institution_ids":["https://openalex.org/I140494188","https://openalex.org/I4210137107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010017654","display_name":"Rafic Youn\u00e8s","orcid":"https://orcid.org/0000-0002-7957-2057","observed_orcids":["https://orcid.org/0000-0002-7957-2057"]},"institutions":[{"id":"https://openalex.org/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Rafic Younes","raw_affiliation_strings":["Faculty of Engineering, Lebanese University, Beirut 1003, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Lebanese University, Beirut 1003, Lebanon","institution_ids":["https://openalex.org/I160368002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032049072","display_name":"Pascal Lafon","orcid":"https://orcid.org/0000-0002-7352-5612","observed_orcids":["https://orcid.org/0000-0002-7352-5612"]},"institutions":[{"id":"https://openalex.org/I140494188","display_name":"Universit\u00e9 de Technologie de Troyes","ror":"https://ror.org/01qhqcj41","country_code":"FR","type":"education","lineage":["https://openalex.org/I140494188"]},{"id":"https://openalex.org/I4210137107","display_name":"Laboratoire des Syst\u00e8mes M\u00e9caniques et d'Ing\u00e9nierie Simultan\u00e9e","ror":"https://ror.org/04damed73","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I140494188","https://openalex.org/I4210110412","https://openalex.org/I4210137107","https://openalex.org/I4210139971"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pascal Lafon","raw_affiliation_strings":["LASMIS Lab, Mechanics Materials Optics and Nanotechnology (M2ON) Department, University of Technology of Troyes, 10010 Troyes, France"],"raw_orcid":"https://orcid.org/0000-0002-7352-5612","affiliations":[{"raw_affiliation_string":"LASMIS Lab, Mechanics Materials Optics and Nanotechnology (M2ON) Department, University of Technology of Troyes, 10010 Troyes, France","institution_ids":["https://openalex.org/I140494188","https://openalex.org/I4210137107"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043188896","display_name":"Jihan Khoder","orcid":"https://orcid.org/0000-0002-0142-3430","observed_orcids":["https://orcid.org/0000-0002-0142-3430"]},"institutions":[{"id":"https://openalex.org/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Jihan Khoder","raw_affiliation_strings":["Faculty of Engineering, Lebanese University, Beirut 1003, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Lebanese University, Beirut 1003, Lebanon","institution_ids":["https://openalex.org/I160368002"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074242979"],"corresponding_institution_ids":["https://openalex.org/I140494188","https://openalex.org/I160368002","https://openalex.org/I4210137107"],"apc_list":{"value":1200,"currency":"CHF","value_usd":1364},"apc_paid":{"value":1200,"currency":"CHF","value_usd":1364},"fwci":6.5191,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.98496454,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"5","issue":"3","first_page":"1961","last_page":"1979"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.5303000211715698,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.5303000211715698,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.44510000944137573,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.008999999612569809,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"multi-objective optimization","score":0.8790000081062317},{"id":"https://openalex.org/keywords/mixed-integer-nonlinear-programming","display_name":"mixed-integer nonlinear programming","score":0.9599999785423279},{"id":"https://openalex.org/keywords/exact-algorithms","display_name":"exact algorithms","score":0.8610000014305115},{"id":"https://openalex.org/keywords/approximation-methods","display_name":"approximation methods","score":0.9470000267028809},{"id":"https://openalex.org/keywords/hybrid-optimization","display_name":"hybrid optimization","score":0.8899999856948853},{"id":"https://openalex.org/keywords/global-optimization","display_name":"global optimization","score":0.5740000009536743}],"concepts":[{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.6728470325469971},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6227564811706543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5930590629577637},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5900017619132996},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5498101115226746},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5211858153343201},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4923039674758911},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4396677017211914},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4174203872680664},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.3720042109489441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3202204406261444},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10439133644104004},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":3,"locations":[{"id":"doi:10.3390/eng5030104","doi":"https://doi.org/10.3390/eng5030104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/eng5030104","pdf_url":"https://www.mdpi.com/2673-4117/5/3/104/pdf?version=1723899950","source":{"id":"https://openalex.org/S4210179454","display_name":"Eng\u2014Advances in Engineering","issn_l":"2673-4117","issn":["2673-4117"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Eng","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04799959v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-04799959","pdf_url":"https://hal.science/hal-04799959/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Eng, 2024, 5 (3), pp.1961-1979. &#x27E8;10.3390/eng5030104&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:334292a9b1444d86ae662d916ed8fd9b","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/334292a9b1444d86ae662d916ed8fd9b","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Eng, Vol 5, Iss 3, Pp 1961-1979 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/eng5030104","doi":"https://doi.org/10.3390/eng5030104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/eng5030104","pdf_url":"https://www.mdpi.com/2673-4117/5/3/104/pdf?version=1723899950","source":{"id":"https://openalex.org/S4210179454","display_name":"Eng\u2014Advances in Engineering","issn_l":"2673-4117","issn":["2673-4117"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Eng","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322377","display_name":"Universit\u00e9 Libanaise","ror":"https://ror.org/05x6qnc69"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401698331.pdf","grobid_xml":"https://content.openalex.org/works/W4401698331.grobid-xml"},"referenced_works_count":86,"referenced_works":["https://openalex.org/W292375506","https://openalex.org/W1486140585","https://openalex.org/W1515177345","https://openalex.org/W1518970501","https://openalex.org/W1572130003","https://openalex.org/W1605128581","https://openalex.org/W1963598301","https://openalex.org/W1975009952","https://openalex.org/W1980410032","https://openalex.org/W1988390667","https://openalex.org/W1990023680","https://openalex.org/W2001741445","https://openalex.org/W2016131362","https://openalex.org/W2023269357","https://openalex.org/W2024008934","https://openalex.org/W2027360559","https://openalex.org/W2039377679","https://openalex.org/W2055418225","https://openalex.org/W2060864429","https://openalex.org/W2064193520","https://openalex.org/W2073135589","https://openalex.org/W2083743691","https://openalex.org/W2101657530","https://openalex.org/W2104670598","https://openalex.org/W2109791710","https://openalex.org/W2116661285","https://openalex.org/W2126105956","https://openalex.org/W2133304166","https://openalex.org/W2135210976","https://openalex.org/W2155014525","https://openalex.org/W2159427933","https://openalex.org/W2168723985","https://openalex.org/W2219010958","https://openalex.org/W2245763252","https://openalex.org/W2277678953","https://openalex.org/W2533664202","https://openalex.org/W2582889117","https://openalex.org/W2687335573","https://openalex.org/W2750734218","https://openalex.org/W2754511173","https://openalex.org/W2760618585","https://openalex.org/W2884165914","https://openalex.org/W2902723719","https://openalex.org/W2921365421","https://openalex.org/W2922002143","https://openalex.org/W2946297054","https://openalex.org/W2947207892","https://openalex.org/W2966382902","https://openalex.org/W3003950842","https://openalex.org/W3005327438","https://openalex.org/W3013226076","https://openalex.org/W3021699445","https://openalex.org/W3023935218","https://openalex.org/W3034157346","https://openalex.org/W3043524013","https://openalex.org/W3085208921","https://openalex.org/W3092592840","https://openalex.org/W3093154146","https://openalex.org/W3102598125","https://openalex.org/W3107459742","https://openalex.org/W3115926713","https://openalex.org/W3118514931","https://openalex.org/W3126941411","https://openalex.org/W3130952407","https://openalex.org/W3148921802","https://openalex.org/W3151184326","https://openalex.org/W3157708694","https://openalex.org/W3162816651","https://openalex.org/W3179231948","https://openalex.org/W3179671600","https://openalex.org/W3194725655","https://openalex.org/W4205732933","https://openalex.org/W4232223209","https://openalex.org/W4240374930","https://openalex.org/W4246565613","https://openalex.org/W4254729356","https://openalex.org/W4383221650","https://openalex.org/W4383221781","https://openalex.org/W4388017354","https://openalex.org/W4388574064","https://openalex.org/W4393295272","https://openalex.org/W4394932985","https://openalex.org/W4396585213","https://openalex.org/W4398178307","https://openalex.org/W4398201330","https://openalex.org/W7150828634"],"related_works":["https://openalex.org/W2133304166","https://openalex.org/W4405863763","https://openalex.org/W4254339897","https://openalex.org/W151227101","https://openalex.org/W4404911779","https://openalex.org/W2074518475","https://openalex.org/W4220712670","https://openalex.org/W2911295736","https://openalex.org/W3085788122","https://openalex.org/W2296425151"],"abstract_inverted_index":{"This":[0,47,144],"paper":[1,90],"provides":[2],"a":[3,41,50,101],"recent":[4],"overview":[5],"of":[6,25,39,44,63,109,131],"the":[7,23,56,61,78,81,92,107,120,129,138,158],"exact,":[8,171],"approximate,":[9,172],"and":[10,27,134,165,173],"hybrid":[11,64,174],"optimization":[12],"methods":[13,111,175],"that":[14,54,123,160,166],"handle":[15],"Multi-Objective":[16],"Mixed-Integer":[17],"Non-Linear":[18],"Programming":[19],"(MO-MINLP)":[20],"problems.":[21,46,180],"Both":[22],"domains":[24],"exact":[26,110],"approximate":[28,115],"research":[29,68,75,83,121,139,159],"have":[30],"experienced":[31],"significant":[32,57],"growth,":[33],"driven":[34],"by":[35],"their":[36],"shared":[37],"goal":[38],"addressing":[40],"wide":[42],"range":[43],"real-world":[45],"work":[48,145],"presents":[49],"comprehensive":[51],"literature":[52],"review":[53],"highlights":[55],"theoretical":[58],"contributions":[59],"in":[60,77,88,141,154],"field":[62],"approaches":[65],"between":[66],"these":[67,132],"areas.":[69],"We":[70],"also":[71],"point":[72],"out":[73,164],"possible":[74],"gaps":[76,140],"literature.":[79],"Hence,":[80],"main":[82],"questions":[84],"to":[85,96,127,147,177],"be":[86],"answered":[87],"this":[89,142,155],"involve":[91],"following:":[93],"(1)":[94],"how":[95],"exactly":[97],"or":[98],"approximately":[99],"solve":[100,178],"MO-MINLP":[102,179],"problem?":[103],"(2)":[104],"What":[105,118],"are":[106,119,124,137],"drawbacks":[108],"as":[112,114],"well":[113],"methods?":[116,133],"(3)":[117],"lines":[122],"currently":[125,168],"underway":[126,169],"enhance":[128],"performances":[130],"(4)":[135],"Where":[136],"field?":[143],"aims":[146],"provide":[148],"enough":[149],"descriptive":[150],"information":[151],"for":[152],"newcomers":[153],"area":[156],"about":[157],"has":[161],"been":[162],"carried":[163],"is":[167],"concerning":[170],"used":[176]},"counts_by_year":[{"year":2026,"cited_by_count":14},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2024-08-20T00:00:00"}
