{"id":"https://openalex.org/W4390534215","doi":"https://doi.org/10.1051/ro/2024003","title":"Linear fractional optimization over the efficient set of multi-objective integer quadratic problem","display_name":"Linear fractional optimization over the efficient set of multi-objective integer quadratic problem","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4390534215","doi":"https://doi.org/10.1051/ro/2024003"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024003","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024003","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro220379.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"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","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"diamond","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro220379.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093868355","display_name":"Ali Bencheikh","orcid":null},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]},{"id":"https://openalex.org/I192268740","display_name":"University of Algiers Benyoucef Benkhedda","ror":"https://ror.org/011r6gp69","country_code":"DZ","type":"education","lineage":["https://openalex.org/I192268740"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Ali Bencheikh","raw_affiliation_strings":["USTHB, Dept. of Operations Research, Faculty of Mathematics, BP32, El-Alia 16111, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"USTHB, Dept. of Operations Research, Faculty of Mathematics, BP32, El-Alia 16111, Algeria","institution_ids":["https://openalex.org/I157169809","https://openalex.org/I192268740"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039539546","display_name":"Mustapha Moula\u00ef","orcid":"https://orcid.org/0000-0002-2013-356X"},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]},{"id":"https://openalex.org/I192268740","display_name":"University of Algiers Benyoucef Benkhedda","ror":"https://ror.org/011r6gp69","country_code":"DZ","type":"education","lineage":["https://openalex.org/I192268740"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mustapha Moula\u00ef","raw_affiliation_strings":["USTHB, Dept. of Operations Research, Faculty of Mathematics, BP32, El-Alia 16111, Algeria"],"raw_orcid":"https://orcid.org/0000-0002-2013-356X","affiliations":[{"raw_affiliation_string":"USTHB, Dept. of Operations Research, Faculty of Mathematics, BP32, El-Alia 16111, Algeria","institution_ids":["https://openalex.org/I157169809","https://openalex.org/I192268740"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":0.1728,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.38041389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"58","issue":"1","first_page":"741","last_page":"758"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9991999864578247,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9857000112533569,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/integer","display_name":"Integer (computer science)","score":0.7215346097946167},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6040470004081726},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5985965728759766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5937029123306274},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5092629194259644},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4713950455188751},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.46199655532836914},{"id":"https://openalex.org/keywords/branch-and-price","display_name":"Branch and price","score":0.4120696187019348},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33933037519454956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2702924609184265}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7215346097946167},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6040470004081726},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5985965728759766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5937029123306274},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5092629194259644},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4713950455188751},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.46199655532836914},{"id":"https://openalex.org/C123558587","wikidata":"https://www.wikidata.org/wiki/Q4956382","display_name":"Branch and price","level":3,"score":0.4120696187019348},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33933037519454956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2702924609184265},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2024003","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024003","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro220379.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"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","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:edpsciences.org:dkey/10.1051/ro/2024003","is_oa":true,"landing_page_url":"https://www.rairo-ro.org/10.1051/ro/2024003/pdf","pdf_url":"https://www.rairo-ro.org/10.1051/ro/2024003/pdf","source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1051/ro/2024003","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1051/ro/2024003","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2024003","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2024/01/ro220379.pdf","source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":true,"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","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320335007","display_name":"Direction G\u00e9n\u00e9rale de la Recherche Scientifique et du D\u00e9veloppement Technologique","ror":"https://ror.org/04jpfrv51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390534215.pdf","grobid_xml":"https://content.openalex.org/works/W4390534215.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1965585126","https://openalex.org/W1980277493","https://openalex.org/W1991005468","https://openalex.org/W1992305657","https://openalex.org/W1992916292","https://openalex.org/W1998693459","https://openalex.org/W2007586481","https://openalex.org/W2010245689","https://openalex.org/W2029209503","https://openalex.org/W2031642968","https://openalex.org/W2046881509","https://openalex.org/W2063060116","https://openalex.org/W2086980698","https://openalex.org/W2089856619","https://openalex.org/W2118402343","https://openalex.org/W2165071086","https://openalex.org/W2169874886","https://openalex.org/W2250294758","https://openalex.org/W2291978598","https://openalex.org/W2766216296","https://openalex.org/W2766490375","https://openalex.org/W2795445152","https://openalex.org/W2911449251","https://openalex.org/W3168032670"],"related_works":["https://openalex.org/W4302819359","https://openalex.org/W2769220156","https://openalex.org/W4210880521","https://openalex.org/W2769538987","https://openalex.org/W2941114593","https://openalex.org/W4300803591","https://openalex.org/W2009796757","https://openalex.org/W4238890272","https://openalex.org/W1711527768","https://openalex.org/W2044902158"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"an":[5,92],"exact":[6],"algorithm":[7,27],"for":[8],"optimizing":[9],"a":[10,20,84],"linear":[11],"fractional":[12],"utility":[13,76],"function":[14],"over":[15],"the":[16,31,38,51,67,70,75,82],"efficient":[17,47,71],"set":[18],"of":[19,55],"multi":[21],"objective":[22,56],"integer":[23,61],"quadratic":[24],"problem.":[25],"The":[26,63],"is":[28,88],"based":[29],"on":[30],"\u201cBranch":[32],"and":[33,46,80,99],"Cut\u201d":[34],"principle,":[35],"which":[36],"combines":[37],"branching":[39],"process":[40],"to":[41,58,69,95],"ensure":[42],"decision":[43],"variables\u2019":[44],"integrity":[45],"cuts":[48],"built":[49],"off":[50],"non-increasing":[52],"gradients\u2019":[53],"directions":[54],"functions":[57],"eliminate":[59],"inefficient":[60],"solutions.":[62],"proposed":[64],"approach":[65,98],"accelerates":[66],"convergence":[68],"solution":[72],"that":[73],"optimizes":[74],"function.":[77],"After":[78],"presenting":[79],"describing":[81],"algorithm,":[83],"detailed":[85],"didactic":[86],"example":[87],"illustrated,":[89],"followed":[90],"by":[91],"experimental":[93],"study":[94],"validate":[96],"our":[97],"show":[100],"computational":[101],"costs.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}