{"id":"https://openalex.org/W4213433964","doi":"https://doi.org/10.1109/tnse.2022.3153095","title":"A Discrete Moth-Flame Optimization With an $l_2$-Norm Constraint for Network Clustering","display_name":"A Discrete Moth-Flame Optimization With an $l_2$-Norm Constraint for Network Clustering","publication_year":2022,"publication_date":"2022-02-23","ids":{"openalex":"https://openalex.org/W4213433964","doi":"https://doi.org/10.1109/tnse.2022.3153095"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2022.3153095","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2022.3153095","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-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/A5100680344","display_name":"Xianghua Li","orcid":"https://orcid.org/0000-0003-0253-3882"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]},{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianghua Li","raw_affiliation_strings":["School of Artificial Intelligence, Optics, and Electronics (iOPEN), Northwestern Polytechnical University, Xian, China","College of Computer and Information Science & College of Software, Southwest University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0003-0253-3882","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Optics, and Electronics (iOPEN), Northwestern Polytechnical University, Xian, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"College of Computer and Information Science & College of Software, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101550167","display_name":"Xin Qi","orcid":"https://orcid.org/0000-0003-4572-059X"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Qi","raw_affiliation_strings":["College of Computer and Information Science & College of Software, Southwest University, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Information Science & College of Software, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064861128","display_name":"Xingjian Liu","orcid":"https://orcid.org/0000-0003-4158-3655"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingjian Liu","raw_affiliation_strings":["College of Computer and Information Science & College of Software, Southwest University, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Information Science & College of Software, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086236078","display_name":"Chao Gao","orcid":"https://orcid.org/0000-0002-5865-2285"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]},{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Gao","raw_affiliation_strings":["School of Artificial Intelligence, Optics, and Electronics (iOPEN), Northwestern Polytechnical University, Xian, China","College of Computer and Information Science & College of Software, Southwest University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0002-5865-2285","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Optics, and Electronics (iOPEN), Northwestern Polytechnical University, Xian, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"College of Computer and Information Science & College of Software, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100422377","display_name":"Zhen Wang","orcid":"https://orcid.org/0000-0002-8182-2852"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Wang","raw_affiliation_strings":["School of Artificial Intelligence, Optics, and Electronics (iOPEN), Northwestern Polytechnical University, Xian, China"],"raw_orcid":"https://orcid.org/0000-0002-8182-2852","affiliations":[{"raw_affiliation_string":"School of Artificial Intelligence, Optics, and Electronics (iOPEN), Northwestern Polytechnical University, Xian, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109399239","display_name":"Fan Zhang","orcid":"https://orcid.org/0000-0002-6714-9534"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fan Zhang","raw_affiliation_strings":["College of Computer and Information Science & College of Software, Southwest University, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Information Science & College of Software, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062375227","display_name":"Jiming Liu","orcid":"https://orcid.org/0000-0002-8669-9064"},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jiming Liu","raw_affiliation_strings":["Department of Computer Science, Hong Kong Baptist University, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0002-8669-9064","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hong Kong Baptist University, Hong Kong","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1229,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.7563867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"3","first_page":"1776","last_page":"1788"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9954000115394592,"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"}},{"id":"https://openalex.org/T11165","display_name":"Image and Video Quality Assessment","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/cluster-analysis","display_name":"Cluster analysis","score":0.6481457948684692},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.555040717124939},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4925433099269867},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4907344579696655},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4882388412952423},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46035999059677124},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.44948703050613403},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4169120788574219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3410000205039978},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3283226788043976},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18415477871894836}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6481457948684692},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.555040717124939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4925433099269867},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4907344579696655},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4882388412952423},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46035999059677124},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.44948703050613403},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4169120788574219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3410000205039978},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3283226788043976},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18415477871894836},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tnse.2022.3153095","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2022.3153095","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G114355967","display_name":null,"funder_award_id":"D5000210738","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2201705706","display_name":null,"funder_award_id":"D5000210827","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3794980888","display_name":"\u6570\u636e\u9a71\u52a8\u7684\u884c\u4e3a\u51b3\u7b56\u7406\u8bba\u3001\u5b9e\u9a8c\u53ca\u5e94\u7528\u7814\u7a76","funder_award_id":"11931015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3798114921","display_name":null,"funder_award_id":"171105","funder_id":"https://openalex.org/F4320334945","funder_display_name":"Fok Ying Tong Education Foundation"},{"id":"https://openalex.org/G4668225214","display_name":null,"funder_award_id":"62025602","funder_id":"https://openalex.org/F4320336125","funder_display_name":"National Science Fund for Distinguished Young Scholars"},{"id":"https://openalex.org/G8164477345","display_name":"\u6570\u636e\u9a71\u52a8\u7684\u793e\u4ea4\u7f51\u7edc\u4f20\u64ad\u63a7\u5236\u5173\u952e\u7406\u8bba\u4e0e\u6280\u672f\u7814\u7a76","funder_award_id":"61976181","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8252796664","display_name":null,"funder_award_id":"U1803263","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G941792394","display_name":null,"funder_award_id":"2022JM-325","funder_id":"https://openalex.org/F4320324173","funder_display_name":"Natural Science Foundation of Shaanxi Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324173","display_name":"Natural Science Foundation of Shaanxi Province","ror":null},{"id":"https://openalex.org/F4320334945","display_name":"Fok Ying Tong Education Foundation","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null},{"id":"https://openalex.org/F4320336125","display_name":"National Science Fund for Distinguished Young Scholars","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W341879454","https://openalex.org/W883434633","https://openalex.org/W1497990247","https://openalex.org/W1971421925","https://openalex.org/W1985625141","https://openalex.org/W1994661745","https://openalex.org/W2038920443","https://openalex.org/W2065179205","https://openalex.org/W2089458547","https://openalex.org/W2094234423","https://openalex.org/W2096166399","https://openalex.org/W2097464974","https://openalex.org/W2103704311","https://openalex.org/W2108031918","https://openalex.org/W2120043163","https://openalex.org/W2125213524","https://openalex.org/W2130545965","https://openalex.org/W2143381319","https://openalex.org/W2155167324","https://openalex.org/W2169490594","https://openalex.org/W2171552940","https://openalex.org/W2228765530","https://openalex.org/W2279005051","https://openalex.org/W2330471763","https://openalex.org/W2466134622","https://openalex.org/W2513970330","https://openalex.org/W2517600007","https://openalex.org/W2522228482","https://openalex.org/W2523540531","https://openalex.org/W2563039760","https://openalex.org/W2566207299","https://openalex.org/W2592380430","https://openalex.org/W2605810061","https://openalex.org/W2613771876","https://openalex.org/W2614053601","https://openalex.org/W2616650140","https://openalex.org/W2747781258","https://openalex.org/W2766252508","https://openalex.org/W2805552432","https://openalex.org/W2885713120","https://openalex.org/W2896014807","https://openalex.org/W2902191103","https://openalex.org/W2910559764","https://openalex.org/W2911319480","https://openalex.org/W2919979744","https://openalex.org/W2926960342","https://openalex.org/W2936227260","https://openalex.org/W2964102700","https://openalex.org/W3014974411","https://openalex.org/W3089511768","https://openalex.org/W3114893929","https://openalex.org/W3134651880","https://openalex.org/W3144393856"],"related_works":["https://openalex.org/W2086397253","https://openalex.org/W2133122801","https://openalex.org/W600422426","https://openalex.org/W2007156430","https://openalex.org/W3081478936","https://openalex.org/W2785612136","https://openalex.org/W2099529706","https://openalex.org/W1988224651","https://openalex.org/W2560916850","https://openalex.org/W2148224044"],"abstract_inverted_index":{"Complex":[0],"network":[1,113],"clustering":[2],"problems":[3],"have":[4],"been":[5],"gained":[6],"great":[7],"popularity":[8],"and":[9,13,55,105,119,149,152,159],"widespread":[10],"researches":[11],"recently,":[12],"plentiful":[14],"optimization":[15,26,87],"algorithms":[16],"are":[17,144],"aimed":[18],"at":[19,29],"this":[20],"problem.":[21],"Among":[22],"these":[23,49],"methods,":[24],"the":[25,34,53,67,70,100,106,124,137,153,156],"methods":[27,50],"aiming":[28],"multiple":[30],"objectives":[31],"can":[32],"break":[33],"limitations":[35],"(e.g.,":[36],"instability)":[37],"of":[38,69,161],"those":[39],"optimizing":[40],"single":[41],"objective.":[42],"However,":[43],"one":[44],"shortcoming":[45],"stands":[46],"out":[47],"that":[48],"cannot":[51],"balance":[52,117],"exploration":[54,118],"exploitation":[56],"well.":[57],"In":[58],"another":[59],"sentence,":[60],"it":[61],"fails":[62],"to":[63,92,116],"optimize":[64],"solutions":[65,72],"on":[66,136,146],"basis":[68],"good":[71],"obtained":[73],"so":[74],"far.":[75],"Inspired":[76],"by":[77],"nature,":[78],"a":[79,95,129],"new":[80],"optimized":[81],"method,":[82],"named":[83],"multi-objective":[84],"discrete":[85],"moth-flame":[86],"(DMFO)":[88],"method":[89,132],"is":[90],"proposed":[91],"achieve":[93],"such":[94],"tradeoff.":[96],"Specifically,":[97],"we":[98,122],"redefine":[99],"simple":[101],"flame":[102],"generation":[103],"(SFG)":[104],"spiral":[107],"flight":[108],"search":[109],"(SFS)":[110],"processes":[111],"with":[112,133],"topology":[114],"structure":[115],"exploitation.":[120],"Moreover,":[121],"present":[123],"DMFO":[125,163],"in":[126],"detail":[127],"utilizing":[128],"Tchebycheff":[130],"decomposition":[131],"an$l_2$-norm":[134],"constraint":[135],"direction":[138],"vector":[139],"(2-Tch).":[140],"Besides":[141],"that,":[142],"experiments":[143],"taken":[145],"both":[147],"synthetic":[148],"real-world":[150],"networks":[151],"results":[154],"demonstrate":[155],"high":[157],"efficiency":[158],"promises":[160],"our":[162],"when":[164],"tackling":[165],"dividing":[166],"complex":[167],"networks.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}