{"id":"https://openalex.org/W2038895831","doi":"https://doi.org/10.1145/1570256.1570292","title":"Solving iterated functions using genetic programming","display_name":"Solving iterated functions using genetic programming","publication_year":2009,"publication_date":"2009-07-08","ids":{"openalex":"https://openalex.org/W2038895831","doi":"https://doi.org/10.1145/1570256.1570292","mag":"2038895831"},"language":"en","primary_location":{"id":"doi:10.1145/1570256.1570292","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1570256.1570292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers","raw_type":"proceedings-article"},"type":"conference-paper","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/A5088013683","display_name":"Michael D. Schmidt","orcid":"https://orcid.org/0000-0002-8062-4491"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Douglas Schmidt","raw_affiliation_strings":["Cornell University, Ithaca, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025894735","display_name":"Hod Lipson","orcid":"https://orcid.org/0000-0003-0769-4618"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hod Lipson","raw_affiliation_strings":["Cornell University, Ithaca, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":0.9748,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.74788962,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"2149","last_page":"2154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":1.0,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9972000122070312,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/genetic-programming","display_name":"Genetic programming","score":0.7524648904800415},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6388522386550903},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6342177391052246},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35476064682006836},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23699963092803955},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2254033088684082}],"concepts":[{"id":"https://openalex.org/C110332635","wikidata":"https://www.wikidata.org/wiki/Q629498","display_name":"Genetic programming","level":2,"score":0.7524648904800415},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6388522386550903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6342177391052246},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35476064682006836},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23699963092803955},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2254033088684082},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1570256.1570292","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1570256.1570292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.660.8404","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.660.8404","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.genetic-programming.org/hc2010/3-Schmidt-Iterated-Functions/Schmidt-Iterated-Functions-Paper.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337395","display_name":"Division of Emerging Frontiers in Research and Innovation","ror":"https://ror.org/0388pet74"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W97364567","https://openalex.org/W1489722004","https://openalex.org/W1540880949","https://openalex.org/W1576818901","https://openalex.org/W1585335425","https://openalex.org/W1861035380","https://openalex.org/W1961482980","https://openalex.org/W1979769287","https://openalex.org/W2051742392","https://openalex.org/W2091338396","https://openalex.org/W2093828424","https://openalex.org/W2097204767","https://openalex.org/W2143810412","https://openalex.org/W2152382764","https://openalex.org/W2170808194","https://openalex.org/W2500251224"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W3103325625","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W1486898455","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"An":[0],"iterated":[1,48,61,127],"function":[2,6,62],"f(x)":[3,66],"is":[4],"a":[5,13,79,106],"that":[7,68,89,114],"when":[8],"composed":[9],"with":[10],"itself,":[11],"produces":[12],"given":[14],"expression":[15],"f(f(x))=g(x).":[16],"Iterated":[17],"functions":[18,49],"are":[19],"essential":[20,120],"constructs":[21],"in":[22],"fractal":[23],"theory":[24],"and":[25],"dynamical":[26],"systems,":[27],"but":[28],"few":[29],"analysis":[30],"techniques":[31,73],"exist":[32],"for":[33,122],"solving":[34],"them":[35],"analytically.":[36],"Here":[37],"we":[38,87],"propose":[39],"using":[40,95],"genetic":[41,96,115],"programming":[42,97,116],"to":[43,47,77,82,100,110,125],"find":[44,78,105],"analytical":[45,72],"solutions":[46,124],"of":[50,64,84],"arbitrary":[51,126],"form.":[52],"We":[53,104],"demonstrate":[54],"this":[55,85,111],"technique":[56],"on":[57],"the":[58],"notoriously":[59],"hard":[60],"problem":[63],"finding":[65,123],"such":[67],"f(f(x))=x2--2.":[69],"While":[70],"some":[71],"have":[74],"been":[75],"developed":[76],"specific":[80],"solution":[81,109],"problems":[83],"form,":[86],"show":[88],"it":[90],"can":[91],"be":[92,118],"readily":[93],"solved":[94],"without":[98],"recourse":[99],"deep":[101],"mathematical":[102],"insight.":[103],"previously":[107],"unknown":[108],"problem,":[112],"suggesting":[113],"may":[117],"an":[119],"tool":[121],"functions.":[128]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}