{"id":"https://openalex.org/W2559173494","doi":"https://doi.org/10.1109/cec.2016.7744343","title":"Truncated expected hypervolume improvement: Exact computation and application","display_name":"Truncated expected hypervolume improvement: Exact computation and application","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2559173494","doi":"https://doi.org/10.1109/cec.2016.7744343","mag":"2559173494"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2016.7744343","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2016.7744343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-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/A5077564991","display_name":"Kaifeng Yang","orcid":"https://orcid.org/0000-0002-3353-3298"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Kaifeng Yang","raw_affiliation_strings":["Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085426879","display_name":"Andr\u00e9 Deutz","orcid":"https://orcid.org/0000-0002-9047-6533"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Andre Deutz","raw_affiliation_strings":["Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008972548","display_name":"Zhiwei Yang","orcid":"https://orcid.org/0000-0001-9896-4518"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Zhiwei Yang","raw_affiliation_strings":["Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062646838","display_name":"Thomas B\u00e4ck","orcid":"https://orcid.org/0000-0001-6768-1478"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Thomas Back","raw_affiliation_strings":["Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007378438","display_name":"Michael Emmerich","orcid":"https://orcid.org/0000-0002-7342-2090"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Michael Emmerich","raw_affiliation_strings":["Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Leiden Institute of Advanced Computer Science, Leiden University, Leiden, CA, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5077564991"],"corresponding_institution_ids":["https://openalex.org/I121797337"],"apc_list":null,"apc_paid":null,"fwci":3.1363,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.92482291,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"4350","last_page":"4357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9919000267982483,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7127981185913086},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.7120945453643799},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6886113882064819},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.6182394623756409},{"id":"https://openalex.org/keywords/kriging","display_name":"Kriging","score":0.5666952133178711},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4586309492588043},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4546331763267517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44117873907089233},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.4352344870567322},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43357789516448975},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24823808670043945},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08288604021072388}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7127981185913086},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.7120945453643799},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6886113882064819},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.6182394623756409},{"id":"https://openalex.org/C81692654","wikidata":"https://www.wikidata.org/wiki/Q225926","display_name":"Kriging","level":2,"score":0.5666952133178711},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4586309492588043},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4546331763267517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44117873907089233},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.4352344870567322},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43357789516448975},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24823808670043945},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08288604021072388},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2016.7744343","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2016.7744343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Congress on Evolutionary Computation (CEC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W86912879","https://openalex.org/W1510052597","https://openalex.org/W1555080919","https://openalex.org/W1947771597","https://openalex.org/W1967710068","https://openalex.org/W2009632801","https://openalex.org/W2029959045","https://openalex.org/W2036476072","https://openalex.org/W2038420231","https://openalex.org/W2043635344","https://openalex.org/W2045173716","https://openalex.org/W2078884695","https://openalex.org/W2106334424","https://openalex.org/W2111526171","https://openalex.org/W2125899728","https://openalex.org/W2126105956","https://openalex.org/W2131627640","https://openalex.org/W2135305876","https://openalex.org/W2136918060","https://openalex.org/W2138309709","https://openalex.org/W2141870007","https://openalex.org/W2151956767","https://openalex.org/W2156267707","https://openalex.org/W2272322821","https://openalex.org/W2548304608","https://openalex.org/W3099242408","https://openalex.org/W6657797417","https://openalex.org/W6925245313"],"related_works":["https://openalex.org/W2090178682","https://openalex.org/W1702471942","https://openalex.org/W2001591765","https://openalex.org/W4241467429","https://openalex.org/W2073147994","https://openalex.org/W2384474142","https://openalex.org/W3083133203","https://openalex.org/W1588199609","https://openalex.org/W2744462909","https://openalex.org/W1971520370"],"abstract_inverted_index":{"In":[0,136],"optimization":[1,59,129],"with":[2],"expensive":[3],"black":[4],"box":[5],"evaluations,":[6],"the":[7,32,37,61,67,71,95,119,145,191,216],"expected":[8,38,62,68,121,147],"improvement":[9,39,123,149],"algorithm":[10],"(also":[11],"called":[12],"efficient":[13,127,162],"global":[14,128,163],"optimization)":[15],"is":[16,90,132,140,155,166,186,194],"a":[17,29,75,101,125],"commonly":[18],"applied":[19],"method.":[20],"It":[21,53,165],"uses":[22,36],"Gaussian":[23],"Processes":[24],"(or":[25],"Kriging)":[26],"to":[27,57,143,215],"build":[28],"model":[30],"of":[31,74,112,174,190],"objective":[33,85,96],"function":[34,97],"and":[35,51,124,151,177,199],"as":[40,157],"an":[41,83,158],"infill":[42,159],"criterion,":[43],"taking":[44],"into":[45],"account":[46],"both":[47],"\u2014":[48],"predictive":[49],"mean":[50],"variance.":[52],"has":[54],"been":[55],"generalized":[56],"multi-objective":[58],"using":[60],"hypervolume":[63,72,122,148],"improvement,":[64],"which":[65],"measures":[66],"gain":[69],"in":[70,161,181,196,210],"indicator":[73],"Pareto":[76],"front":[77],"approximation.":[78],"However,":[79],"this":[80,116,137,211],"criterion":[81,160],"assumes":[82],"unbounded":[84],"space":[86],"even":[87],"if":[88],"it":[89,139,154,169],"often":[91],"known":[92],"a-priori":[93,114,175],"that":[94,131,168],"values":[98],"are":[99,213],"within":[100],"prescribed":[102],"range,":[103],"e.g.,":[104],"lower":[105],"bounded":[106],"by":[107],"zero.":[108],"To":[109],"take":[110],"advantage":[111],"such":[113,184],"knowledge,":[115],"paper":[117,138,212],"introduces":[118],"truncated":[120,146],"multiobjective":[126],"method":[130],"based":[133],"on":[134],"it.":[135],"shown":[141,167],"how":[142],"compute":[144],"exactly":[150],"efficiently.":[152],"Then":[153],"tested":[156],"optimization.":[164,206],"can":[170],"effectively":[171],"make":[172],"use":[173],"knowledge":[176,185],"achieve":[178],"better":[179],"results":[180],"cases":[182],"where":[183],"given.":[187],"The":[188,207],"usefulness":[189],"new":[192],"approach":[193],"demonstrated":[195],"benchmark":[197],"examples":[198],"applications":[200],"from":[201],"robust":[202],"PID":[203],"(proportionalintegral-derivative)":[204],"controller":[205],"empirical":[208],"studies":[209],"confined":[214],"bi-objective":[217],"case.":[218]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}