{"id":"https://openalex.org/W7214775269","doi":"https://doi.org/10.3390/fractalfract10110771","title":"Hybrid Fractal\u2013Parametric Modeling and NSGA-II Optimization of Geometric Material-Volume Reduction in Generative Architectural Fa\u00e7ades","display_name":"Hybrid Fractal\u2013Parametric Modeling and NSGA-II Optimization of Geometric Material-Volume Reduction in Generative Architectural Fa\u00e7ades","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7214775269","doi":"https://doi.org/10.3390/fractalfract10110771"},"language":"en","primary_location":{"id":"doi:10.3390/fractalfract10110771","doi":"https://doi.org/10.3390/fractalfract10110771","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110771","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/fractalfract10110771","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075706075","display_name":"Golib Berdiev","orcid":"https://orcid.org/0000-0003-0075-5414","observed_orcids":["https://orcid.org/0000-0003-0075-5414"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Golib Berdiev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012998962","display_name":"Shahzoda Anarova","orcid":"https://orcid.org/0000-0001-5303-3461","observed_orcids":["https://orcid.org/0000-0001-5303-3461","https://orcid.org/0009-0007-5913-8302"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shahzoda Anarova","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153447799","display_name":"Navruz Khujakulov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Navruz Khujakulov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5075706075"],"corresponding_institution_ids":[],"apc_list":{"value":2700,"currency":"CHF","value_usd":3258},"apc_paid":{"value":2700,"currency":"CHF","value_usd":3258},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.73688703,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"11","first_page":"771","last_page":"771"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13518","display_name":"Architecture and Computational Design","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2216","display_name":"Architecture"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13518","display_name":"Architecture and Computational Design","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2216","display_name":"Architecture"},"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/T13133","display_name":"Architecture and Art History Studies","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1213","display_name":"Visual Arts and Performing Arts"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractal-geometry","display_name":"fractal geometry","score":0.9049999713897705},{"id":"https://openalex.org/keywords/generative-design","display_name":"generative design","score":0.5569999814033508},{"id":"https://openalex.org/keywords/building-facades","display_name":"building exteriors","score":0.8709999918937683},{"id":"https://openalex.org/keywords/iterated-function-systems","display_name":"iterated function systems","score":0.8640000224113464},{"id":"https://openalex.org/keywords/box-counting-dimension","display_name":"box-counting dimension","score":0.8029999732971191},{"id":"https://openalex.org/keywords/material-efficiency","display_name":"material efficiency","score":0.7760000228881836},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"multi-objective optimization","score":0.8479999899864197},{"id":"https://openalex.org/keywords/nsga-ii","display_name":"NSGA-II","score":0.9290000200271606},{"id":"https://openalex.org/keywords/pareto-front","display_name":"Pareto front","score":0.7879999876022339},{"id":"https://openalex.org/keywords/parametric-modeling","display_name":"parametric modeling","score":0.8420000076293945},{"id":"https://openalex.org/keywords/blender","display_name":"Blender","score":0.3540000021457672},{"id":"https://openalex.org/keywords/early-stage-design-exploration","display_name":"early-stage design exploration","score":0.7429999709129333}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5572999715805054},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.5087000131607056},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.492000013589859},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44600000977516174},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.4311999976634979},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4302999973297119},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42820000648498535},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.42730000615119934},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.42239999771118164},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4099999964237213},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.3700999915599823},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.34040001034736633},{"id":"https://openalex.org/C184408114","wikidata":"https://www.wikidata.org/wiki/Q1502022","display_name":"Generative Design","level":3,"score":0.3379000127315521},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.3255999982357025},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C24574437","wikidata":"https://www.wikidata.org/wiki/Q7135228","display_name":"Parametric model","level":3,"score":0.30880001187324524},{"id":"https://openalex.org/C186394612","wikidata":"https://www.wikidata.org/wiki/Q7098942","display_name":"Optimal design","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C2987595161","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimization algorithm","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C199639397","wikidata":"https://www.wikidata.org/wiki/Q1788588","display_name":"Engineering drawing","level":1,"score":0.26910001039505005},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.2655999958515167},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/fractalfract10110771","doi":"https://doi.org/10.3390/fractalfract10110771","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110771","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},{"id":"doi:10.20944/preprints202609.2432.v1","doi":"https://doi.org/10.20944/preprints202609.2432.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202609.2432.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.3390/fractalfract10110771","doi":"https://doi.org/10.3390/fractalfract10110771","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract10110771","pdf_url":null,"source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W560630400","https://openalex.org/W1983036870","https://openalex.org/W2000690667","https://openalex.org/W2014440501","https://openalex.org/W2031232041","https://openalex.org/W2032632859","https://openalex.org/W2035906911","https://openalex.org/W2039915758","https://openalex.org/W2041243828","https://openalex.org/W2085512126","https://openalex.org/W2088891828","https://openalex.org/W2093784257","https://openalex.org/W2094176506","https://openalex.org/W2107506137","https://openalex.org/W2125899728","https://openalex.org/W2126105956","https://openalex.org/W2147241601","https://openalex.org/W2332597905","https://openalex.org/W2511955001","https://openalex.org/W2791482837","https://openalex.org/W2939125753","https://openalex.org/W3021613070","https://openalex.org/W3115195799","https://openalex.org/W3153725732","https://openalex.org/W3213579748","https://openalex.org/W3214775353","https://openalex.org/W4200580548","https://openalex.org/W4206237136","https://openalex.org/W4236189709","https://openalex.org/W4238652859","https://openalex.org/W4249775755","https://openalex.org/W4324057990","https://openalex.org/W4365512143","https://openalex.org/W4390755221","https://openalex.org/W4392198183","https://openalex.org/W4399932868","https://openalex.org/W4405494978","https://openalex.org/W4408783815","https://openalex.org/W4412691818","https://openalex.org/W4413376531","https://openalex.org/W4414609831","https://openalex.org/W4417013574","https://openalex.org/W7148433446"],"related_works":["https://openalex.org/W4408783815","https://openalex.org/W2613429969","https://openalex.org/W4394815072","https://openalex.org/W135539698","https://openalex.org/W2952316514","https://openalex.org/W1535169809","https://openalex.org/W1932341080","https://openalex.org/W7172399638","https://openalex.org/W3041319603","https://openalex.org/W7125878891"],"abstract_inverted_index":{"Fractal":[0],"geometry":[1],"provides":[2],"a":[3,27,49,79,99,145,157],"compact":[4],"mathematical":[5],"framework":[6],"for":[7,161],"generating":[8],"and":[9,45,70,117,121,149],"measuring":[10],"multi-scale":[11],"architectural":[12],"form,":[13],"but":[14],"its":[15],"integration":[16],"with":[17,98],"material-aware":[18],"generative":[19],"fa\u00e7ade":[20,164],"optimization":[21,47,97],"remains":[22],"limited.":[23],"This":[24],"study":[25],"introduces":[26],"Hybrid":[28],"Fractal\u2013Parametric":[29],"Model":[30],"(HFPM)":[31],"that":[32],"combines":[33],"recursively":[34],"composed":[35],"affine":[36],"iterated-function-system":[37],"transformations,":[38],"parametric":[39],"control,":[40],"finite-scale":[41,81],"box-counting,":[42],"three-dimensional":[43],"extrusion,":[44],"NSGA-II":[46,96],"in":[48],"reproducible":[50,158],"Python\u2013Blender":[51],"workflow.":[52],"The":[53,106],"design":[54,93],"vector":[55],"P":[56],"=":[57,133,136],"(r,":[58],"s,":[59],"\u03b8,":[60],"d,":[61],"t)":[62],"controls":[63],"recursion,":[64],"scale,":[65],"rotation,":[66],"retained":[67],"branch":[68],"density,":[69],"thickness.":[71],"Material":[72],"volume":[73,140],"is":[74,84],"minimized":[75,85],"while":[76],"deviation":[77],"from":[78],"baseline":[80,131],"box-counting":[82],"dimension":[83],"simultaneously.":[86],"A":[87],"balanced":[88],"300-configuration":[89],"experiment":[90],"characterized":[91],"the":[92,124,130],"space":[94],"before":[95],"population":[100],"of":[101],"40":[102],"over":[103],"15":[104],"generations.":[105],"optimizer":[107],"evaluated":[108],"603":[109],"unique":[110],"non-baseline":[111],"configurations;":[112],"602":[113],"passed":[114],"all":[115],"geometric":[116],"numerical":[118],"validation":[119],"checks,":[120],"39":[122],"formed":[123],"final":[125],"Pareto":[126],"set.":[127],"Relative":[128],"to":[129],"(Df":[132],"1.9077;":[134],"Vm":[135],"0.9228":[137],"m\u00b3),":[138],"material":[139],"decreased":[141],"by":[142,150],"34.9%":[143],"within":[144,152],"1%":[146],"Df":[147],"tolerance":[148],"44.6%":[151],"2%.":[153],"HFPM":[154],"therefore":[155],"exposes":[156],"material\u2013complexity":[159],"trade-off":[160],"early-stage":[162],"fractal":[163],"exploration":[165],"without":[166],"making":[167],"unsupported":[168],"structural-performance":[169],"claims.":[170]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-30T00:00:00"}