{"id":"https://openalex.org/W7135073829","doi":"https://doi.org/10.1109/clei67442.2025.11420710","title":"Shape-Constrained Hybrid Deep Learning\u2013Genetic Programming Algorithm for Symbolic Regression","display_name":"Shape-Constrained Hybrid Deep Learning\u2013Genetic Programming Algorithm for Symbolic Regression","publication_year":2025,"publication_date":"2025-10-27","ids":{"openalex":"https://openalex.org/W7135073829","doi":"https://doi.org/10.1109/clei67442.2025.11420710"},"language":null,"primary_location":{"id":"doi:10.1109/clei67442.2025.11420710","is_oa":false,"landing_page_url":"https://doi.org/10.1109/clei67442.2025.11420710","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 LI Latin American Computer Conference (CLEI)","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/A5116830895","display_name":"Rodrigo Gordienko","orcid":null},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Rodrigo Gordienko","raw_affiliation_strings":["Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040557863","display_name":"Miguel\u00e1ngel D\u00edaz","orcid":null},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Miguel\u00e1ngel D\u00edaz","raw_affiliation_strings":["Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073891151","display_name":"Jimena Ferreira","orcid":"https://orcid.org/0000-0002-8848-8404"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Jimena Ferreira","raw_affiliation_strings":["Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) and Instituto de Ingenier&#x00ED;a Qu&#x00ED;mica (IIQ) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) and Instituto de Ingenier&#x00ED;a Qu&#x00ED;mica (IIQ) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay","institution_ids":["https://openalex.org/I180910786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091770128","display_name":"Mart\u00edn Pedemonte","orcid":"https://orcid.org/0000-0002-8348-0921"},"institutions":[{"id":"https://openalex.org/I180910786","display_name":"Universidad de la Rep\u00fablica de Uruguay","ror":"https://ror.org/030bbe882","country_code":"UY","type":"education","lineage":["https://openalex.org/I180910786"]}],"countries":["UY"],"is_corresponding":false,"raw_author_name":"Mart\u00edn Pedemonte","raw_affiliation_strings":["Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad de la Rep&#x00FA;blica (UDELAR),Instituto de Computaci&#x00F3;n (INCO) Facultad de Ingenier&#x00ED;a,Montevideo,Uruguay","institution_ids":["https://openalex.org/I180910786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I180910786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.82207684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":0.9210000038146973,"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":0.9210000038146973,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.023099999874830246,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.018200000748038292,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/symbolic-regression","display_name":"Symbolic regression","score":0.9199000000953674},{"id":"https://openalex.org/keywords/genetic-programming","display_name":"Genetic programming","score":0.7210000157356262},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5311999917030334},{"id":"https://openalex.org/keywords/genetic-algorithm","display_name":"Genetic algorithm","score":0.4535999894142151},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.44519999623298645},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4426000118255615},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4372999966144562}],"concepts":[{"id":"https://openalex.org/C2776400721","wikidata":"https://www.wikidata.org/wiki/Q18171762","display_name":"Symbolic regression","level":3,"score":0.9199000000953674},{"id":"https://openalex.org/C110332635","wikidata":"https://www.wikidata.org/wiki/Q629498","display_name":"Genetic programming","level":2,"score":0.7210000157356262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5983999967575073},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5311999917030334},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5070000290870667},{"id":"https://openalex.org/C8880873","wikidata":"https://www.wikidata.org/wiki/Q187787","display_name":"Genetic algorithm","level":2,"score":0.4535999894142151},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4426000118255615},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4372999966144562},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4250999987125397},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4052000045776367},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3889000117778778},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3310000002384186},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.3246999979019165},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.28790000081062317},{"id":"https://openalex.org/C65620979","wikidata":"https://www.wikidata.org/wiki/Q7661176","display_name":"Symbolic data analysis","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2578999996185303}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/clei67442.2025.11420710","is_oa":false,"landing_page_url":"https://doi.org/10.1109/clei67442.2025.11420710","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 LI Latin American Computer Conference (CLEI)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310753","display_name":"Agencia Nacional de Investigaci\u00f3n e Innovaci\u00f3n","ror":"https://ror.org/03egaj678"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1795093649","https://openalex.org/W2096166399","https://openalex.org/W2121162457","https://openalex.org/W2126105956","https://openalex.org/W2145479420","https://openalex.org/W2768421170","https://openalex.org/W2790062217","https://openalex.org/W2899283552","https://openalex.org/W2966361623","https://openalex.org/W2987597555","https://openalex.org/W3016401366","https://openalex.org/W3150767555","https://openalex.org/W4220904807","https://openalex.org/W4235721129","https://openalex.org/W4253529704","https://openalex.org/W4293857795","https://openalex.org/W4310079394","https://openalex.org/W4315643982","https://openalex.org/W4321350776","https://openalex.org/W4322739118","https://openalex.org/W4366262984","https://openalex.org/W4385245566","https://openalex.org/W4391249853","https://openalex.org/W4392567326","https://openalex.org/W4407633383","https://openalex.org/W7133191970"],"related_works":[],"abstract_inverted_index":{"Symbolic":[0,129,210],"regression":[1,113],"aims":[2],"to":[3,42,48,55,190,262],"discover":[4],"a":[5,11,19,155],"symbolic":[6,112],"equation":[7],"that":[8,50,90,160,220,233],"best":[9],"describes":[10],"given":[12],"dataset.":[13],"It":[14],"is":[15,38,71,228],"commonly":[16],"formulated":[17],"as":[18,94,100,127],"single-objective":[20,178],"problem":[21,68],"focused":[22],"on":[23,116,203],"minimizing":[24,82],"prediction":[25,163],"error,":[26],"typically":[27],"using":[28,146],"genetic":[29,124],"programming-based":[30],"algorithms.":[31],"However,":[32],"in":[33,196,266],"many":[34],"engineering":[35],"applications,":[36],"it":[37],"crucial":[39],"not":[40,62,234],"only":[41,235],"achieve":[43],"high":[44],"accuracy":[45],"but":[46,182,240],"also":[47,241],"ensure":[49],"the":[51,67,83,105,139,151,166,173,177,208,237,244,251,257],"resulting":[52],"model":[53,264],"adheres":[54],"physico-chemical":[56],"laws":[57],"and":[58,120,165,213,247],"constraints,":[59],"which":[60,79],"are":[61,98],"always":[63],"explicitly":[64],"incorporated":[65],"into":[66,144],"formulation.":[69],"This":[70,136],"often":[72],"addressed":[73],"by":[74],"introducing":[75],"an":[76],"additional":[77],"objective,":[78],"may":[80],"involve":[81],"number":[84,167],"of":[85,107,141,158,168,180,230,250,259],"undefined":[86],"points":[87],"or":[88],"those":[89],"violate":[91],"constraints":[92,97,143,195],"such":[93,126],"monotonicity.":[95],"These":[96,254],"known":[99],"shape":[101,142,246],"constraints.In":[102],"recent":[103],"years,":[104],"design":[106],"deep":[108],"neural":[109,118],"networks":[110],"for":[111],"(primarily":[114],"based":[115],"recurrent":[117],"networks)":[119],"their":[121],"hybridization":[122],"with":[123,194,224],"programming,":[125],"Deep":[128],"Optimization":[130],"(DSO),":[131],"has":[132],"attracted":[133],"significant":[134],"interest.":[135],"work":[137],"explores":[138],"incorporation":[140],"DSO":[145,159,181],"two":[147],"different":[148],"approaches.":[149],"In":[150,172],"first,":[152],"we":[153,175],"analyze":[154],"multi-objective":[156],"extension":[157],"simultaneously":[161],"minimizes":[162],"error":[164],"constraint-violating":[169],"(out-of-spec)":[170],"points.":[171],"second,":[174],"retain":[176],"formulation":[179],"incorporate":[183],"Deb\u2019s":[184,225],"constraint-handling":[185],"selection":[186,226],"operator,":[187,227],"specially":[188],"designed":[189],"address":[191],"optimization":[192],"problems":[193],"Genetic":[197],"Algorithms.The":[198],"experimental":[199],"evaluation":[200],"was":[201],"conducted":[202],"several":[204],"benchmark":[205],"functions":[206],"from":[207,214],"Feynman":[209],"Regression":[211],"Database":[212],"Vladislavleva\u2019s":[215],"work.":[216],"Our":[217],"results":[218],"show":[219],"DSO,":[221],"when":[222],"combined":[223],"capable":[229],"identifying":[231],"models":[232],"fit":[236],"data":[238],"accurately,":[239],"better":[242],"capture":[243],"functional":[245],"physical":[248],"principles":[249],"underlying":[252],"systems.":[253],"findings":[255],"highlight":[256],"potential":[258],"this":[260],"approach":[261],"improve":[263],"reliability":[265],"complex":[267],"real-world":[268],"scenarios.":[269]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2026-03-13T00:00:00"}
