{"id":"https://openalex.org/W3163434833","doi":"https://doi.org/10.1007/s40747-021-00389-8","title":"A neuro-swarming intelligent heuristic for second-order nonlinear Lane\u2013Emden multi-pantograph delay differential system","display_name":"A neuro-swarming intelligent heuristic for second-order nonlinear Lane\u2013Emden multi-pantograph delay differential system","publication_year":2021,"publication_date":"2021-05-07","ids":{"openalex":"https://openalex.org/W3163434833","doi":"https://doi.org/10.1007/s40747-021-00389-8","mag":"3163434833"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-021-00389-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-021-00389-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-021-00389-8.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"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":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/s40747-021-00389-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020317036","display_name":"Zulqurnain Sabir","orcid":"https://orcid.org/0000-0001-7466-6233"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Zulqurnain Sabir","raw_affiliation_strings":["Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100740838","display_name":"Muhammad Asif Zahoor Raja","orcid":"https://orcid.org/0000-0001-9953-822X"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Muhammad Asif Zahoor Raja","raw_affiliation_strings":["Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Yunlin, Douliou, 64002, Taiwan, ROC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Yunlin, Douliou, 64002, Taiwan, ROC","institution_ids":["https://openalex.org/I75357094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023041667","display_name":"Dac\u2010Nhuong Le","orcid":"https://orcid.org/0000-0003-2601-2803"},"institutions":[{"id":"https://openalex.org/I4210146698","display_name":"Hai Phong University of Management and Technology","ror":"https://ror.org/04gb9ay54","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210146698"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Dac-Nhuong Le","raw_affiliation_strings":["Faculty of Information Technology, Haiphong University, 180000, Haiphong, Vietnam"],"raw_orcid":"https://orcid.org/0000-0003-2601-2803","affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Haiphong University, 180000, Haiphong, Vietnam","institution_ids":["https://openalex.org/I4210146698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080090568","display_name":"Ayman A. Aly","orcid":"https://orcid.org/0000-0002-8383-8014"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ayman A. Aly","raw_affiliation_strings":["Department of Mechanical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif, 21944, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif, 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023041667"],"corresponding_institution_ids":["https://openalex.org/I4210146698"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1320,"currency":"GBP","value_usd":1619},"fwci":2.2538,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.86917477,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"8","issue":"3","first_page":"1987","last_page":"2000"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10842","display_name":"Railway Engineering and Dynamics","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10842","display_name":"Railway Engineering and Dynamics","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9379000067710876,"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/T11568","display_name":"Railway Systems and Energy Efficiency","score":0.9096999764442444,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.7302376627922058},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6983073353767395},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6236969828605652},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6037235260009766},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4909820854663849},{"id":"https://openalex.org/keywords/differential-evolution","display_name":"Differential evolution","score":0.46674638986587524},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.46422716975212097},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.42822521924972534},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.423404723405838},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41423434019088745},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38412198424339294},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3518526554107666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21410351991653442}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.7302376627922058},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6983073353767395},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6236969828605652},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6037235260009766},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4909820854663849},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.46674638986587524},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.46422716975212097},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.42822521924972534},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.423404723405838},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41423434019088745},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38412198424339294},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3518526554107666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21410351991653442},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40747-021-00389-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-021-00389-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-021-00389-8.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"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":"Complex &amp; Intelligent Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s40747-021-00389-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-021-00389-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-021-00389-8.pdf","source":{"id":"https://openalex.org/S3035462843","display_name":"Complex & Intelligent Systems","issn_l":"2198-6053","issn":["2198-6053","2199-4536"],"is_oa":true,"is_in_doaj":true,"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":"Complex &amp; Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6879358432","display_name":null,"funder_award_id":"TURSP-2020/77","funder_id":"https://openalex.org/F4320323722","funder_display_name":"Taif University"},{"id":"https://openalex.org/G7299194679","display_name":null,"funder_award_id":"TURSP-2020","funder_id":"https://openalex.org/F4320323722","funder_display_name":"Taif University"}],"funders":[{"id":"https://openalex.org/F4320323722","display_name":"Taif University","ror":"https://ror.org/014g1a453"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3163434833.pdf","grobid_xml":"https://content.openalex.org/works/W3163434833.grobid-xml"},"referenced_works_count":83,"referenced_works":["https://openalex.org/W970187520","https://openalex.org/W1104640671","https://openalex.org/W1526455201","https://openalex.org/W1533970237","https://openalex.org/W1586658033","https://openalex.org/W1623895684","https://openalex.org/W1820051232","https://openalex.org/W1966816682","https://openalex.org/W1974104513","https://openalex.org/W2007646242","https://openalex.org/W2012328214","https://openalex.org/W2014001466","https://openalex.org/W2022462160","https://openalex.org/W2027671672","https://openalex.org/W2034094163","https://openalex.org/W2044524076","https://openalex.org/W2050195882","https://openalex.org/W2063292380","https://openalex.org/W2085628012","https://openalex.org/W2087707879","https://openalex.org/W2097227533","https://openalex.org/W2116318141","https://openalex.org/W2122175906","https://openalex.org/W2134848150","https://openalex.org/W2145113795","https://openalex.org/W2155559562","https://openalex.org/W2158630456","https://openalex.org/W2214842323","https://openalex.org/W2283542711","https://openalex.org/W2312266205","https://openalex.org/W2384058350","https://openalex.org/W2411809432","https://openalex.org/W2498401782","https://openalex.org/W2517876334","https://openalex.org/W2589249848","https://openalex.org/W2607503854","https://openalex.org/W2610571865","https://openalex.org/W2732014993","https://openalex.org/W2741906455","https://openalex.org/W2791909561","https://openalex.org/W2792873050","https://openalex.org/W2793678410","https://openalex.org/W2798572826","https://openalex.org/W2798741797","https://openalex.org/W2811259241","https://openalex.org/W2889803518","https://openalex.org/W2890106249","https://openalex.org/W2900729111","https://openalex.org/W2938724855","https://openalex.org/W2941028263","https://openalex.org/W2943421318","https://openalex.org/W2946330977","https://openalex.org/W2953204627","https://openalex.org/W2965022506","https://openalex.org/W3003679051","https://openalex.org/W3010793677","https://openalex.org/W3011998913","https://openalex.org/W3025292751","https://openalex.org/W3026764435","https://openalex.org/W3027696403","https://openalex.org/W3028247906","https://openalex.org/W3033468301","https://openalex.org/W3036059498","https://openalex.org/W3037708891","https://openalex.org/W3038344063","https://openalex.org/W3039345564","https://openalex.org/W3040259304","https://openalex.org/W3040738612","https://openalex.org/W3041784508","https://openalex.org/W3045108043","https://openalex.org/W3091827982","https://openalex.org/W3100383449","https://openalex.org/W3102507384","https://openalex.org/W3106296080","https://openalex.org/W3109534075","https://openalex.org/W3112173448","https://openalex.org/W3127748774","https://openalex.org/W3131403687","https://openalex.org/W3134725663","https://openalex.org/W3147355507","https://openalex.org/W3150569976","https://openalex.org/W3156691680","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3019402777","https://openalex.org/W4386596916","https://openalex.org/W2087240539","https://openalex.org/W3212544526","https://openalex.org/W4236520801","https://openalex.org/W2031835531","https://openalex.org/W2388590088","https://openalex.org/W2105887828","https://openalex.org/W2003904901","https://openalex.org/W2090436135"],"abstract_inverted_index":{"Abstract":[0],"The":[1,77,94],"current":[2],"study":[3],"is":[4,58,82],"related":[5],"to":[6,101,118],"present":[7,102],"a":[8,55,103],"novel":[9],"neuro-swarming":[10],"intelligent":[11],"heuristic":[12],"for":[13,73,113],"nonlinear":[14],"second-order":[15],"Lane\u2013Emden":[16],"multi-pantograph":[17],"delay":[18],"differential":[19],"(NSO-LE-MPDD)":[20],"model":[21],"by":[22,60],"applying":[23],"the":[24,51,62,74,86,97,110,114,125,129,133,139],"approximation":[25],"proficiency":[26],"of":[27,36,71,79,84,89,96,138],"artificial":[28],"neural":[29],"networks":[30],"(ANNs)":[31],"and":[32,91,106,136],"local/global":[33],"search":[34],"capabilities":[35],"particle":[37],"swarm":[38],"optimization":[39,117],"(PSO)":[40],"together":[41],"with":[42,68,120],"efficient/quick":[43],"interior-point":[44],"(IP)":[45],"approach,":[46],"i.e.,":[47],"ANN-PSOIP":[48,53,98,140],"scheme.":[49,93,141],"In":[50],"designed":[52],"scheme,":[54],"merit":[56],"function":[57],"proposed":[59],"using":[61,85,128],"mean":[63],"square":[64],"error":[65],"sense":[66],"along":[67],"continuous":[69],"mapping":[70],"ANNs":[72,111],"NSO-LE-MPDD":[75],"model.":[76],"training":[78],"these":[80],"nets":[81],"capable":[83],"integrated":[87],"competence":[88],"PSO":[90],"IP":[92],"inspiration":[95],"approach":[99],"instigates":[100],"reliable,":[104],"steadfast,":[105],"consistent":[107],"arrangement":[108],"relates":[109],"strength":[112],"soft":[115],"computing":[116],"handle":[119],"such":[121],"inspiring":[122],"classifications.":[123],"Furthermore,":[124],"statistical":[126],"soundings":[127],"different":[130],"operators":[131],"certify":[132],"convergence,":[134],"accurateness,":[135],"precision":[137]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
