{"id":"https://openalex.org/W4322730981","doi":"https://doi.org/10.1109/tsmc.2023.3245212","title":"Two-Stage Reinforcement Learning-Based Differential Evolution for Solving Nonlinear Equations","display_name":"Two-Stage Reinforcement Learning-Based Differential Evolution for Solving Nonlinear Equations","publication_year":2023,"publication_date":"2023-03-01","ids":{"openalex":"https://openalex.org/W4322730981","doi":"https://doi.org/10.1109/tsmc.2023.3245212"},"language":"en","primary_location":{"id":"doi:10.1109/tsmc.2023.3245212","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2023.3245212","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","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/A5027300195","display_name":"Zuowen Liao","orcid":"https://orcid.org/0000-0002-4436-6878"},"institutions":[{"id":"https://openalex.org/I4210128032","display_name":"Beibu Gulf University","ror":"https://ror.org/031j0at32","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210128032"]},{"id":"https://openalex.org/I4210139142","display_name":"Development Research Center","ror":"https://ror.org/04m6cjv19","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210139142","https://openalex.org/I4210155611"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zuowen Liao","raw_affiliation_strings":["Beibu Gulf Ocean Development Research Center, Beibu Gulf University, Qinzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-4436-6878","affiliations":[{"raw_affiliation_string":"Beibu Gulf Ocean Development Research Center, Beibu Gulf University, Qinzhou, China","institution_ids":["https://openalex.org/I4210128032","https://openalex.org/I4210139142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013105439","display_name":"Wenyin Gong","orcid":"https://orcid.org/0000-0003-1610-6865"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenyin Gong","raw_affiliation_strings":["School of computer Science, China University of Geosciences, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0003-1610-6865","affiliations":[{"raw_affiliation_string":"School of computer Science, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023809706","display_name":"Shuijia Li","orcid":"https://orcid.org/0000-0003-3838-0072"},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuijia Li","raw_affiliation_strings":["School of computer Science, China University of Geosciences, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0003-3838-0072","affiliations":[{"raw_affiliation_string":"School of computer Science, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7588,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.95690143,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"53","issue":"7","first_page":"4279","last_page":"4290"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9983000159263611,"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":0.9983000159263611,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9962999820709229,"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":0.9876000285148621,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.7986769676208496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.637804388999939},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.633041501045227},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5300179719924927},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5244365334510803},{"id":"https://openalex.org/keywords/differential-evolution","display_name":"Differential evolution","score":0.5138443112373352},{"id":"https://openalex.org/keywords/mutation","display_name":"Mutation","score":0.4937020242214203},{"id":"https://openalex.org/keywords/test-suite","display_name":"Test suite","score":0.4880474805831909},{"id":"https://openalex.org/keywords/suite","display_name":"Suite","score":0.4316038489341736},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3933420181274414},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.25960198044776917},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2588309943675995},{"id":"https://openalex.org/keywords/test-case","display_name":"Test case","score":0.2149893343448639}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.7986769676208496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.637804388999939},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.633041501045227},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5300179719924927},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5244365334510803},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.5138443112373352},{"id":"https://openalex.org/C501734568","wikidata":"https://www.wikidata.org/wiki/Q42918","display_name":"Mutation","level":3,"score":0.4937020242214203},{"id":"https://openalex.org/C151552104","wikidata":"https://www.wikidata.org/wiki/Q7705809","display_name":"Test suite","level":4,"score":0.4880474805831909},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.4316038489341736},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3933420181274414},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.25960198044776917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2588309943675995},{"id":"https://openalex.org/C128942645","wikidata":"https://www.wikidata.org/wiki/Q1568346","display_name":"Test case","level":3,"score":0.2149893343448639},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmc.2023.3245212","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmc.2023.3245212","pdf_url":null,"source":{"id":"https://openalex.org/S4210209078","display_name":"IEEE Transactions on Systems Man and Cybernetics Systems","issn_l":"2168-2216","issn":["2168-2216","2168-2232"],"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 Systems, Man, and Cybernetics: Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1539849825","display_name":null,"funder_award_id":"62076225","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1595159159","https://openalex.org/W1785500154","https://openalex.org/W1965392777","https://openalex.org/W1968005908","https://openalex.org/W1990180092","https://openalex.org/W1997949764","https://openalex.org/W1998444286","https://openalex.org/W2049193681","https://openalex.org/W2083281224","https://openalex.org/W2117000100","https://openalex.org/W2146713522","https://openalex.org/W2158308038","https://openalex.org/W2159308419","https://openalex.org/W2287228090","https://openalex.org/W2310612427","https://openalex.org/W2595292627","https://openalex.org/W2595753752","https://openalex.org/W2622727889","https://openalex.org/W2745449279","https://openalex.org/W2755582626","https://openalex.org/W2757662287","https://openalex.org/W2794711922","https://openalex.org/W2799780652","https://openalex.org/W2883636246","https://openalex.org/W2887471996","https://openalex.org/W2938111495","https://openalex.org/W2949998775","https://openalex.org/W2955147151","https://openalex.org/W2968010987","https://openalex.org/W2993081139","https://openalex.org/W2998407949","https://openalex.org/W3003887406","https://openalex.org/W3041013467","https://openalex.org/W3084357507","https://openalex.org/W3087921643","https://openalex.org/W3157421340","https://openalex.org/W3160562782","https://openalex.org/W3162017678","https://openalex.org/W3163105451","https://openalex.org/W3200051949","https://openalex.org/W3209089360","https://openalex.org/W3216080622","https://openalex.org/W4210819183","https://openalex.org/W4225851404","https://openalex.org/W4228999655","https://openalex.org/W4232088056","https://openalex.org/W4286893914","https://openalex.org/W4292254663"],"related_works":["https://openalex.org/W4231704780","https://openalex.org/W1485837041","https://openalex.org/W3204955359","https://openalex.org/W2370079837","https://openalex.org/W2726178318","https://openalex.org/W2111826695","https://openalex.org/W1972575153","https://openalex.org/W1988293173","https://openalex.org/W2726904590","https://openalex.org/W2885003276"],"abstract_inverted_index":{"Solving":[0],"nonlinear":[1],"equations":[2],"(NEs)":[3],"requires":[4],"the":[5,57,64,70,97,118,132,143,147,151],"algorithm":[6,59,144],"to":[7,34,60],"locate":[8],"multiple":[9],"roots":[10],"of":[11,43,73,120],"NEs":[12,38,128],"in":[13],"one":[14],"run.":[15],"In":[16],"this":[17,114],"article,":[18],"a":[19],"generic":[20],"framework":[21],"based":[22],"on":[23],"two-stage":[24],"reinforcement":[25],"learning":[26],"(RL)":[27],"and":[28,51,89,101,106,125,145],"differential":[29],"evolution":[30],"(DE)":[31],"is":[32,66,84],"proposed":[33,152],"effectively":[35],"deal":[36],"with":[37,159],"problems.":[39],"The":[40,135],"major":[41],"advantage":[42],"our":[44,121],"approach":[45],"are:":[46],"1)":[47],"different":[48,74,103],"niching":[49,75],"methods":[50,76],"mutation":[52,92],"strategies":[53,93],"are":[54,94,129],"integrated":[55,112],"into":[56,113],"DE":[58],"assist":[61],"evolution;":[62],"2)":[63],"diversity":[65],"maintained":[67],"by":[68],"utilizing":[69],"search":[71],"characteristics":[72],"at":[77],"population":[78],"level;":[79],"3)":[80],"additionally,":[81],"each":[82],"individual":[83],"regarded":[85],"as":[86,96,131],"an":[87],"agent,":[88],"three":[90],"classical":[91],"used":[95],"agent\u2019s":[98],"alternative":[99],"actions;":[100],"4)":[102],"state":[104],"settings":[105],"reward":[107],"function":[108],"can":[109,141],"be":[110],"easily":[111],"framework.":[115],"To":[116],"verify":[117],"performance":[119,157],"approach,":[122],"30":[123],"problems":[124],"18":[126],"new":[127],"selected":[130],"test":[133],"suite.":[134],"experimental":[136],"results":[137],"demonstrate":[138],"that":[139],"RL":[140],"facilitate":[142],"improve":[146],"problem-solving":[148],"ability.":[149],"Moreover,":[150],"method":[153],"also":[154],"obtains":[155],"competitive":[156],"compared":[158],"other":[160],"peer":[161],"algorithms.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}