{"id":"https://openalex.org/W4285731150","doi":"https://doi.org/10.1007/s10489-022-03796-7","title":"Development and application of equilibrium optimizer for optimal power flow calculation of power system","display_name":"Development and application of equilibrium optimizer for optimal power flow calculation of power system","publication_year":2022,"publication_date":"2022-07-18","ids":{"openalex":"https://openalex.org/W4285731150","doi":"https://doi.org/10.1007/s10489-022-03796-7","pmid":"https://pubmed.ncbi.nlm.nih.gov/35875200"},"language":"en","primary_location":{"id":"doi:10.1007/s10489-022-03796-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10489-022-03796-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10489-022-03796-7.pdf","source":{"id":"https://openalex.org/S74726891","display_name":"Applied Intelligence","issn_l":"0924-669X","issn":["0924-669X","1573-7497"],"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":"Applied Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10489-022-03796-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056436780","display_name":"Essam H. Houssein","orcid":"https://orcid.org/0000-0002-8127-7233"},"institutions":[{"id":"https://openalex.org/I89466785","display_name":"Minia University","ror":"https://ror.org/02hcv4z63","country_code":"EG","type":"education","lineage":["https://openalex.org/I89466785"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Essam H. Houssein","raw_affiliation_strings":["Faculty of Computers and Information, Minia University, 61519 Minia, Egypt","Faculty of Computers and Information, Minia University, 61519, Minia, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-8127-7233","affiliations":[{"raw_affiliation_string":"Faculty of Computers and Information, Minia University, 61519 Minia, Egypt","institution_ids":["https://openalex.org/I89466785"]},{"raw_affiliation_string":"Faculty of Computers and Information, Minia University, 61519, Minia, Egypt","institution_ids":["https://openalex.org/I89466785"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084091847","display_name":"Mohamed H. Hassan","orcid":"https://orcid.org/0000-0003-1754-4883"},"institutions":[{"id":"https://openalex.org/I4210126896","display_name":"New and Renewable Energy Authority","ror":"https://ror.org/030zrse19","country_code":"EG","type":"government","lineage":["https://openalex.org/I4210126896"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mohamed H. Hassan","raw_affiliation_strings":["Ministry of Electricity and Renewable Energy, Cairo, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ministry of Electricity and Renewable Energy, Cairo, Egypt","institution_ids":["https://openalex.org/I4210126896"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014245455","display_name":"Mohamed A. Mahdy","orcid":"https://orcid.org/0000-0002-6303-6954"},"institutions":[{"id":"https://openalex.org/I113643904","display_name":"Beni-Suef University","ror":"https://ror.org/05pn4yv70","country_code":"EG","type":"education","lineage":["https://openalex.org/I113643904"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Mohamed A. Mahdy","raw_affiliation_strings":["Faculty of Computers and Artificial Intelligence, Beni-Suef University, Beni-Suef, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computers and Artificial Intelligence, Beni-Suef University, Beni-Suef, Egypt","institution_ids":["https://openalex.org/I113643904"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012474682","display_name":"Salah Kamel","orcid":"https://orcid.org/0000-0001-9505-5386"},"institutions":[{"id":"https://openalex.org/I86310350","display_name":"Aswan University","ror":"https://ror.org/048qnr849","country_code":"EG","type":"education","lineage":["https://openalex.org/I86310350"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Salah Kamel","raw_affiliation_strings":["Electrical Engineering Department, Faculty of Engineering, Aswan University, 81542 Aswan, Egypt","Electrical Engineering Department, Faculty of Engineering, Aswan University, 81542, Aswan, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Faculty of Engineering, Aswan University, 81542 Aswan, Egypt","institution_ids":["https://openalex.org/I86310350"]},{"raw_affiliation_string":"Electrical Engineering Department, Faculty of Engineering, Aswan University, 81542, Aswan, Egypt","institution_ids":["https://openalex.org/I86310350"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5056436780"],"corresponding_institution_ids":["https://openalex.org/I89466785"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":7.571,"has_fulltext":true,"cited_by_count":85,"citation_normalized_percentile":{"value":0.98136689,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"53","issue":"6","first_page":"7232","last_page":"7253"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10454","display_name":"Optimal Power Flow Distribution","score":0.9998999834060669,"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/T10454","display_name":"Optimal Power Flow Distribution","score":0.9998999834060669,"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/T10223","display_name":"Microgrid Control and Optimization","score":0.9991000294685364,"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/T10424","display_name":"Electric Power System Optimization","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7362026572227478},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5961712002754211},{"id":"https://openalex.org/keywords/wilcoxon-signed-rank-test","display_name":"Wilcoxon signed-rank test","score":0.5225990414619446},{"id":"https://openalex.org/keywords/power-flow","display_name":"Power flow","score":0.49563610553741455},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4930877387523651},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47495365142822266},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4485534131526947},{"id":"https://openalex.org/keywords/imperialist-competitive-algorithm","display_name":"Imperialist competitive algorithm","score":0.43739423155784607},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3952488303184509},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3905596137046814},{"id":"https://openalex.org/keywords/electric-power-system","display_name":"Electric power system","score":0.38553348183631897},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.15126848220825195}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7362026572227478},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5961712002754211},{"id":"https://openalex.org/C206041023","wikidata":"https://www.wikidata.org/wiki/Q1751970","display_name":"Wilcoxon signed-rank test","level":3,"score":0.5225990414619446},{"id":"https://openalex.org/C2986056383","wikidata":"https://www.wikidata.org/wiki/Q556030","display_name":"Power flow","level":4,"score":0.49563610553741455},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4930877387523651},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47495365142822266},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4485534131526947},{"id":"https://openalex.org/C101219045","wikidata":"https://www.wikidata.org/wiki/Q10859646","display_name":"Imperialist competitive algorithm","level":4,"score":0.43739423155784607},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3952488303184509},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3905596137046814},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.38553348183631897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.15126848220825195},{"id":"https://openalex.org/C12868164","wikidata":"https://www.wikidata.org/wiki/Q1424533","display_name":"Mann\u2013Whitney U test","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10489-022-03796-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10489-022-03796-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10489-022-03796-7.pdf","source":{"id":"https://openalex.org/S74726891","display_name":"Applied Intelligence","issn_l":"0924-669X","issn":["0924-669X","1573-7497"],"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":"Applied Intelligence","raw_type":"journal-article"},{"id":"pmid:35875200","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35875200","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,"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":"Applied intelligence (Dordrecht, Netherlands)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:9289660","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9289660","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,"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","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Appl Intell (Dordr)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s10489-022-03796-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10489-022-03796-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10489-022-03796-7.pdf","source":{"id":"https://openalex.org/S74726891","display_name":"Applied Intelligence","issn_l":"0924-669X","issn":["0924-669X","1573-7497"],"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":"Applied Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6600000262260437}],"awards":[{"id":"https://openalex.org/G6911737017","display_name":"CENTRO PARA LA INVESTIGACION EN ENERGIA SOLAR (SERC-CHILE)","funder_award_id":"15110019","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"}],"funders":[{"id":"https://openalex.org/F4320321655","display_name":"Science and Technology Development Fund","ror":"https://ror.org/044vr6g03"},{"id":"https://openalex.org/F4320327648","display_name":"Minia University","ror":"https://ror.org/02hcv4z63"},{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285731150.pdf","grobid_xml":"https://content.openalex.org/works/W4285731150.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W1765350388","https://openalex.org/W1857789879","https://openalex.org/W1941097134","https://openalex.org/W1986805488","https://openalex.org/W2040725548","https://openalex.org/W2067291211","https://openalex.org/W2076972511","https://openalex.org/W2143532287","https://openalex.org/W2159427933","https://openalex.org/W2228745449","https://openalex.org/W2282226143","https://openalex.org/W2287041580","https://openalex.org/W2287116896","https://openalex.org/W2299619383","https://openalex.org/W2319538269","https://openalex.org/W2395034616","https://openalex.org/W2407185667","https://openalex.org/W2509733445","https://openalex.org/W2511569622","https://openalex.org/W2528180509","https://openalex.org/W2539267016","https://openalex.org/W2577463458","https://openalex.org/W2605396865","https://openalex.org/W2732796807","https://openalex.org/W2768181028","https://openalex.org/W2777438255","https://openalex.org/W2782513934","https://openalex.org/W2790106051","https://openalex.org/W2810268721","https://openalex.org/W2810512128","https://openalex.org/W2883722516","https://openalex.org/W2889127870","https://openalex.org/W2897855835","https://openalex.org/W2909969407","https://openalex.org/W2922798329","https://openalex.org/W2985845430","https://openalex.org/W2996361803","https://openalex.org/W3009979760","https://openalex.org/W3011338927","https://openalex.org/W3036044602","https://openalex.org/W3042674228","https://openalex.org/W3068591736","https://openalex.org/W3083172984","https://openalex.org/W3113722716","https://openalex.org/W3120153362","https://openalex.org/W3137672894","https://openalex.org/W3191435006","https://openalex.org/W3192582371","https://openalex.org/W3193211895","https://openalex.org/W3196661916","https://openalex.org/W3198056226","https://openalex.org/W3198071122","https://openalex.org/W3199464050","https://openalex.org/W3206450200","https://openalex.org/W3208908984","https://openalex.org/W3214181042","https://openalex.org/W3217000788","https://openalex.org/W4200437144","https://openalex.org/W4200517031","https://openalex.org/W4210686785","https://openalex.org/W4213222064","https://openalex.org/W4220884221","https://openalex.org/W4224308947"],"related_works":["https://openalex.org/W2135912799","https://openalex.org/W3085397617","https://openalex.org/W2100132513","https://openalex.org/W2137444486","https://openalex.org/W2434800423","https://openalex.org/W4299900939","https://openalex.org/W3024990376","https://openalex.org/W2941846679","https://openalex.org/W2014360508","https://openalex.org/W2562788565"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"an":[3],"enhanced":[4],"version":[5],"of":[6,43,81,88,104,149,169,229],"Equilibrium":[7,46],"Optimizer":[8,47],"(EO)":[9,48],"called":[10],"(EEO)":[11],"for":[12,163,265],"solving":[13],"global":[14,61],"optimization":[15,62,134],"and":[16,49,98,139,144,154,181,207,247],"the":[17,34,41,44,78,82,101,110,116,123,124,157,170,177,189,196,212,227,251],"optimal":[18],"power":[19,243],"flow":[20],"(OPF)":[21],"problems.":[22,66,268],"The":[23,38,67,127,147,166,216],"proposed":[24,68,117,171,197],"EEO":[25,69,118,172,217,256],"algorithm":[26,39,173,180,198,257],"includes":[27],"a":[28,132,260],"new":[29],"performance":[30,148],"reinforcement":[31],"strategy":[32],"with":[33,136,236],"L\u00e9vy":[35],"Flight":[36],"mechanism.":[37],"addresses":[40],"shortcomings":[42],"original":[45,178,213],"aims":[50],"to":[51,60,86,121,141,176],"provide":[52,259],"better":[53,200],"solutions":[54,202,264],"(than":[55],"those":[56,87,182],"provided":[57],"by":[58,73,109],"EO)":[59],"problems,":[63],"especially":[64],"OPF":[65,125,128,267],"efficiency":[70],"was":[71,107,119,219],"confirmed":[72],"comparing":[74],"its":[75],"results":[76,106,168,193,208,253],"on":[77,156],"ten":[79],"functions":[80],"CEC'20":[83],"test":[84,161],"suite,":[85],"other":[89,185],"algorithms,":[90,93],"including":[91],"high-performance":[92],"i.e.,":[94],"CMA-ES,":[95],"IMODE,":[96],"AGSK":[97],"LSHADE_cnEpSin.":[99],"Moreover,":[100],"statistical":[102],"significance":[103],"these":[105],"validated":[108],"Wilcoxon's":[111],"rank-sum":[112],"test.":[113],"After":[114],"that,":[115],"applied":[120],"solve":[122],"problem.":[126],"is":[129,152,174],"formulated":[130],"as":[131,209,211],"nonlinear":[133],"problem":[135],"conflicting":[137],"objectives":[138],"subjected":[140],"both":[142],"equality":[143],"inequality":[145],"constraints.":[146],"this":[150],"technique":[151],"deliberated":[153],"evaluated":[155],"standard":[158],"IEEE":[159],"30-bus":[160],"system":[162],"different":[164,223,230,266],"objectives.":[165],"obtained":[167,183],"compared":[175],"EO":[179,214],"using":[184],"techniques":[186],"mentioned":[187],"in":[188],"literature.":[190],"These":[191],"Simulation":[192],"revealed":[194],"that":[195,225,255],"provides":[199],"optimized":[201],"than":[203],"20":[204],"published":[205],"methods":[206],"well":[210],"algorithm.":[215],"superiority":[218],"demonstrated":[220],"through":[221],"six":[222],"cases,":[224],"involved":[226],"minimization":[228],"objectives:":[231],"fuel":[232,234],"cost,":[233],"cost":[235],"valve-point":[237],"loading":[238],"effect,":[239],"emission,":[240],"total":[241],"active":[242],"losses,":[244],"voltage":[245,248],"deviation,":[246],"instability.":[249],"Also,":[250],"comparison":[252],"indicate":[254],"can":[258],"robust,":[261],"high-quality":[262],"feasible":[263]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":26},{"year":2024,"cited_by_count":30},{"year":2023,"cited_by_count":22},{"year":2022,"cited_by_count":4}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}