{"id":"https://openalex.org/W3213216247","doi":"https://doi.org/10.1007/s40747-021-00568-7","title":"Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling","display_name":"Polynomial Response Surface based on basis function selection by multitask optimization and ensemble modeling","publication_year":2021,"publication_date":"2021-11-10","ids":{"openalex":"https://openalex.org/W3213216247","doi":"https://doi.org/10.1007/s40747-021-00568-7","mag":"3213216247"},"language":"en","primary_location":{"id":"doi:10.1007/s40747-021-00568-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-021-00568-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-021-00568-7.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/s40747-021-00568-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101420527","display_name":"Yong Zhao","orcid":"https://orcid.org/0000-0002-8420-0135"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yong Zhao","raw_affiliation_strings":["College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090824447","display_name":"Siyu Ye","orcid":"https://orcid.org/0000-0003-4254-1043"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Siyu Ye","raw_affiliation_strings":["College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China"],"raw_orcid":"https://orcid.org/0000-0003-4254-1043","affiliations":[{"raw_affiliation_string":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082047088","display_name":"Xianqi Chen","orcid":"https://orcid.org/0000-0002-3744-6001"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianqi Chen","raw_affiliation_strings":["College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090784323","display_name":"Yufeng Xia","orcid":"https://orcid.org/0000-0003-2178-0248"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yufeng Xia","raw_affiliation_strings":["College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103268977","display_name":"Xiaohu Zheng","orcid":"https://orcid.org/0000-0003-4568-4277"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohu Zheng","raw_affiliation_strings":["College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, Hunan, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101420527"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":{"value":1320,"currency":"GBP","value_usd":1619},"apc_paid":{"value":1320,"currency":"GBP","value_usd":1619},"fwci":1.9683,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.88355497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"8","issue":"2","first_page":"1015","last_page":"1034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9987999796867371,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9839000105857849,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6692202091217041},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.6320100426673889},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.6216660737991333},{"id":"https://openalex.org/keywords/akaike-information-criterion","display_name":"Akaike information criterion","score":0.6191085577011108},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5359329581260681},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5057344436645508},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4808676838874817},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.4522538483142853},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4250373840332031},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3941565752029419},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39156609773635864},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3713372051715851},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3392762839794159}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6692202091217041},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.6320100426673889},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.6216660737991333},{"id":"https://openalex.org/C126674687","wikidata":"https://www.wikidata.org/wiki/Q1662573","display_name":"Akaike information criterion","level":2,"score":0.6191085577011108},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5359329581260681},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5057344436645508},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4808676838874817},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.4522538483142853},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4250373840332031},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3941565752029419},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39156609773635864},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3713372051715851},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3392762839794159},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40747-021-00568-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-021-00568-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-021-00568-7.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/s40747-021-00568-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40747-021-00568-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40747-021-00568-7.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":[{"id":"https://metadata.un.org/sdg/10","score":0.5699999928474426,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2404692483","display_name":null,"funder_award_id":"11725211","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3213216247.pdf","grobid_xml":"https://content.openalex.org/works/W3213216247.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W190984618","https://openalex.org/W1968371014","https://openalex.org/W1974478886","https://openalex.org/W1989574703","https://openalex.org/W2000626676","https://openalex.org/W2012176413","https://openalex.org/W2059831678","https://openalex.org/W2071204941","https://openalex.org/W2079542341","https://openalex.org/W2082992023","https://openalex.org/W2083542829","https://openalex.org/W2086223770","https://openalex.org/W2088990166","https://openalex.org/W2093022009","https://openalex.org/W2093229042","https://openalex.org/W2093269116","https://openalex.org/W2102154426","https://openalex.org/W2119401655","https://openalex.org/W2121121871","https://openalex.org/W2122825543","https://openalex.org/W2135046866","https://openalex.org/W2139967004","https://openalex.org/W2142663632","https://openalex.org/W2294818690","https://openalex.org/W2344351270","https://openalex.org/W2429108336","https://openalex.org/W2498649834","https://openalex.org/W2518825602","https://openalex.org/W2625566893","https://openalex.org/W2750146215","https://openalex.org/W2756659234","https://openalex.org/W2776317535","https://openalex.org/W2784682078","https://openalex.org/W2790182051","https://openalex.org/W2792873660","https://openalex.org/W2796292185","https://openalex.org/W2810440851","https://openalex.org/W2891186800","https://openalex.org/W2896193347","https://openalex.org/W3043062030","https://openalex.org/W3100456593","https://openalex.org/W3124489140","https://openalex.org/W4206550329","https://openalex.org/W4236993164"],"related_works":["https://openalex.org/W4385957992","https://openalex.org/W4229079080","https://openalex.org/W4206534706","https://openalex.org/W4385965371","https://openalex.org/W4200027074","https://openalex.org/W4386025632","https://openalex.org/W3006943036","https://openalex.org/W4200511449","https://openalex.org/W4211177414","https://openalex.org/W4299487748"],"abstract_inverted_index":{"Abstract":[0],"Polynomial":[1],"Regression":[2],"Surface":[3],"(PRS)":[4],"is":[5,23,59,72,88,107,131,148],"a":[6,40,47,86,127],"commonly":[7],"used":[8],"surrogate":[9],"model":[10],"for":[11,61,83],"its":[12,27],"simplicity,":[13],"good":[14],"interpretability,":[15],"and":[16,55,82,115,158,176,199,217,225,233],"computational":[17],"efficiency.":[18],"The":[19,142],"performance":[20],"of":[21,144,155,162,208,237],"PRS":[22,48],"largely":[24],"dependent":[25],"on":[26,52,179],"basis":[28,37,63,146,164,172,213],"functions.":[29],"With":[30],"limited":[31],"samples,":[32],"how":[33],"to":[34,133,151,231],"correctly":[35],"select":[36],"functions":[38,165,173],"remains":[39],"challenging":[41],"problem.":[42],"To":[43,93],"improve":[44],"prediction":[45,197],"accuracy,":[46],"modeling":[49,57],"approach":[50],"based":[51,178],"multitask":[53],"optimization":[54,98,113,124],"ensemble":[56,129],"(PRS-MOEM)":[58],"proposed":[60,132],"rational":[62],"function":[64,147,214],"selection":[65,215],"with":[66,104,195],"robustness.":[67],"First,":[68],"the":[69,78,112,135,139,152,156,159,163,168,171,180,189,193,201,206,212,235],"training":[70,209],"set":[71],"partitioned":[73],"into":[74,138],"multiple":[75,97,136],"subsets":[76],"by":[77,91,117],"cross":[79],"validation":[80],"method,":[81],"each":[84,145],"subset":[85],"sub-model":[87],"independently":[89],"constructed":[90],"optimization.":[92],"effectively":[94,187],"solve":[95],"these":[96,122],"tasks,":[99],"an":[100,226],"improved":[101],"evolutionary":[102],"algorithm":[103],"transfer":[105],"migration":[106],"developed,":[108],"which":[109],"can":[110,186,219],"enhance":[111],"efficiency":[114],"robustness":[116,218],"useful":[118],"information":[119,183],"exchange":[120],"between":[121],"similar":[123],"tasks.":[125],"Second,":[126],"novel":[128],"method":[130],"integrate":[134],"sub-models":[137,157,194],"final":[140],"model.":[141],"significance":[143],"scored":[149],"according":[150],"error":[153],"estimation":[154],"occurrence":[160],"frequency":[161],"in":[166],"all":[167],"sub-models.":[169],"Then":[170],"are":[174,229],"ranked":[175],"selected":[177],"bias-corrected":[181],"Akaike\u2019s":[182],"criterion.":[184],"PRS-MOEM":[185],"mitigate":[188],"negative":[190],"influence":[191],"from":[192,205],"large":[196],"error,":[198],"alleviate":[200],"uncertain":[202],"impact":[203],"resulting":[204],"randomness":[207],"subsets.":[210],"Thus":[211],"accuracy":[216],"be":[220],"enhanced.":[221],"Seven":[222],"numerical":[223],"examples":[224],"engineering":[227],"problem":[228],"utilized":[230],"test":[232],"verify":[234],"effectiveness":[236],"PRS-MOEM.":[238]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
