{"id":"https://openalex.org/W2102044362","doi":"https://doi.org/10.1017/s0963548312000600","title":"Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions","display_name":"Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions","publication_year":2013,"publication_date":"2013-01-09","ids":{"openalex":"https://openalex.org/W2102044362","doi":"https://doi.org/10.1017/s0963548312000600","mag":"2102044362"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548312000600","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000600","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://orbit.dtu.dk/en/publications/6f7a4db7-d551-4c5d-a057-f4656fb445a2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038689623","display_name":"Carsten Witt","orcid":"https://orcid.org/0000-0002-6105-7700"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"CARSTEN WITT","raw_affiliation_strings":["DTU Informatics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark (e-mail:","Department of Applied Mathematics and Computer Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DTU Informatics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark (e-mail:","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038689623"],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":null,"apc_paid":null,"fwci":17.5686,"has_fulltext":false,"cited_by_count":217,"citation_normalized_percentile":{"value":0.99337629,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"22","issue":"2","first_page":"294","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9997000098228455,"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"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9965000152587891,"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/heuristic","display_name":"Heuristic","score":0.6309802532196045},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4935845136642456},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4399099349975586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3976738750934601}],"concepts":[{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6309802532196045},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4935845136642456},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4399099349975586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3976738750934601}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548312000600","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000600","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/6f7a4db7-d551-4c5d-a057-f4656fb445a2","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/6f7a4db7-d551-4c5d-a057-f4656fb445a2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Witt , C 2013 , ' Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions ' , Combinatorics, Probability & Computing , vol. 22 , no. 2 , pp. 294-318 . https://doi.org/10.1017/S0963548312000600","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/6f7a4db7-d551-4c5d-a057-f4656fb445a2","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/6f7a4db7-d551-4c5d-a057-f4656fb445a2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Witt , C 2013 , ' Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions ' , Combinatorics, Probability & Computing , vol. 22 , no. 2 , pp. 294-318 . https://doi.org/10.1017/S0963548312000600","raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1488747864","https://openalex.org/W1553838525","https://openalex.org/W1593495653","https://openalex.org/W1605768620","https://openalex.org/W1632066424","https://openalex.org/W1652824837","https://openalex.org/W1834691232","https://openalex.org/W1970025632","https://openalex.org/W1973749901","https://openalex.org/W1983804795","https://openalex.org/W1996375957","https://openalex.org/W2006309149","https://openalex.org/W2035300004","https://openalex.org/W2045438907","https://openalex.org/W2053222431","https://openalex.org/W2075706745","https://openalex.org/W2080956517","https://openalex.org/W2083320113","https://openalex.org/W2084149434","https://openalex.org/W2100137329","https://openalex.org/W2121811374","https://openalex.org/W2138926459","https://openalex.org/W2155926177","https://openalex.org/W2156622046","https://openalex.org/W2165220807","https://openalex.org/W2295428206","https://openalex.org/W2911346016","https://openalex.org/W3100597221","https://openalex.org/W4231916799","https://openalex.org/W4292058084"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"The":[0],"analysis":[1],"of":[2,8,15,23,39,50],"randomized":[3],"search":[4],"heuristics":[5],"on":[6,47],"classes":[7],"functions":[9],"is":[10,86,162,172],"fundamental":[11],"to":[12,70,89,174,185],"the":[13,16,21,35,48,55,154,169,181,190,195,201],"understanding":[14],"underlying":[17],"stochastic":[18],"process":[19],"and":[20,81,94,121,135,168],"development":[22],"suitable":[24],"proof":[25],"techniques.":[26],"Recently,":[27],"remarkable":[28],"progress":[29],"has":[30],"been":[31],"made":[32],"in":[33,60,79],"bounding":[34],"expected":[36,106],"optimization":[37,108],"time":[38,109],"a":[40,130,146,152],"simple":[41],"evolutionary":[42],"algorithm,":[43],"called":[44],"(1+1)":[45,170],"EA,":[46],"class":[49],"linear":[51,166],"functions.":[52],"We":[53],"improve":[54],"previously":[56],"best":[57],"known":[58],"bound":[59],"this":[61],"setting":[62],"from":[63],"(1.39+":[64],"o":[65],"(1))":[66],"en":[67,71],"ln":[68,72],"n":[69,73,77,117,119,125,144,161],"+":[74],"O":[75,115],"(":[76],")":[78,120,128],"expectation":[80],"with":[82],"high":[83],"probability,":[84],"which":[85,104,136],"tight":[87,138],"up":[88],"lower-order":[90],"terms.":[91],"Moreover,":[92],"upper":[93],"lower":[95],"bounds":[96],"for":[97,129,145,164],"arbitrary":[98],"mutation":[99,156,196],"probabilities":[100],"p":[101,113,122,140,158],"are":[102,137],"derived,":[103],"imply":[105],"polynomial":[107],"as":[110,112],"long":[111],"=":[114,123,141,159],"((ln":[116],")/":[118],"\u03a9(":[124],"\u2212":[126],"C":[127,132],"constant":[131,147],">":[133,149],"0,":[134],"if":[139],"c":[142,148],"/":[143],"0.":[150],"As":[151],"consequence,":[153],"standard":[155],"probability":[157],"1/":[160],"optimal":[163,177],"all":[165],"functions,":[167],"EA":[171],"found":[173],"be":[175,186],"an":[176],"mutation-based":[178],"algorithm.":[179],"Furthermore,":[180],"algorithm":[182],"turns":[183],"out":[184],"surprisingly":[187],"robust":[188],"since":[189],"large":[191],"neighbourhood":[192],"explored":[193],"by":[194],"operator":[197],"does":[198],"not":[199],"disrupt":[200],"search.":[202]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":27},{"year":2018,"cited_by_count":31},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}