{"id":"https://openalex.org/W3191334631","doi":"https://doi.org/10.1109/cec45853.2021.9504711","title":"An Approximation-based Chemical Reaction Algorithm for Combinatorial Multi-Objective Bi-level Optimization Problems","display_name":"An Approximation-based Chemical Reaction Algorithm for Combinatorial Multi-Objective Bi-level Optimization Problems","publication_year":2021,"publication_date":"2021-06-28","ids":{"openalex":"https://openalex.org/W3191334631","doi":"https://doi.org/10.1109/cec45853.2021.9504711","mag":"3191334631"},"language":"en","primary_location":{"id":"doi:10.1109/cec45853.2021.9504711","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec45853.2021.9504711","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042057923","display_name":"Malek Abbassi","orcid":"https://orcid.org/0000-0002-4252-4254"},"institutions":[{"id":"https://openalex.org/I4210099416","display_name":"Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes","ror":"https://ror.org/00t3fpp34","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I198244214","https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993","https://openalex.org/I4210099416","https://openalex.org/I4210123221","https://openalex.org/I4210159245","https://openalex.org/I4387154249"]},{"id":"https://openalex.org/I4210140729","display_name":"Institut Sup\u00e9rieur de Gestion de Tunis","ror":"https://ror.org/04w9mdw91","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496","https://openalex.org/I4210140729"]},{"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/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]},{"id":"https://openalex.org/I3019848993","display_name":"Mines Saint-\u00c9tienne","ror":"https://ror.org/05a1dws80","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993"]}],"countries":["FR","TN"],"is_corresponding":true,"raw_author_name":"Malek Abbassi","raw_affiliation_strings":["Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, CMP, Gardanne, France","SMART Lab, Institut Superieur de Gestion de Tunis, Universit\u00e9 de Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, CMP, Gardanne, France","institution_ids":["https://openalex.org/I3019848993","https://openalex.org/I4210099416","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"SMART Lab, Institut Superieur de Gestion de Tunis, Universit\u00e9 de Tunis, Tunisia","institution_ids":["https://openalex.org/I4210140729","https://openalex.org/I108714496"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040931960","display_name":"Abir Chaabani","orcid":"https://orcid.org/0000-0003-0283-6111"},"institutions":[{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]},{"id":"https://openalex.org/I4210140729","display_name":"Institut Sup\u00e9rieur de Gestion de Tunis","ror":"https://ror.org/04w9mdw91","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496","https://openalex.org/I4210140729"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Abir Chaabani","raw_affiliation_strings":["SMART Lab, Institut Superieur de Gestion de Tunis, Universit\u00e9 de Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"SMART Lab, Institut Superieur de Gestion de Tunis, Universit\u00e9 de Tunis, Tunisia","institution_ids":["https://openalex.org/I4210140729","https://openalex.org/I108714496"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028612749","display_name":"Lamjed Ben Sa\u00efd","orcid":"https://orcid.org/0000-0001-9225-884X"},"institutions":[{"id":"https://openalex.org/I4210140729","display_name":"Institut Sup\u00e9rieur de Gestion de Tunis","ror":"https://ror.org/04w9mdw91","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496","https://openalex.org/I4210140729"]},{"id":"https://openalex.org/I108714496","display_name":"Tunis University","ror":"https://ror.org/02q1spa57","country_code":"TN","type":"education","lineage":["https://openalex.org/I108714496"]}],"countries":["TN"],"is_corresponding":false,"raw_author_name":"Lamjed Ben Said","raw_affiliation_strings":["SMART Lab, Institut Superieur de Gestion de Tunis, Universit\u00e9 de Tunis, Tunisia"],"affiliations":[{"raw_affiliation_string":"SMART Lab, Institut Superieur de Gestion de Tunis, Universit\u00e9 de Tunis, Tunisia","institution_ids":["https://openalex.org/I4210140729","https://openalex.org/I108714496"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040988044","display_name":"Nabil Absi","orcid":"https://orcid.org/0000-0002-9701-5772"},"institutions":[{"id":"https://openalex.org/I4210099416","display_name":"Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes","ror":"https://ror.org/00t3fpp34","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I198244214","https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993","https://openalex.org/I4210099416","https://openalex.org/I4210123221","https://openalex.org/I4210159245","https://openalex.org/I4387154249"]},{"id":"https://openalex.org/I3019848993","display_name":"Mines Saint-\u00c9tienne","ror":"https://ror.org/05a1dws80","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993"]},{"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nabil Absi","raw_affiliation_strings":["Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, CMP, Gardanne, France"],"affiliations":[{"raw_affiliation_string":"Mines Saint-Etienne, Univ Clermont Auvergne, CNRS, UMR 6158 LIMOS, CMP, Gardanne, France","institution_ids":["https://openalex.org/I3019848993","https://openalex.org/I4210099416","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042057923"],"corresponding_institution_ids":["https://openalex.org/I108714496","https://openalex.org/I1294671590","https://openalex.org/I3019848993","https://openalex.org/I4210099416","https://openalex.org/I4210140729"],"apc_list":null,"apc_paid":null,"fwci":0.151,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55391623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1627","last_page":"1634"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9986000061035156,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9984999895095825,"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/T11053","display_name":"Process Optimization and Integration","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.6709151268005371},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6558637619018555},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6062703728675842},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5220919847488403},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4917488396167755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4427244961261749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3059815764427185}],"concepts":[{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.6709151268005371},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6558637619018555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6062703728675842},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5220919847488403},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4917488396167755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4427244961261749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3059815764427185}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec45853.2021.9504711","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec45853.2021.9504711","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1530116698","https://openalex.org/W1604175135","https://openalex.org/W2001759562","https://openalex.org/W2007103412","https://openalex.org/W2016969860","https://openalex.org/W2042980903","https://openalex.org/W2068191845","https://openalex.org/W2071707442","https://openalex.org/W2079881116","https://openalex.org/W2136554306","https://openalex.org/W2254218369","https://openalex.org/W2587953039","https://openalex.org/W2777647696","https://openalex.org/W2807256486","https://openalex.org/W2884337142","https://openalex.org/W2999998384","https://openalex.org/W3080250077","https://openalex.org/W3091163952","https://openalex.org/W3149404301"],"related_works":["https://openalex.org/W2366525864","https://openalex.org/W4285140130","https://openalex.org/W3104770499","https://openalex.org/W4285677055","https://openalex.org/W1992731528","https://openalex.org/W2007843488","https://openalex.org/W1994436307","https://openalex.org/W1987021796","https://openalex.org/W2795565301","https://openalex.org/W2785349417"],"abstract_inverted_index":{"Multi-objective":[0,108],"Bi-Level":[1],"Optimization":[2,111],"Problem":[3,199],"(MBLOP)":[4],"is":[5,16,88,120,141,184],"defined":[6],"as":[7,123],"a":[8,27,60,124,150,187,219],"mathematical":[9],"program":[10],"where":[11],"one":[12],"multi-objective":[13,85,189],"optimization":[14,76],"task":[15],"constrained":[17],"with":[18,156],"another":[19],"one.":[20],"In":[21],"this":[22,98],"way,":[23],"the":[24,33,36,47,52,68,78,84,127,135,162,169,175,179,192,205,228],"evaluation":[25,34,57],"of":[26,35,63,70,80,103,164,178,191,207,222,230,237],"single":[28],"upper":[29],"level":[30,39,129,137],"solution":[31],"necessitates":[32],"whole":[37,176],"lower":[38,128,136],"problem.":[40],"This":[41],"fact":[42],"brings":[43],"new":[44,188],"complexities":[45],"to":[46,51,73,83,126,132,186,211],"bi-level":[48,75],"framework,":[49],"added":[50],"conflicting":[53],"objectives":[54],"and":[55],"their":[56],"which":[58,113,226],"need":[59],"large":[61,220],"number":[62,69,79,163,221],"Function":[64],"Evaluations":[65],"(FEs).":[66],"Despite":[67],"works":[71],"dedicated":[72],"solve":[74],"problems,":[77],"methods":[81],"applied":[82,185],"combinatorial":[86],"case":[87],"much":[89],"reduced.":[90],"Motivated":[91],"by":[92,143,168],"these":[93],"observations,":[94],"we":[95,114],"propose":[96],"in":[97,216],"paper":[99],"an":[100],"approximation-based":[101],"version":[102],"our":[104,208,231],"recently":[105],"proposed":[106,182],"Bi-level":[107,194],"Chemical":[109],"Reaction":[110],"(BMCRO),":[112],"called":[115],"BMCROII.":[116],"The":[117,181,201],"approximation":[118,170],"technique":[119,171],"adopted":[121],"here":[122],"surrogate":[125],"leading":[130],"then":[131],"generate":[133],"efficiently":[134],"optimality.":[138],"Our":[139],"choice":[140],"justified":[142],"two":[144],"main":[145],"arguments.":[146],"First,":[147],"BMCRO":[148],"applies":[149],"Quick":[151],"Non-Dominated":[152],"Sorting":[153],"Algorithm":[154],"(Q-NDSA)":[155],"quasi-linear":[157],"computational":[158],"time":[159],"complexity.":[160],"Second,":[161],"FEs":[165],"savings":[166,223],"gained":[167],"can":[172],"hugely":[173],"improve":[174],"efficiency":[177],"method.":[180],"algorithm":[183,209],"formulation":[190],"well-known":[193],"Multi":[195],"Depot":[196],"Vehicle":[197],"Routing":[198],"(BMDVRP).":[200],"statistical":[202],"analysis":[203],"demonstrates":[204],"outperformance":[206],"compared":[210],"prominent":[212],"baseline":[213],"algorithms":[214],"available":[215],"literature.":[217],"Indeed,":[218],"are":[224],"detected":[225],"confirms":[227],"merits":[229],"proposal":[232],"for":[233],"solving":[234],"such":[235],"type":[236],"NP-hard":[238],"problems.":[239]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
