{"id":"https://openalex.org/W7120113566","doi":"https://doi.org/10.1002/net.70025","title":"On the Multi\u2010Commodity Flow With Convex Objective Function: Column\u2010Generation Approaches","display_name":"On the Multi\u2010Commodity Flow With Convex Objective Function: Column\u2010Generation Approaches","publication_year":2026,"publication_date":"2026-01-10","ids":{"openalex":"https://openalex.org/W7120113566","doi":"https://doi.org/10.1002/net.70025"},"language":"en","primary_location":{"id":"doi:10.1002/net.70025","is_oa":true,"landing_page_url":"https://doi.org/10.1002/net.70025","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/net.70025","source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/net.70025","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5122598542","display_name":"Beraud\u2010Sudreau Guillaume","orcid":null},"institutions":[{"id":"https://openalex.org/I4210123571","display_name":"Huawei Technologies (France)","ror":"https://ror.org/02rbzf697","country_code":"FR","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210123571"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Beraud\u2010Sudreau Guillaume","raw_affiliation_strings":["Huawei Technologies Ltd., Paris Research Center  Boulogne\u2010Billancourt France"],"raw_orcid":"https://orcid.org/0009-0000-6686-8476","affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd., Paris Research Center  Boulogne\u2010Billancourt France","institution_ids":["https://openalex.org/I4210123571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122472173","display_name":"L\u00e9tocart Lucas","orcid":null},"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/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210156583","display_name":"Laboratoire d'Informatique de Paris-Nord","ror":"https://ror.org/05g1zjw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210156583","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"L\u00e9tocart Lucas","raw_affiliation_strings":["Universit\u00e9 Sorbonne Paris Nord, CNRS Laboratoire d'Informatique de Paris Nord, LIPN  Villetaneuse France"],"raw_orcid":"https://orcid.org/0000-0002-4919-9036","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Sorbonne Paris Nord, CNRS Laboratoire d'Informatique de Paris Nord, LIPN  Villetaneuse France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210156583","https://openalex.org/I1294671590","https://openalex.org/I4210091279"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5122409514","display_name":"Magnouche Youcef","orcid":null},"institutions":[{"id":"https://openalex.org/I4210123571","display_name":"Huawei Technologies (France)","ror":"https://ror.org/02rbzf697","country_code":"FR","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210123571"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Magnouche Youcef","raw_affiliation_strings":["Huawei Technologies Ltd., Paris Research Center  Boulogne\u2010Billancourt France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd., Paris Research Center  Boulogne\u2010Billancourt France","institution_ids":["https://openalex.org/I4210123571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5122470796","display_name":"Martin S\u00e9bastien","orcid":null},"institutions":[{"id":"https://openalex.org/I4210123571","display_name":"Huawei Technologies (France)","ror":"https://ror.org/02rbzf697","country_code":"FR","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210123571"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Martin S\u00e9bastien","raw_affiliation_strings":["Huawei Technologies Ltd., Paris Research Center  Boulogne\u2010Billancourt France"],"raw_orcid":"https://orcid.org/0000-0002-8528-6698","affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd., Paris Research Center  Boulogne\u2010Billancourt France","institution_ids":["https://openalex.org/I4210123571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5122598542"],"corresponding_institution_ids":["https://openalex.org/I4210123571"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05610689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":"3","first_page":"322","last_page":"338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10847","display_name":"Advanced Optical Network Technologies","score":0.5741999745368958,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10847","display_name":"Advanced Optical Network Technologies","score":0.5741999745368958,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.16449999809265137,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10714","display_name":"Software-Defined Networks and 5G","score":0.1006999984383583,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/regular-polygon","display_name":"Regular polygon","score":0.6255999803543091},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6116999983787537},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5960000157356262},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.5047000050544739},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.47620001435279846},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.4747999906539917},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.45320001244544983},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.42160001397132874}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7098000049591064},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6255999803543091},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6116999983787537},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5960000157356262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5263000130653381},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.47620001435279846},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.4747999906539917},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.42160001397132874},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3441999852657318},{"id":"https://openalex.org/C192126672","wikidata":"https://www.wikidata.org/wiki/Q1068715","display_name":"Telecommunications network","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.3010999858379364},{"id":"https://openalex.org/C114563136","wikidata":"https://www.wikidata.org/wiki/Q19725982","display_name":"Network planning and design","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.27959999442100525},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.26330000162124634}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.70025","is_oa":true,"landing_page_url":"https://doi.org/10.1002/net.70025","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/net.70025","source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/net.70025","is_oa":true,"landing_page_url":"https://doi.org/10.1002/net.70025","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/net.70025","source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7120113566.pdf","grobid_xml":"https://content.openalex.org/works/W7120113566.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W2005069425","https://openalex.org/W2021136283","https://openalex.org/W2045068465","https://openalex.org/W2069808690","https://openalex.org/W2097155690","https://openalex.org/W2111162397","https://openalex.org/W2112952306","https://openalex.org/W2136885855","https://openalex.org/W2140409200","https://openalex.org/W2171830873","https://openalex.org/W2585959123","https://openalex.org/W2613070411","https://openalex.org/W4231610975","https://openalex.org/W4250589301","https://openalex.org/W4293860921"],"related_works":[],"abstract_inverted_index":{"ABSTRACT":[0],"The":[1,164],"purpose":[2],"of":[3,32,78,152],"this":[4,65],"work":[5],"is":[6,22,42,69],"to":[7,23,98,137],"develop":[8],"an":[9],"algorithmic":[10],"optimization":[11],"approach":[12,133],"for":[13,84,175],"a":[14,59,129,172],"capacitated":[15],"multi\u2010commodity":[16,92],"flow":[17,93],"problem,":[18],"where":[19,29,48],"the":[20,25,30,55,73,90,107,120,139],"objective":[21,41],"minimize":[24],"total":[26],"link":[27,60],"costs,":[28],"cost":[31,142,155],"each":[33,123],"arc":[34,146],"increases":[35],"convexly":[36,140],"with":[37,145],"its":[38,101],"utilization.":[39],"This":[40,87],"particularly":[43],"relevant":[44],"in":[45,119,179],"telecommunication":[46,181],"networks,":[47],"device":[49],"performance":[50],"can":[51,111],"deteriorate":[52],"significantly":[53],"as":[54],"available":[56,79],"bandwidth":[57],"on":[58],"becomes":[61],"limited.":[62],"By":[63],"optimizing":[64],"convex":[66,91,153,161],"function,":[67],"traffic":[68],"efficiently":[70],"distributed":[71,114],"across":[72,115],"network,":[74],"ensuring":[75],"optimal":[76],"use":[77],"resources":[80],"and":[81,95,103],"preserving":[82],"capacity":[83],"future":[85],"demands.":[86],"paper":[88],"describes":[89],"problem":[94],"presents":[96],"methodologies":[97],"solve":[99],"both":[100],"Splittable":[102,108],"Unsplittable":[104,121],"variants.":[105],"In":[106],"version,":[109,122],"flows":[110,178],"be":[112,126],"fractionally":[113],"multiple":[116],"paths,":[117],"while":[118],"commodity":[124],"must":[125],"routed":[127],"through":[128],"single":[130],"path.":[131],"Our":[132],"employs":[134],"Column\u2010Generation":[135],"techniques":[136],"address":[138],"increasing":[141,154,162],"functions":[143],"associated":[144],"utilization,":[147],"effectively":[148],"accommodating":[149],"various":[150],"forms":[151],"functions,":[156],"including":[157],"non\u2010differentiable":[158],"or":[159],"black\u2010box":[160],"functions.":[163],"proposed":[165],"methods":[166],"demonstrate":[167],"strong":[168],"computational":[169],"efficiency,":[170],"offering":[171],"robust":[173],"framework":[174],"managing":[176],"network":[177],"complex":[180],"environments.":[182]},"counts_by_year":[],"updated_date":"2026-03-12T06:13:28.667946","created_date":"2026-01-10T00:00:00"}
