{"id":"https://openalex.org/W2953554272","doi":"https://doi.org/10.1109/access.2019.2924931","title":"Robust Optimization for Micromachine Design Problems Involving Multimodal Distributions","display_name":"Robust Optimization for Micromachine Design Problems Involving Multimodal Distributions","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2953554272","doi":"https://doi.org/10.1109/access.2019.2924931","mag":"2953554272"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2924931","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2924931","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08746211.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08746211.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071739169","display_name":"Zhiliang Huang","orcid":"https://orcid.org/0000-0002-7840-8976"},"institutions":[{"id":"https://openalex.org/I39521962","display_name":"Hunan City University","ror":"https://ror.org/01vd7vb53","country_code":"CN","type":"education","lineage":["https://openalex.org/I39521962"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. L. Huang","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China"],"raw_orcid":"https://orcid.org/0000-0002-7840-8976","affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China","institution_ids":["https://openalex.org/I39521962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101667424","display_name":"Jing Zhang","orcid":"https://orcid.org/0009-0004-1479-3803"},"institutions":[{"id":"https://openalex.org/I39521962","display_name":"Hunan City University","ror":"https://ror.org/01vd7vb53","country_code":"CN","type":"education","lineage":["https://openalex.org/I39521962"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"J. W. Zhang","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China","institution_ids":["https://openalex.org/I39521962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003522036","display_name":"T. Kishore Kumar","orcid":"https://orcid.org/0000-0001-9928-1647"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Tarun Kumar","raw_affiliation_strings":["Department of Electronics and Electrical Communication Engineering, IIT Kharagpur, Kharagpur, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Electrical Communication Engineering, IIT Kharagpur, Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049047503","display_name":"Tongguang Yang","orcid":"https://orcid.org/0000-0003-3880-8980"},"institutions":[{"id":"https://openalex.org/I39521962","display_name":"Hunan City University","ror":"https://ror.org/01vd7vb53","country_code":"CN","type":"education","lineage":["https://openalex.org/I39521962"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"T. G. Yang","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China","institution_ids":["https://openalex.org/I39521962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101706669","display_name":"Shuifeng Deng","orcid":"https://orcid.org/0009-0008-1736-9126"},"institutions":[{"id":"https://openalex.org/I39521962","display_name":"Hunan City University","ror":"https://ror.org/01vd7vb53","country_code":"CN","type":"education","lineage":["https://openalex.org/I39521962"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"S. G. Deng","raw_affiliation_strings":["School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical and Electrical Engineering, Hunan City University, Yiyang, China","institution_ids":["https://openalex.org/I39521962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037071828","display_name":"F. Y. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"F. Y. Li","raw_affiliation_strings":["College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China","institution_ids":["https://openalex.org/I56934997"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.6455,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76183746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"7","issue":null,"first_page":"91838","last_page":"91849"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9998000264167786,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7106396555900574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6844103336334229},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5711483955383301},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5288682579994202},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4857485890388489},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.4713546633720398},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.46172967553138733},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4390444755554199},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.41257986426353455},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38506388664245605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21429181098937988},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.2131960093975067},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09208494424819946}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7106396555900574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6844103336334229},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5711483955383301},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5288682579994202},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4857485890388489},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.4713546633720398},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.46172967553138733},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4390444755554199},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.41257986426353455},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38506388664245605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21429181098937988},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2131960093975067},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09208494424819946},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2924931","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2924931","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08746211.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:851c8b5ea2ab4df68c7822e195ddc61f","is_oa":false,"landing_page_url":"https://doaj.org/article/851c8b5ea2ab4df68c7822e195ddc61f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 91838-91849 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2924931","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2924931","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08746211.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3400631736","display_name":null,"funder_award_id":"2017JJ2022","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G5460185075","display_name":null,"funder_award_id":"51490662","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5881457459","display_name":null,"funder_award_id":"2019JJ40296","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G8544525171","display_name":null,"funder_award_id":"2016JJ2012","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2953554272.pdf","grobid_xml":"https://content.openalex.org/works/W2953554272.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W38477147","https://openalex.org/W74954028","https://openalex.org/W171143577","https://openalex.org/W580181017","https://openalex.org/W1513595735","https://openalex.org/W1519405745","https://openalex.org/W1978367676","https://openalex.org/W1991060553","https://openalex.org/W1993377828","https://openalex.org/W1993422931","https://openalex.org/W2003363885","https://openalex.org/W2007973956","https://openalex.org/W2010000350","https://openalex.org/W2015064969","https://openalex.org/W2018614861","https://openalex.org/W2022873827","https://openalex.org/W2032963210","https://openalex.org/W2047973167","https://openalex.org/W2049633694","https://openalex.org/W2076184585","https://openalex.org/W2083004653","https://openalex.org/W2087755223","https://openalex.org/W2094176506","https://openalex.org/W2099192586","https://openalex.org/W2104266414","https://openalex.org/W2107788734","https://openalex.org/W2140223291","https://openalex.org/W2140496876","https://openalex.org/W2145952084","https://openalex.org/W2152555872","https://openalex.org/W2163862895","https://openalex.org/W2290446981","https://openalex.org/W2327944507","https://openalex.org/W2502655619","https://openalex.org/W2525082097","https://openalex.org/W2615737084","https://openalex.org/W2745747553","https://openalex.org/W2782781832","https://openalex.org/W2803039928","https://openalex.org/W2808775206","https://openalex.org/W2899116600","https://openalex.org/W4214754825","https://openalex.org/W4236775215","https://openalex.org/W6751538720"],"related_works":["https://openalex.org/W3149055374","https://openalex.org/W2053131036","https://openalex.org/W2216231335","https://openalex.org/W3195104199","https://openalex.org/W4386254288","https://openalex.org/W4292572523","https://openalex.org/W2809352861","https://openalex.org/W2056349093","https://openalex.org/W2952007803","https://openalex.org/W2919687292"],"abstract_inverted_index":{"The":[0,121,158],"conventional":[1,37],"robust":[2,53],"optimization":[3,54,132],"methods":[4],"usually":[5],"focus":[6],"on":[7],"problems":[8,64],"with":[9,23],"unimodal":[10],"random":[11,17,32,67],"variables.":[12,68],"In":[13],"real":[14],"applications,":[15],"input":[16],"variables":[18,33],"may":[19],"follow":[20],"multimodal":[21,31,66,96],"distributions":[22],"multiple":[24],"peaks":[25],"in":[26,114,174],"their":[27],"probability":[28,86,112,127],"density.":[29],"When":[30],"are":[34],"involved,":[35],"the":[36,41,76,80,84,88,95,99,111,115,126,130,141,163,171],"methods,":[38,43],"such":[39],"as":[40],"mean-variance-based":[42],"will":[44],"be":[45],"not":[46],"accurate.":[47],"This":[48,136],"paper":[49],"presents":[50],"an":[51,154],"efficient":[52],"method,":[55],"which":[56,91],"provides":[57],"a":[58,147,150],"potential":[59],"computational":[60],"tool":[61],"for":[62],"engineering":[63,167],"involving":[65],"A":[69,101],"robustness":[70],"metric":[71],"is":[72,106,138],"formulated":[73],"by":[74],"introducing":[75],"concept":[77],"of":[78,87,98,118,176],"accepting/rejecting":[79],"limit":[81],"to":[82,108,140,170],"calculate":[83],"failure":[85],"performance":[89,173],"response,":[90],"can":[92],"directly":[93],"capture":[94],"characteristics":[97],"performance.":[100],"second-order":[102],"higher":[103],"moment":[104],"method":[105,137,164],"presented":[107],"efficiently":[109],"conduct":[110],"calculation":[113,128],"inner":[116],"loop":[117],"design":[119,131,144],"optimization.":[120],"proposed":[122],"decoupling":[123],"strategy":[124],"drives":[125],"and":[129,134,153,179],"sequentially":[133],"alternately.":[135],"applied":[139],"three":[142],"micromachine":[143],"problems,":[145],"including":[146],"sweat-rate":[148],"sensor,":[149,152],"piezoelectric":[151],"image":[155],"sensing":[156],"module.":[157],"numerical":[159],"results":[160],"show":[161],"that":[162],"has":[165],"excellent":[166],"practicality":[168],"due":[169],"comprehensive":[172],"terms":[175],"efficiency,":[177],"accuracy,":[178],"convergence.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}