{"id":"https://openalex.org/W4328029481","doi":"https://doi.org/10.1111/cgf.14698","title":"Large\u2010Scale Worst\u2010Case Topology Optimization","display_name":"Large\u2010Scale Worst\u2010Case Topology Optimization","publication_year":2022,"publication_date":"2022-10-01","ids":{"openalex":"https://openalex.org/W4328029481","doi":"https://doi.org/10.1111/cgf.14698"},"language":"en","primary_location":{"id":"doi:10.1111/cgf.14698","is_oa":false,"landing_page_url":"https://doi.org/10.1111/cgf.14698","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","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/A5100740778","display_name":"Di Zhang","orcid":"https://orcid.org/0000-0003-0176-3424"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Di Zhang","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036422892","display_name":"Xiaoya Zhai","orcid":"https://orcid.org/0000-0002-5209-8738"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoya Zhai","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000841004","display_name":"Xiao\u2010Ming Fu","orcid":"https://orcid.org/0000-0001-8479-0107"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao\u2010Ming Fu","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101497069","display_name":"Heming Wang","orcid":"https://orcid.org/0000-0003-3861-0624"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heming Wang","raw_affiliation_strings":["Harrow International School Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harrow International School Hong Kong","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100635702","display_name":"Ligang Liu","orcid":"https://orcid.org/0000-0003-4352-1431"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ligang Liu","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5036422892"],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.8069,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.69633165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"41","issue":"7","first_page":"529","last_page":"540"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9908000230789185,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9550999999046326,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.7534151077270508},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7262288331985474},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.5809151530265808},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.5721357464790344},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5398200750350952},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5291322469711304},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5106850266456604},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4305698275566101},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41168057918548584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19982457160949707},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.13080397248268127}],"concepts":[{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.7534151077270508},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7262288331985474},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5809151530265808},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.5721357464790344},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5398200750350952},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5291322469711304},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5106850266456604},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4305698275566101},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41168057918548584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19982457160949707},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.13080397248268127},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/cgf.14698","is_oa":false,"landing_page_url":"https://doi.org/10.1111/cgf.14698","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3361998035","display_name":null,"funder_award_id":"62025207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8215243081","display_name":null,"funder_award_id":"WK0010000075","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W305632992","https://openalex.org/W1989391437","https://openalex.org/W1992388930","https://openalex.org/W2008064893","https://openalex.org/W2013832277","https://openalex.org/W2019550344","https://openalex.org/W2035238076","https://openalex.org/W2044809217","https://openalex.org/W2067977245","https://openalex.org/W2068668671","https://openalex.org/W2073208891","https://openalex.org/W2079865456","https://openalex.org/W2082772288","https://openalex.org/W2086223322","https://openalex.org/W2086674516","https://openalex.org/W2092801729","https://openalex.org/W2115495036","https://openalex.org/W2122712204","https://openalex.org/W2132034927","https://openalex.org/W2140349915","https://openalex.org/W2260417192","https://openalex.org/W2329216708","https://openalex.org/W2512094111","https://openalex.org/W2554319423","https://openalex.org/W2738015770","https://openalex.org/W2738624871","https://openalex.org/W2902393810","https://openalex.org/W2903298682","https://openalex.org/W2942685005","https://openalex.org/W3038590430","https://openalex.org/W3042448745","https://openalex.org/W3105070525","https://openalex.org/W3110066891","https://openalex.org/W3128774147","https://openalex.org/W3133560517","https://openalex.org/W3184592058","https://openalex.org/W3204708751"],"related_works":["https://openalex.org/W2046491619","https://openalex.org/W2389142552","https://openalex.org/W2239929624","https://openalex.org/W2883804989","https://openalex.org/W2081304691","https://openalex.org/W3018492858","https://openalex.org/W2127556255","https://openalex.org/W279903623","https://openalex.org/W3040505186","https://openalex.org/W3124542853"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"propose":[2],"a":[3,15,27,113,129],"novel":[4],"topology":[5,51],"optimization":[6],"method":[7,30,45,63,123],"to":[8,23,38,46,64],"efficiently":[9],"minimize":[10],"the":[11,35,40,55,60,66,71,77,81,86,92],"maximum":[12,36],"compliance":[13],"for":[14,49,69,112],"high\u2010resolution":[16],"model":[17,114],"bearing":[18],"uncertain":[19],"external":[20],"loads.":[21],"Central":[22],"this":[24],"approach":[25,104],"is":[26],"modified":[28],"power":[29],"that":[31],"can":[32],"quickly":[33],"compute":[34],"eigenvalue":[37],"evaluate":[39],"worst\u2010case":[41,56,78],"compliance,":[42,57,79],"enabling":[43],"our":[44,89,103,122],"be":[47],"suitable":[48],"large\u2010scale":[50,109],"optimization.":[52],"After":[53],"obtaining":[54],"we":[58],"use":[59],"adjoint":[61],"variable":[62],"perform":[65],"sensitivity":[67,82],"analysis":[68],"updating":[70,85],"density":[72,87],"variables.":[73],"By":[74],"iteratively":[75],"computing":[76],"performing":[80],"analysis,":[83],"and":[84,100,118],"variables,":[88],"algorithm":[90],"achieves":[91],"optimized":[93],"models":[94],"with":[95,132,139],"high":[96],"efficiency.":[97],"The":[98],"capability":[99],"feasibility":[101],"of":[102,115],"are":[105],"demonstrated":[106],"over":[107],"various":[108],"models.":[110],"Typically,":[111],"size":[116],"512\u00d7170\u00d7170":[117],"69934":[119],"loading":[120],"nodes,":[121],"took":[124],"about":[125],"50":[126],"minutes":[127],"on":[128],"desktop":[130],"computer":[131],"an":[133],"NVIDIA":[134],"GTX":[135],"1080Ti":[136],"graphics":[137],"card":[138],"11":[140],"GB":[141],"memory.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}