{"id":"https://openalex.org/W4223638124","doi":"https://doi.org/10.1142/s0217595922500142","title":"Maximum Entropy Bi-Objective Model and its Evolutionary Algorithm for Portfolio Optimization","display_name":"Maximum Entropy Bi-Objective Model and its Evolutionary Algorithm for Portfolio Optimization","publication_year":2022,"publication_date":"2022-04-11","ids":{"openalex":"https://openalex.org/W4223638124","doi":"https://doi.org/10.1142/s0217595922500142"},"language":"en","primary_location":{"id":"doi:10.1142/s0217595922500142","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595922500142","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","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/A5018281460","display_name":"Liu Chun-an","orcid":"https://orcid.org/0000-0002-5072-9698"},"institutions":[{"id":"https://openalex.org/I2799293361","display_name":"Baoji University of Arts and Sciences","ror":"https://ror.org/05nx0xs09","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799293361"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chun-An Liu","raw_affiliation_strings":["School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, P. R. China","institution_ids":["https://openalex.org/I2799293361"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Qian Lei","orcid":null},"institutions":[{"id":"https://openalex.org/I180632629","display_name":"Xi'an International Studies University","ror":"https://ror.org/05gcme754","country_code":"CN","type":"education","lineage":["https://openalex.org/I180632629"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qian Lei","raw_affiliation_strings":["Center for Foreign Linguistics and Applied, Linguistics Research, School of English Studies, Xi\u2019an International Studies University, Xi\u2019an, Shaanxi 710128, P. R. China","Center for Foreign Linguistics and Applied, Linguistics Research, School of English Studies, Xi'an International Studies University, Xi'an, Shaanxi 710128, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Foreign Linguistics and Applied, Linguistics Research, School of English Studies, Xi\u2019an International Studies University, Xi\u2019an, Shaanxi 710128, P. R. China","institution_ids":["https://openalex.org/I180632629"]},{"raw_affiliation_string":"Center for Foreign Linguistics and Applied, Linguistics Research, School of English Studies, Xi'an International Studies University, Xi'an, Shaanxi 710128, P. R. China","institution_ids":["https://openalex.org/I180632629"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101047161","display_name":"Huamin Jia","orcid":null},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Huamin Jia","raw_affiliation_strings":["Avionics CNS System Design & ATM, Centre for Aeronautics, Cranfield University, England MK43 0AL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Avionics CNS System Design & ATM, Centre for Aeronautics, Cranfield University, England MK43 0AL, UK","institution_ids":["https://openalex.org/I82284825"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018281460"],"corresponding_institution_ids":["https://openalex.org/I2799293361"],"apc_list":null,"apc_paid":null,"fwci":0.8167,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.74013005,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"39","issue":"06","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9955999851226807,"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/T11801","display_name":"Reservoir Engineering and Simulation Methods","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/portfolio-optimization","display_name":"Portfolio optimization","score":0.7376026511192322},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.713837742805481},{"id":"https://openalex.org/keywords/efficient-frontier","display_name":"Efficient frontier","score":0.6397949457168579},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.5122920274734497},{"id":"https://openalex.org/keywords/crossover","display_name":"Crossover","score":0.47076013684272766},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.4701782763004303},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.46706610918045044},{"id":"https://openalex.org/keywords/portfolio","display_name":"Portfolio","score":0.43184274435043335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42982804775238037},{"id":"https://openalex.org/keywords/investment-strategy","display_name":"Investment strategy","score":0.4204406440258026},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.41872477531433105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41180485486984253},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.16674956679344177},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.16582977771759033},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0914425253868103}],"concepts":[{"id":"https://openalex.org/C202655437","wikidata":"https://www.wikidata.org/wiki/Q7231728","display_name":"Portfolio optimization","level":3,"score":0.7376026511192322},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.713837742805481},{"id":"https://openalex.org/C51485801","wikidata":"https://www.wikidata.org/wiki/Q16966861","display_name":"Efficient frontier","level":3,"score":0.6397949457168579},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.5122920274734497},{"id":"https://openalex.org/C122507166","wikidata":"https://www.wikidata.org/wiki/Q628906","display_name":"Crossover","level":2,"score":0.47076013684272766},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.4701782763004303},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.46706610918045044},{"id":"https://openalex.org/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.43184274435043335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42982804775238037},{"id":"https://openalex.org/C103144560","wikidata":"https://www.wikidata.org/wiki/Q2670999","display_name":"Investment strategy","level":3,"score":0.4204406440258026},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.41872477531433105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41180485486984253},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.16674956679344177},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.16582977771759033},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0914425253868103},{"id":"https://openalex.org/C183582576","wikidata":"https://www.wikidata.org/wiki/Q184783","display_name":"Market liquidity","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0217595922500142","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595922500142","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:39:y:2022:i:06:n:s0217595922500142","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0217595922500142","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W124595874","https://openalex.org/W901952859","https://openalex.org/W1516216243","https://openalex.org/W1516760870","https://openalex.org/W1559956479","https://openalex.org/W1647779468","https://openalex.org/W1976658031","https://openalex.org/W1976767421","https://openalex.org/W1998777544","https://openalex.org/W2015856032","https://openalex.org/W2031362562","https://openalex.org/W2032453361","https://openalex.org/W2032475783","https://openalex.org/W2038865108","https://openalex.org/W2042456949","https://openalex.org/W2045513909","https://openalex.org/W2045547871","https://openalex.org/W2064975791","https://openalex.org/W2069243496","https://openalex.org/W2073103707","https://openalex.org/W2099733750","https://openalex.org/W2106334424","https://openalex.org/W2111951371","https://openalex.org/W2113188547","https://openalex.org/W2135863358","https://openalex.org/W2139755682","https://openalex.org/W2142735801","https://openalex.org/W2143245714","https://openalex.org/W2151237529","https://openalex.org/W2155019998","https://openalex.org/W2162613513","https://openalex.org/W2165129372","https://openalex.org/W2170221568","https://openalex.org/W2190253220","https://openalex.org/W2294333872","https://openalex.org/W2602972600","https://openalex.org/W2735643051","https://openalex.org/W2766543954","https://openalex.org/W2784884531","https://openalex.org/W2884673195","https://openalex.org/W2912000148","https://openalex.org/W4206237891","https://openalex.org/W4236670843","https://openalex.org/W4244685734"],"related_works":["https://openalex.org/W4387811153","https://openalex.org/W2489358856","https://openalex.org/W4312259442","https://openalex.org/W2581916338","https://openalex.org/W4211157640","https://openalex.org/W3198789915","https://openalex.org/W4381827008","https://openalex.org/W4387934239","https://openalex.org/W4386639229","https://openalex.org/W4382404075"],"abstract_inverted_index":{"Diversification":[0],"of":[1,12,33,104,168,178,203,212],"investment":[2,24,187,249],"is":[3,16,48,64,76,88,182,201],"a":[4,37,49,65,82,101,140,147,155],"well-established":[5],"practice":[6],"for":[7,20,251],"reducing":[8],"the":[9,31,45,57,61,73,92,113,120,128,132,137,161,165,169,176,179,198,213,217,227,234],"total":[10],"risk":[11,25],"investing.":[13],"Portfolio":[14],"optimization":[15,41,95,188],"an":[17],"effective":[18],"way":[19],"investors":[21,252],"to":[22,55,71,90,99,158,226,253],"disperse":[23],"and":[26,60,117,146,164,193,208,223,248,255],"increase":[27],"portfolio":[28,40,58,74,94,107,229,246],"return.":[29],"Under":[30],"assumption":[32],"no":[34],"short":[35],"selling,":[36],"bi-objective":[38,93],"minimizing":[39],"model,":[42],"in":[43,78,136],"which":[44,125],"first":[46],"objective":[47,63,138],"semi-absolute":[50],"deviation":[51],"mean":[52],"function":[53,69],"used":[54,70],"measure":[56,72],"risk,":[59],"second":[62],"maximum":[66,83],"entropy":[67,84],"smooth":[68],"return,":[75],"given":[77],"this":[79],"paper.":[80],"Also,":[81,216],"multi-objective":[85,237],"evolutionary":[86,238],"algorithm":[87,171,181,200,219],"designed":[89],"solve":[91],"model.":[96],"In":[97],"order":[98],"obtain":[100,221],"sufficient":[102],"number":[103],"uniformly":[105],"distributed":[106],"Pareto":[108,115,206,230],"optimal":[109,245],"solutions":[110,207],"located":[111],"on":[112],"true":[114,228],"frontier":[116,133,231],"fully":[118],"exploit":[119],"useful":[121],"asset":[122,257],"combination":[123],"modes":[124],"can":[126,220,242],"lead":[127],"search":[129],"process":[130],"toward":[131],"direction":[134],"quickly":[135],"space,":[139],"subspace":[141,148],"multi-parent":[142],"uniform":[143],"crossover":[144],"operator":[145,151],"decomposition":[149],"mutation":[150],"are":[152,172],"given.":[153],"Furthermore,":[154],"normalization":[156],"method":[157],"deal":[159],"with":[160,233],"tight":[162],"constraint":[163],"convergence":[166,225],"analysis":[167],"proposed":[170,180,199,218],"also":[173,243],"discussed.":[174],"Finally,":[175],"performance":[177,191],"verified":[183],"by":[184],"five":[185],"benchmark":[186],"problems.":[189],"The":[190,240],"evaluations":[192],"results":[194],"analyses":[195],"illustrate":[196],"that":[197],"capable":[202],"identifying":[204],"good":[205],"maintaining":[209],"adequate":[210],"diversity":[211],"evolution":[214],"population.":[215],"faster":[222],"better":[224],"compared":[232],"three":[235],"state-of-the-art":[236],"algorithms.":[239],"result":[241],"provide":[244],"plan":[247],"strategy":[250],"allocate":[254],"manage":[256],"effectively.":[258]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}