{"id":"https://openalex.org/W3116599870","doi":"https://doi.org/10.1007/s11047-020-09834-y","title":"The fractal geometry of fitness landscapes at the local optima level","display_name":"The fractal geometry of fitness landscapes at the local optima level","publication_year":2020,"publication_date":"2020-12-19","ids":{"openalex":"https://openalex.org/W3116599870","doi":"https://doi.org/10.1007/s11047-020-09834-y","mag":"3116599870"},"language":"en","primary_location":{"id":"doi:10.1007/s11047-020-09834-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-020-09834-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-020-09834-y.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11047-020-09834-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074122533","display_name":"Sarah L. Thomson","orcid":"https://orcid.org/0000-0001-6971-7817"},"institutions":[{"id":"https://openalex.org/I12093191","display_name":"University of Stirling","ror":"https://ror.org/045wgfr59","country_code":"GB","type":"education","lineage":["https://openalex.org/I12093191"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Sarah L. Thomson","raw_affiliation_strings":["Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK","University of Stirling (Stirling FK9 4LA - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK","institution_ids":["https://openalex.org/I12093191"]},{"raw_affiliation_string":"University of Stirling (Stirling FK9 4LA - United Kingdom)","institution_ids":["https://openalex.org/I12093191"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090624529","display_name":"Gabriela Ochoa","orcid":"https://orcid.org/0000-0001-7649-5669"},"institutions":[{"id":"https://openalex.org/I12093191","display_name":"University of Stirling","ror":"https://ror.org/045wgfr59","country_code":"GB","type":"education","lineage":["https://openalex.org/I12093191"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Gabriela Ochoa","raw_affiliation_strings":["Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK","University of Stirling (Stirling FK9 4LA - United Kingdom)"],"affiliations":[{"raw_affiliation_string":"Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK","institution_ids":["https://openalex.org/I12093191"]},{"raw_affiliation_string":"University of Stirling (Stirling FK9 4LA - United Kingdom)","institution_ids":["https://openalex.org/I12093191"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078220546","display_name":"Seb\u00e1stien V\u00e9rel","orcid":"https://orcid.org/0000-0003-1661-4093"},"institutions":[{"id":"https://openalex.org/I2802487185","display_name":"Universit\u00e9 du littoral c\u00f4te d'opale","ror":"https://ror.org/02gdcg342","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802487185"]},{"id":"https://openalex.org/I4387154658","display_name":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale","ror":"https://ror.org/00tm1qp20","country_code":null,"type":"facility","lineage":["https://openalex.org/I2802487185","https://openalex.org/I4387154658"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S\u00e9bastien Verel","raw_affiliation_strings":["Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale, Univ. Littoral C\u00f4te d\u2019Opale, F-62100, Calais, France","LISIC - Laboratoire d'Informatique Signal et Image de la C\u00f4te d'Opale (Maison de la Recherche Blaise Pascal 50, rue Ferdinand Buisson BP 719 62228 Calais Cedex - France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale, Univ. Littoral C\u00f4te d\u2019Opale, F-62100, Calais, France","institution_ids":["https://openalex.org/I2802487185"]},{"raw_affiliation_string":"LISIC - Laboratoire d'Informatique Signal et Image de la C\u00f4te d'Opale (Maison de la Recherche Blaise Pascal 50, rue Ferdinand Buisson BP 719 62228 Calais Cedex - France)","institution_ids":["https://openalex.org/I4387154658"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074122533"],"corresponding_institution_ids":["https://openalex.org/I12093191"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.2743,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66205906,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"2","first_page":"317","last_page":"333"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9847000241279602,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9847000241279602,"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.9775999784469604,"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"}},{"id":"https://openalex.org/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.7649064064025879},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.7081080675125122},{"id":"https://openalex.org/keywords/fitness-landscape","display_name":"Fitness landscape","score":0.6244868040084839},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5939067006111145},{"id":"https://openalex.org/keywords/local-optimum","display_name":"Local optimum","score":0.5184604525566101},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5109926462173462},{"id":"https://openalex.org/keywords/fractal-analysis","display_name":"Fractal analysis","score":0.5092424154281616},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4751843512058258},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44670921564102173},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4308144152164459},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38620898127555847},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35772833228111267},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25002729892730713},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1627936065196991},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11159294843673706}],"concepts":[{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.7649064064025879},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.7081080675125122},{"id":"https://openalex.org/C91852762","wikidata":"https://www.wikidata.org/wiki/Q3307742","display_name":"Fitness landscape","level":3,"score":0.6244868040084839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5939067006111145},{"id":"https://openalex.org/C141934464","wikidata":"https://www.wikidata.org/wiki/Q3305386","display_name":"Local optimum","level":2,"score":0.5184604525566101},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5109926462173462},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.5092424154281616},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4751843512058258},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44670921564102173},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4308144152164459},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38620898127555847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35772833228111267},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25002729892730713},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1627936065196991},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11159294843673706},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11047-020-09834-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-020-09834-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-020-09834-y.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03098496v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03098496","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"Natural Computing, 2022, 21 (2), pp.317-333. &#x27E8;10.1007/s11047-020-09834-y&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:dspace.stir.ac.uk:1893/32149","is_oa":true,"landing_page_url":"http://hdl.handle.net/1893/32149","pdf_url":null,"source":{"id":"https://openalex.org/S4306400268","display_name":"Stirling Online Research Repository (University of Stirling)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I12093191","host_organization_name":"University of Stirling","host_organization_lineage":["https://openalex.org/I12093191"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s11047-020-09834-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11047-020-09834-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11047-020-09834-y.pdf","source":{"id":"https://openalex.org/S149828480","display_name":"Natural Computing","issn_l":"1567-7818","issn":["1567-7818","1572-9796"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Natural Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3116599870.pdf","grobid_xml":"https://content.openalex.org/works/W3116599870.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W1411006099","https://openalex.org/W1503085769","https://openalex.org/W1556137908","https://openalex.org/W1568601672","https://openalex.org/W1862390599","https://openalex.org/W1967426304","https://openalex.org/W1967607711","https://openalex.org/W1971700807","https://openalex.org/W1973353128","https://openalex.org/W1991818682","https://openalex.org/W2024956277","https://openalex.org/W2042051539","https://openalex.org/W2043807498","https://openalex.org/W2057728542","https://openalex.org/W2075909822","https://openalex.org/W2084512390","https://openalex.org/W2093083775","https://openalex.org/W2098677716","https://openalex.org/W2101221513","https://openalex.org/W2102262771","https://openalex.org/W2107709238","https://openalex.org/W2133291040","https://openalex.org/W2144349513","https://openalex.org/W2149474855","https://openalex.org/W2160058983","https://openalex.org/W2161032864","https://openalex.org/W2167577506","https://openalex.org/W2180904362","https://openalex.org/W2198983756","https://openalex.org/W2219036994","https://openalex.org/W2335790881","https://openalex.org/W2474645015","https://openalex.org/W2563613854","https://openalex.org/W2592397440","https://openalex.org/W2618079578","https://openalex.org/W2754051486","https://openalex.org/W2783131004","https://openalex.org/W2784190987","https://openalex.org/W2803257757","https://openalex.org/W2809732001","https://openalex.org/W2888078032","https://openalex.org/W2888161290","https://openalex.org/W3101111722","https://openalex.org/W3102600948","https://openalex.org/W4207063358","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2605357193","https://openalex.org/W2169163271","https://openalex.org/W2142398281","https://openalex.org/W2116069637","https://openalex.org/W2011014349","https://openalex.org/W2209700215","https://openalex.org/W1986922629","https://openalex.org/W2474645015","https://openalex.org/W2125813753","https://openalex.org/W2804635689"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"local":[2,7],"optima":[3,8],"network":[4],"(LON)":[5],"encodes":[6],"connectivity":[9],"in":[10,106,111,116],"the":[11,48,62,98,107],"fitness":[12],"landscape":[13],"of":[14,51,84,100,133],"a":[15,32,36,43],"combinatorial":[16],"optimisation":[17],"problem.":[18,64],"Recently,":[19],"LONs":[20,52,85,134],"have":[21],"been":[22],"studied":[23],"for":[24],"their":[25],"fractal":[26,49,82,104],"dimension":[27,30,38],".":[28],"Fractal":[29],"is":[31],"complexity":[33],"index":[34],"where":[35],"non-integer":[37],"can":[39,86,109],"be":[40],"assigned":[41],"to":[42,58,75,88],"pattern.":[44],"This":[45],"paper":[46],"investigates":[47],"nature":[50,56],"and":[53,71,80,90,102,130],"how":[54],"that":[55,77,81,97],"relates":[57],"metaheuristic":[59],"performance":[60],"on":[61],"underlying":[63],"We":[65],"use":[66],"visual":[67,131],"analysis,":[68,70],"correlation":[69],"machine":[72],"learning":[73],"techniques":[74],"demonstrate":[76],"relationships":[78],"exist":[79],"features":[83],"contribute":[87,110],"explaining":[89],"predicting":[91],"algorithm":[92],"performance.":[93],"The":[94],"results":[95],"show":[96],"extent":[99],"multifractality":[101],"high":[103],"dimensions":[105],"LON":[108],"this":[112,138],"way":[113],"when":[114],"placed":[115],"regression":[117],"models":[118],"with":[119,127],"other":[120],"predictors.":[121],"Features":[122],"are":[123],"also":[124],"individually":[125],"correlated":[126],"search":[128],"performance,":[129],"analysis":[132],"shows":[135],"insight":[136],"into":[137],"relationship.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
