{"id":"https://openalex.org/W7127045937","doi":"https://doi.org/10.1038/s41598-026-35846-2","title":"Based on binary evolution operator-enhanced black-kite algorithm with natural replacement for engineering numerical optimization problems","display_name":"Based on binary evolution operator-enhanced black-kite algorithm with natural replacement for engineering numerical optimization problems","publication_year":2026,"publication_date":"2026-02-01","ids":{"openalex":"https://openalex.org/W7127045937","doi":"https://doi.org/10.1038/s41598-026-35846-2","pmid":"https://pubmed.ncbi.nlm.nih.gov/41622298"},"language":"en","primary_location":{"id":"doi:10.1038/s41598-026-35846-2","doi":"https://doi.org/10.1038/s41598-026-35846-2","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-35846-2","pdf_url":"https://www.nature.com/articles/s41598-026-35846-2.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","doyens","jufo-1","ki-jl-1","medline","norway-1"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.nature.com/articles/s41598-026-35846-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124731952","display_name":"Huayang Sun","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I85430964","display_name":"Jinzhou Medical University","ror":"https://ror.org/02yd1yr68","country_code":"CN","type":"education","lineage":["https://openalex.org/I85430964"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huayang Sun","raw_affiliation_strings":["School of Health Management, Jinzhou Medical University, Jinzhou, 121001, Liaoning Province, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Health Management, Jinzhou Medical University, Jinzhou, 121001, Liaoning Province, China","institution_ids":["https://openalex.org/I85430964"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124717388","display_name":"Naisheng Tang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naisheng Tang","raw_affiliation_strings":["School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124745265","display_name":"Ziyi Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziyi Li","raw_affiliation_strings":["College of Mathematical Sciences, Sichuan Normal University, Chengdu, 610066, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematical Sciences, Sichuan Normal University, Chengdu, 610066, China","institution_ids":["https://openalex.org/I63354593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5124714480","display_name":"Hao Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I162706563","display_name":"Hoseo University","ror":"https://ror.org/01qyd4k24","country_code":"KR","type":"education","lineage":["https://openalex.org/I162706563"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Hao Chen","raw_affiliation_strings":["School of Business Administration, Hoseo University, 12 Hoseodae-Gil, Dongnam-Gu, Cheonan-Si 31066, Republic of Korea. 20245800@vision.hoseo.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Business Administration, Hoseo University, 12 Hoseodae-Gil, Dongnam-Gu, Cheonan-Si 31066, Republic of Korea. 20245800@vision.hoseo.edu","institution_ids":["https://openalex.org/I162706563"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5124714480"],"corresponding_institution_ids":["https://openalex.org/I162706563"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07244589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"1","first_page":"6881","last_page":"6881"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":1.0,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.0,"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/T12391","display_name":"Artificial Immune Systems Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/metaheuristic-optimization","display_name":"metaheuristic optimization","score":0.8659999966621399},{"id":"https://openalex.org/keywords/simulated-binary-crossover","display_name":"simulated binary crossover","score":0.9279999732971191},{"id":"https://openalex.org/keywords/population-initialization","display_name":"population initialization","score":0.7829999923706055},{"id":"https://openalex.org/keywords/premature-convergence","display_name":"premature convergence","score":0.7139999866485596},{"id":"https://openalex.org/keywords/multi-knapsack-problem","display_name":"multi-knapsack problem","score":0.9120000004768372},{"id":"https://openalex.org/keywords/engineering-design-optimization","display_name":"engineering design optimization","score":0.7450000047683716},{"id":"https://openalex.org/keywords/cec-benchmark-functions","display_name":"CEC benchmark functions","score":0.7749999761581421},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"combinatorial optimization","score":0.7039999961853027}],"concepts":[{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.707099974155426},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6959999799728394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.667900025844574},{"id":"https://openalex.org/C122507166","wikidata":"https://www.wikidata.org/wiki/Q628906","display_name":"Crossover","level":2,"score":0.6270999908447266},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6032999753952026},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5860999822616577},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5503000020980835},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5291000008583069},{"id":"https://openalex.org/C58758708","wikidata":"https://www.wikidata.org/wiki/Q7240233","display_name":"Premature convergence","level":3,"score":0.519599974155426},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4781000018119812},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47589999437332153},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4000000059604645},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C158154518","wikidata":"https://www.wikidata.org/wiki/Q7310970","display_name":"Relevance (law)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C110850998","wikidata":"https://www.wikidata.org/wiki/Q5377895","display_name":"Engineering optimization","level":3,"score":0.3671000003814697},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C4935549","wikidata":"https://www.wikidata.org/wiki/Q6822261","display_name":"Meta-optimization","level":3,"score":0.3167000114917755},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.28349998593330383},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C150185637","wikidata":"https://www.wikidata.org/wiki/Q7705773","display_name":"Test functions for optimization","level":4,"score":0.26660001277923584},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25369998812675476}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1038/s41598-026-35846-2","doi":"https://doi.org/10.1038/s41598-026-35846-2","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-35846-2","pdf_url":"https://www.nature.com/articles/s41598-026-35846-2.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","doyens","jufo-1","ki-jl-1","medline","norway-1"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},{"id":"pmid:41622298","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41622298","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific reports","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:1a3b9eccb5c94924a33e1fd743555e73","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/1a3b9eccb5c94924a33e1fd743555e73","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scientific Reports, Vol 16, Iss 1 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:12916902","doi":null,"is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12916902/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sci Rep","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1038/s41598-026-35846-2","doi":"https://doi.org/10.1038/s41598-026-35846-2","is_oa":true,"landing_page_url":"https://doi.org/10.1038/s41598-026-35846-2","pdf_url":"https://www.nature.com/articles/s41598-026-35846-2.pdf","source":{"id":"https://openalex.org/S196734849","display_name":"Scientific Reports","issn_l":"2045-2322","issn":["2045-2322"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","doyens","jufo-1","ki-jl-1","medline","norway-1"],"host_organization":"https://openalex.org/P4310319908","host_organization_name":"Nature Portfolio","host_organization_lineage":["https://openalex.org/P4310319908","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Nature Portfolio","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Reports","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7127045937.pdf","grobid_xml":"https://content.openalex.org/works/W7127045937.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W1839137930","https://openalex.org/W1987115965","https://openalex.org/W1999077811","https://openalex.org/W2061438946","https://openalex.org/W2091638274","https://openalex.org/W2152195021","https://openalex.org/W2155529731","https://openalex.org/W2374769484","https://openalex.org/W2519501408","https://openalex.org/W2612450917","https://openalex.org/W2919979744","https://openalex.org/W2921715603","https://openalex.org/W3012087746","https://openalex.org/W3014974411","https://openalex.org/W3112756409","https://openalex.org/W3119051141","https://openalex.org/W3162154139","https://openalex.org/W3171014503","https://openalex.org/W3184813331","https://openalex.org/W4223526404","https://openalex.org/W4223633975","https://openalex.org/W4230167402","https://openalex.org/W4250503569","https://openalex.org/W4283012435","https://openalex.org/W4286565494","https://openalex.org/W4292083457","https://openalex.org/W4295409151","https://openalex.org/W4296123387","https://openalex.org/W4309914081","https://openalex.org/W4320487090","https://openalex.org/W4323922821","https://openalex.org/W4361007812","https://openalex.org/W4362724099","https://openalex.org/W4381136739","https://openalex.org/W4385076271","https://openalex.org/W4386052425","https://openalex.org/W4389396452","https://openalex.org/W4390946240","https://openalex.org/W4393115836","https://openalex.org/W4395008965","https://openalex.org/W4398794149","https://openalex.org/W4401337332","https://openalex.org/W4403035882","https://openalex.org/W4404068077","https://openalex.org/W4405612878","https://openalex.org/W4405925385","https://openalex.org/W4406475282","https://openalex.org/W4406934138","https://openalex.org/W4407271009","https://openalex.org/W4409216601","https://openalex.org/W4409479946","https://openalex.org/W4410201721","https://openalex.org/W4410581016","https://openalex.org/W4411334118","https://openalex.org/W4411373441","https://openalex.org/W4417164655"],"related_works":[],"abstract_inverted_index":{"This":[0],"study":[1],"proposes":[2],"an":[3],"enhanced":[4],"Black-kite":[5],"Algorithm":[6],"(BKA),":[7],"termed":[8],"SMNBKA-ICMIC,":[9],"to":[10,22,34,43,53,115],"improve":[11],"optimization":[12,110],"performance.":[13],"The":[14,59],"algorithm":[15,85],"introduces":[16],"four":[17],"key":[18],"improvements:":[19],"ICMIC-based":[20],"initialization":[21],"enhance":[23],"population":[24],"diversity,":[25],"integration":[26],"of":[27,41,93,100,106],"the":[28,74,84,98,125],"Simulated":[29],"Binary":[30],"Crossover":[31],"(SBX)":[32],"operator":[33],"strengthen":[35],"exploration,":[36],"a":[37,48,90,129,140],"refined":[38],"position-update":[39],"formula":[40],"migration":[42],"mitigate":[44],"premature":[45],"convergence,":[46],"and":[47,56,71,118,146],"novel":[49],"natural":[50],"replacement":[51],"mechanism":[52],"balance":[54],"global":[55],"local":[57],"search.":[58],"SMNBKA-ICMIC":[60,138],"demonstrates":[61,86],"exceptional":[62],"performance":[63,88],"in":[64,80,103,124],"benchmark":[65],"functions":[66],"from":[67,77],"CEC":[68],"2017,":[69],"2020,":[70],"2022,":[72],"securing":[73],"top":[75,99],"rank":[76],"best":[78,101],"value":[79,102],"these":[81],"tests.":[82],"Additionally,":[83],"superior":[87],"across":[89],"diverse":[91],"set":[92],"representative":[94],"benchmarks.":[95],"It":[96],"achieves":[97],"9":[104],"out":[105],"10":[107],"complex":[108,150],"engineering":[109],"problems\u2014chosen":[111],"for":[112,132,149],"their":[113],"relevance":[114],"real-world":[116],"design":[117],"control":[119],"challenges\u2014and":[120],"exhibits":[121],"remarkable":[122],"effectiveness":[123],"canonical":[126],"multi-knapsack":[127],"problem,":[128],"standard":[130],"test":[131],"combinatorial":[133],"optimization.":[134,152],"These":[135],"results":[136],"validate":[137],"as":[139],"state-of-the-art":[141],"metaheuristic,":[142],"ensuring":[143],"robust":[144],"convergence":[145],"practical":[147],"utility":[148],"numerical":[151]},"counts_by_year":[],"updated_date":"2026-09-11T09:22:31.653822","created_date":"2026-02-03T00:00:00"}
