{"id":"https://openalex.org/W4387091849","doi":"https://doi.org/10.1007/s00186-023-00836-x","title":"Approximating multiobjective optimization problems: How exact can you be?","display_name":"Approximating multiobjective optimization problems: How exact can you be?","publication_year":2023,"publication_date":"2023-09-27","ids":{"openalex":"https://openalex.org/W4387091849","doi":"https://doi.org/10.1007/s00186-023-00836-x"},"language":"en","primary_location":{"id":"doi:10.1007/s00186-023-00836-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00186-023-00836-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-023-00836-x.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00186-023-00836-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002493273","display_name":"Cristina Bazgan","orcid":"https://orcid.org/0000-0002-5460-6222"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Cristina Bazgan","raw_affiliation_strings":["CNRS, LAMSADE, Universit\u00e9 Paris-Dauphine, PSL Reseach University, 75016, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, LAMSADE, Universit\u00e9 Paris-Dauphine, PSL Reseach University, 75016, Paris, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005087258","display_name":"Arne Herzel","orcid":"https://orcid.org/0000-0001-6230-1253"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]},{"id":"https://openalex.org/I309496635","display_name":"Weihenstephan-Triesdorf University of Applied Sciences","ror":"https://ror.org/00gzkxz88","country_code":"DE","type":"education","lineage":["https://openalex.org/I309496635"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Arne Herzel","raw_affiliation_strings":["Department of Mathematics, University of Kaiserslautern-Landau, Paul-Ehrlich-Str. 14, 67663, Kaiserslautern, Germany","TUM Campus Straubing for Biotechnology and Sustainability, Weihenstephan-Triesdorf University of Applied Sciences, Am Essigberg 3, 94315, Straubing, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kaiserslautern-Landau, Paul-Ehrlich-Str. 14, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"TUM Campus Straubing for Biotechnology and Sustainability, Weihenstephan-Triesdorf University of Applied Sciences, Am Essigberg 3, 94315, Straubing, Germany","institution_ids":["https://openalex.org/I309496635"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107846021","display_name":"Stefan Ruzika","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Ruzika","raw_affiliation_strings":["Department of Mathematics, University of Kaiserslautern-Landau, Paul-Ehrlich-Str. 14, 67663, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kaiserslautern-Landau, Paul-Ehrlich-Str. 14, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050306276","display_name":"Clemens Thielen","orcid":"https://orcid.org/0000-0003-0897-3571"},"institutions":[{"id":"https://openalex.org/I309496635","display_name":"Weihenstephan-Triesdorf University of Applied Sciences","ror":"https://ror.org/00gzkxz88","country_code":"DE","type":"education","lineage":["https://openalex.org/I309496635"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Clemens Thielen","raw_affiliation_strings":["Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstr. 3, 85748, Garching bei M\u00fcnchen, Germany","TUM Campus Straubing for Biotechnology and Sustainability, Weihenstephan-Triesdorf University of Applied Sciences, Am Essigberg 3, 94315, Straubing, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0897-3571","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstr. 3, 85748, Garching bei M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"TUM Campus Straubing for Biotechnology and Sustainability, Weihenstephan-Triesdorf University of Applied Sciences, Am Essigberg 3, 94315, Straubing, Germany","institution_ids":["https://openalex.org/I309496635"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061295470","display_name":"Daniel Vanderpooten","orcid":"https://orcid.org/0000-0002-5934-0603"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Daniel Vanderpooten","raw_affiliation_strings":["CNRS, LAMSADE, Universit\u00e9 Paris-Dauphine, PSL Reseach University, 75016, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, LAMSADE, Universit\u00e9 Paris-Dauphine, PSL Reseach University, 75016, Paris, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5002493273"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I56435720"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.3885,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55805806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"100","issue":"1","first_page":"5","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9952999949455261,"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":0.9952999949455261,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9945999979972839,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9779999852180481,"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/algorithm","display_name":"Algorithm","score":0.6118504405021667},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39642202854156494},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3318782448768616}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6118504405021667},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39642202854156494},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3318782448768616}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00186-023-00836-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00186-023-00836-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-023-00836-x.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04792033v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04792033","pdf_url":"https://hal.science/hal-04792033/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"Mathematical Methods of Operations Research, 2023, 100 (1), pp.5-25. &#x27E8;10.1007/s00186-023-00836-x&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:econstor.eu:10419/313669","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/313669","pdf_url":"https://www.econstor.eu/bitstream/10419/313669/1/s00186-023-00836-x.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:econstor.eu:10419/317041","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/317041","pdf_url":"https://www.econstor.eu/bitstream/10419/317041/1/00186_2023_Article_836.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:RePEc:spr:mathme:v:100:y:2024:i:1:d:10.1007_s00186-023-00836-x","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00186-023-00836-x","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1732096","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1732096","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1763490","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1763490","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00186-023-00836-x","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00186-023-00836-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-023-00836-x.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387091849.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W80157279","https://openalex.org/W1928381443","https://openalex.org/W2026427926","https://openalex.org/W2038225707","https://openalex.org/W2039219233","https://openalex.org/W2040924621","https://openalex.org/W2128953879","https://openalex.org/W2129143099","https://openalex.org/W2132147722","https://openalex.org/W2148712149","https://openalex.org/W2551495248","https://openalex.org/W3099831561","https://openalex.org/W3128852614"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2317200988","https://openalex.org/W2376932109","https://openalex.org/W2382290278","https://openalex.org/W2350741829"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,95],"well":[3],"known":[4],"that,":[5],"under":[6],"very":[7],"weak":[8],"assumptions,":[9],"multiobjective":[10,141,220],"optimization":[11,221],"problems":[12,103],"admit":[13],"$$(1+\\varepsilon":[14,116,248],",\\dots":[15,117,249],",1+\\varepsilon":[16,118,250],")$$":[17,119,251],"<mml:math":[18,40,60,75,87,120,192,252],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[19,41,61,76,88,121,193,253],"<mml:mrow>":[20,77,89,122,194,254],"<mml:mo>(</mml:mo>":[21,123,255],"<mml:mn>1</mml:mn>":[22,28,63,78,124,130,195,256,262],"<mml:mo>+</mml:mo>":[23,29,79,125,131,196,257,263],"<mml:mi>\u03b5</mml:mi>":[24,30,42,64,80,90,126,132,197,258,264],"<mml:mo>,</mml:mo>":[25,27,127,129,259,261],"<mml:mo>\u22ef</mml:mo>":[26,128,260],"<mml:mo>)</mml:mo>":[31,133,265],"</mml:mrow>":[32,81,93,134,198,266],"</mml:math>":[33,43,66,82,94,135,199,267],"-approximation":[34,268],"sets":[35,45,163,212,230],"(also":[36],"called":[37],"$$\\varepsilon":[38,85],"$$":[39,74,191],"-Pareto":[44],")":[46],"of":[47,53,72,151,177,181,189,207,234,246],"polynomial":[48],"cardinality":[49,245],"(in":[50],"the":[51,54,96,107,140,144,152,182,205,235,243],"size":[52],"instance":[55],"and":[56,238],"in":[57,139,149,155,179,200],"$$\\frac{1}{\\varepsilon":[58],"}$$":[59],"<mml:mfrac>":[62],"</mml:mfrac>":[65],").":[67],"While":[68],"an":[69,174],"approximation":[70,113,145,162,175,211,229],"guarantee":[71,176,188],"$$1+\\varepsilon":[73,190],"for":[83,101,218],"any":[84],"&gt;0$$":[86],"<mml:mo>&gt;</mml:mo>":[91],"<mml:mn>0</mml:mn>":[92],"best":[97],"one":[98],"can":[99,136],"expect":[100],"singleobjective":[102],"(apart":[104],"from":[105],"solving":[106],"problem":[108],"to":[109,166,216,242],"optimality),":[110],"even":[111],"better":[112],"guarantees":[114],"than":[115],"be":[137,147],"considered":[138],"case":[142],"since":[143],"might":[146],"exact":[148,161,210,228],"some":[150,180],"objectives.":[153],"Hence,":[154],"this":[156],"paper,":[157],"we":[158,224],"consider":[159],"partially":[160,209,227],"that":[164,213],"require":[165],"approximate":[167],"each":[168],"feasible":[169],"solution":[170],"exactly,":[171],"i.e.,":[172],"with":[173],"1,":[178],"objectives":[183],"while":[184],"still":[185],"obtaining":[186],"a":[187,247],"all":[201],"others.":[202],"We":[203],"characterize":[204],"types":[206],"polynomial-cardinality,":[208],"are":[214],"guaranteed":[215],"exist":[217],"general":[219],"problems.":[222],"Moreover,":[223],"study":[225],"minimum-cardinality":[226],"concerning":[231],"(weak)":[232],"efficiency":[233],"contained":[236],"solutions":[237],"relate":[239],"their":[240],"cardinalities":[241],"minimum":[244],"set.":[269]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-09-28T00:00:00"}
