{"id":"https://openalex.org/W4386380125","doi":"https://doi.org/10.1007/s10957-023-02285-2","title":"A Solver for Multiobjective Mixed-Integer Convex and Nonconvex Optimization","display_name":"A Solver for Multiobjective Mixed-Integer Convex and Nonconvex Optimization","publication_year":2023,"publication_date":"2023-09-01","ids":{"openalex":"https://openalex.org/W4386380125","doi":"https://doi.org/10.1007/s10957-023-02285-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-023-02285-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-023-02285-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02285-2.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02285-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020142332","display_name":"Gabriele Eichfelder","orcid":"https://orcid.org/0000-0002-1938-6316"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gabriele Eichfelder","raw_affiliation_strings":["Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Po 10 05 65, 98684, Ilmenau, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1938-6316","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Po 10 05 65, 98684, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052388878","display_name":"Oliver Stein","orcid":"https://orcid.org/0000-0001-9514-6317"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Oliver Stein","raw_affiliation_strings":["Institute for Operations Research, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany"],"raw_orcid":"https://orcid.org/0000-0001-9514-6317","affiliations":[{"raw_affiliation_string":"Institute for Operations Research, Karlsruhe Institute of Technology (KIT), 76128, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090014256","display_name":"Leo Warnow","orcid":"https://orcid.org/0000-0002-2177-8466"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Leo Warnow","raw_affiliation_strings":["Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Po 10 05 65, 98684, Ilmenau, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2177-8466","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Po 10 05 65, 98684, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052388878"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":6.1035,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.97725569,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"203","issue":"2","first_page":"1736","last_page":"1766"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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":0.9994999766349792,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9958999752998352,"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":0.9955999851226807,"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/mathematics","display_name":"Mathematics","score":0.6986883282661438},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6902778148651123},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6525229811668396},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5448676347732544},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5360204577445984},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.49811768531799316},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.48926588892936707},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45439010858535767},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.43725669384002686},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.4265693128108978},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3828210234642029},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3643907308578491},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.3314596712589264},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21837103366851807}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6986883282661438},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6902778148651123},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6525229811668396},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5448676347732544},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5360204577445984},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.49811768531799316},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.48926588892936707},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45439010858535767},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.43725669384002686},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.4265693128108978},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3828210234642029},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3643907308578491},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3314596712589264},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21837103366851807},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10957-023-02285-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-023-02285-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02285-2.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000162197","is_oa":true,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000162197","pdf_url":"https://publikationen.bibliothek.kit.edu/1000162197/151323387","source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"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":"Journal of Optimization Theory and Applications","raw_type":"doc-type:article"},{"id":"pmh:oai:www.db-thueringen.de:dbt_mods_00068413","is_oa":true,"landing_page_url":"https://www.db-thueringen.de/receive/dbt_mods_00068413","pdf_url":"https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00069812/1573-2878_203_2024_2_1736-1766.pdf","source":{"id":"https://openalex.org/S4306400120","display_name":"Common Library Network (Der Gemeinsame Bibliotheksverbund)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210149878","host_organization_name":"Verbundzentrale des GBV","host_organization_lineage":["https://openalex.org/I4210149878"],"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:joptap:v:203:y:2024:i:2:d:10.1007_s10957-023-02285-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-023-02285-2","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":"doi:10.5445/ir/1000162197","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000162197","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s10957-023-02285-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-023-02285-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-023-02285-2.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8031306723","display_name":null,"funder_award_id":"432218631","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386380125.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W138692475","https://openalex.org/W178772886","https://openalex.org/W596285643","https://openalex.org/W615245433","https://openalex.org/W1483874187","https://openalex.org/W1981009968","https://openalex.org/W1984425167","https://openalex.org/W2032234281","https://openalex.org/W2037534711","https://openalex.org/W2048944090","https://openalex.org/W2058329377","https://openalex.org/W2064823886","https://openalex.org/W2078600458","https://openalex.org/W2087591761","https://openalex.org/W2155014525","https://openalex.org/W2407151459","https://openalex.org/W2418368257","https://openalex.org/W2512482484","https://openalex.org/W2582889117","https://openalex.org/W2607047547","https://openalex.org/W2804784253","https://openalex.org/W2899062086","https://openalex.org/W2964996841","https://openalex.org/W2966382902","https://openalex.org/W2977396163","https://openalex.org/W3118872643","https://openalex.org/W3124460525","https://openalex.org/W3146520007","https://openalex.org/W3172965851","https://openalex.org/W3175896303","https://openalex.org/W3202889218","https://openalex.org/W3207466956","https://openalex.org/W3216881728","https://openalex.org/W4220712670","https://openalex.org/W4242862890","https://openalex.org/W4283774417","https://openalex.org/W4292864963","https://openalex.org/W4302557773","https://openalex.org/W4385491520","https://openalex.org/W4389463704"],"related_works":["https://openalex.org/W2374624997","https://openalex.org/W2363904277","https://openalex.org/W868123585","https://openalex.org/W2578380588","https://openalex.org/W2375652826","https://openalex.org/W981962503","https://openalex.org/W4296997005","https://openalex.org/W2300145982","https://openalex.org/W2128601753","https://openalex.org/W4237382690"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2,207],"proposes":[3],"a":[4,70,77,136,209,218,233],"general":[5],"framework":[6],"for":[7,41,84,128,145,184,214,229,235,249],"solving":[8],"multiobjective":[9,48,87,129,172,211,236],"nonconvex":[10,52,86,238],"optimization":[11,14,53,131,239],"problems,":[12],"i.e.,":[13],"problems":[15,54,216],"in":[16,73,100,162,222],"which":[17,79,166],"multiple":[18],"objective":[19,33],"functions":[20],"have":[21],"to":[22,93,104,118,197],"be":[23],"optimized":[24],"simultaneously.":[25],"Thereby,":[26],"the":[27,32,44,59,74,94,147,163,185,189,198,203,206,223,230,244,250],"nonconvexity":[28],"might":[29],"come":[30],"from":[31,38,171,194],"or":[34,37],"constraint":[35],"functions,":[36],"integrality":[39],"conditions":[40],"some":[42],"of":[43,61,139,149,160,188,246],"variables.":[45],"In":[46],"particular,":[47],"mixed-integer":[49,95,130,173,190,212,237],"convex":[50,174,179,186,215],"and":[51,57,112,126],"are":[55,116,135,167],"covered":[56],"form":[58],"motivation":[60],"our":[62],"studies.":[63],"The":[64],"presented":[65],"algorithm":[66,121],"is":[67,97,123,143,227,240],"based":[68,168],"on":[69,169,202],"branch-and-bound":[71,152],"method":[72,92,153],"pre-image":[75],"space,":[76],"technique":[78],"was":[80],"already":[81],"successfully":[82],"applied":[83],"continuous":[85,178],"optimization.":[88,175],"However,":[89],"extending":[90],"this":[91,140,150],"setting":[96],"not":[98],"straightforward,":[99],"particular":[101],"with":[102,157,181,217,258],"regard":[103],"convergence":[105],"results.":[106],"More":[107],"precisely,":[108],"new":[109,151,210,251],"branching":[110],"rules":[111],"lower":[113],"bounding":[114],"procedures":[115],"needed":[117],"obtain":[119],"an":[120],"that":[122],"practically":[124],"applicable":[125],"convergent":[127],"problems.":[132],"Corresponding":[133],"results":[134,245],"main":[137],"contribution":[138],"paper.":[141],"What":[142,226],"more,":[144,228],"improving":[146],"performance":[148],"we":[154,255],"enhance":[155],"it":[156,257],"two":[158],"types":[159],"cuts":[161,183],"image":[164,191,224],"space":[165],"ideas":[170],"Those":[176],"combine":[177],"relaxations":[180],"adaptive":[182],"hull":[187],"set,":[192],"derived":[193],"supporting":[195],"hyperplanes":[196],"relaxed":[199],"sets.":[200],"Based":[201],"above":[204],"ingredients,":[205],"provides":[208],"solver":[213,234],"stopping":[219],"criterion":[220],"purely":[221],"space.":[225],"first":[231],"time":[232],"presented.":[241],"We":[242],"provide":[243],"numerical":[247],"tests":[248],"algorithm.":[252],"Where":[253],"possible,":[254],"compare":[256],"existing":[259],"procedures.":[260]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
