{"id":"https://openalex.org/W4415960266","doi":"https://doi.org/10.48550/arxiv.2510.16943","title":"Peering Inside the Black Box: Uncovering LLM Errors in Optimization Modelling through Component-Level Evaluation","display_name":"Peering Inside the Black Box: Uncovering LLM Errors in Optimization Modelling through Component-Level Evaluation","publication_year":2025,"publication_date":"2025-10-19","ids":{"openalex":"https://openalex.org/W4415960266","doi":"https://doi.org/10.48550/arxiv.2510.16943"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2510.16943","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.16943","pdf_url":"https://arxiv.org/pdf/2510.16943","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.16943","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120280397","display_name":"Dania Refai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Refai, Dania","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058370129","display_name":"Moataz Ahmed","orcid":"https://orcid.org/0000-0003-0042-8819"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ahmed, Moataz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.16089999675750732,"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/T10028","display_name":"Topic Modeling","score":0.16089999675750732,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.14059999585151672,"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"}},{"id":"https://openalex.org/T11636","display_name":"Artificial Intelligence in Healthcare and Education","score":0.06449999660253525,"subfield":{"id":"https://openalex.org/subfields/2718","display_name":"Health Informatics"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6133999824523926},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5407000184059143},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5249999761581421},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4586000144481659},{"id":"https://openalex.org/keywords/constraint-logic-programming","display_name":"Constraint logic programming","score":0.41940000653266907},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4133000075817108},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.412200003862381},{"id":"https://openalex.org/keywords/constraint-satisfaction","display_name":"Constraint satisfaction","score":0.4020000100135803}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6381000280380249},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6133999824523926},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5407000184059143},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5249999761581421},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.477400004863739},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4586000144481659},{"id":"https://openalex.org/C176783269","wikidata":"https://www.wikidata.org/wiki/Q5164378","display_name":"Constraint logic programming","level":4,"score":0.41940000653266907},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.412200003862381},{"id":"https://openalex.org/C44616089","wikidata":"https://www.wikidata.org/wiki/Q30158686","display_name":"Constraint satisfaction","level":3,"score":0.4020000100135803},{"id":"https://openalex.org/C173404611","wikidata":"https://www.wikidata.org/wiki/Q528588","display_name":"Constraint programming","level":3,"score":0.39410001039505005},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.35600000619888306},{"id":"https://openalex.org/C81669768","wikidata":"https://www.wikidata.org/wiki/Q2359161","display_name":"Precision and recall","level":2,"score":0.33899998664855957},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.3257000148296356},{"id":"https://openalex.org/C29230964","wikidata":"https://www.wikidata.org/wiki/Q5164376","display_name":"Constraint learning","level":5,"score":0.3077000081539154},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30059999227523804},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.298799991607666},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2793999910354614},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2721000015735626},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2581000030040741},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.16943","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.16943","pdf_url":"https://arxiv.org/pdf/2510.16943","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.16943","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.16943","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.16943","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.16943","pdf_url":"https://arxiv.org/pdf/2510.16943","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Large":[0],"language":[1,10],"models":[2],"(LLMs)":[3],"are":[4],"increasingly":[5],"used":[6],"to":[7],"convert":[8],"natural":[9],"descriptions":[11],"into":[12],"mathematical":[13],"optimization":[14,98,203],"formulations.":[15,51],"Current":[16],"evaluations":[17],"often":[18],"treat":[19],"formulations":[20],"as":[21,62],"a":[22,44,194],"whole,":[23],"relying":[24],"on":[25,83,131],"coarse":[26],"metrics":[27,60,152],"like":[28],"solution":[29,145],"accuracy":[30],"or":[31,36],"runtime,":[32],"which":[33,139],"obscure":[34],"structural":[35,142],"numerical":[37],"errors.":[38],"In":[39],"this":[40],"study,":[41],"we":[42],"present":[43],"comprehensive,":[45],"component-level":[46],"evaluation":[47,199],"framework":[48,58,192],"for":[49,66,167,196],"LLM-generated":[50],"Beyond":[52],"the":[53],"conventional":[54],"optimality":[55],"gap,":[56],"our":[57],"introduces":[59],"such":[61],"precision":[63,148],"and":[64,69,72,79,86,94,118,135,144,149,183],"recall":[65,134],"decision":[67,150],"variables":[68],"constraints,":[70],"constraint":[71,133,137,172,178],"objective":[73],"root":[74],"mean":[75],"squared":[76],"error":[77],"(RMSE),":[78],"efficiency":[80],"indicators":[81],"based":[82],"token":[84],"usage":[85],"latency.":[87],"We":[88],"evaluate":[89],"GPT-5,":[90],"LLaMA":[91],"3.1":[92],"Instruct,":[93],"DeepSeek":[95],"Math":[96],"across":[97],"problems":[99],"of":[100,200],"varying":[101],"complexity":[102],"under":[103],"six":[104],"prompting":[105,120],"strategies.":[106],"Results":[107],"show":[108],"that":[109,126],"GPT-5":[110],"consistently":[111],"outperforms":[112],"other":[113],"models,":[114],"with":[115],"chain-of-thought,":[116],"self-consistency,":[117],"modular":[119],"proving":[121],"most":[122],"effective.":[123],"Analysis":[124],"indicates":[125],"solver":[127],"performance":[128],"depends":[129],"primarily":[130],"high":[132],"low":[136],"RMSE,":[138],"together":[140],"ensure":[141],"correctness":[143],"reliability.":[146],"Constraint":[147],"variable":[151],"play":[153],"secondary":[154],"roles,":[155],"while":[156],"concise":[157,185],"outputs":[158,186],"enhance":[159],"computational":[160,188],"efficiency.":[161,189],"These":[162],"findings":[163],"highlight":[164],"three":[165],"principles":[166],"NLP-to-optimization":[168],"modeling:":[169],"(i)":[170],"Complete":[171],"coverage":[173],"prevents":[174],"violations,":[175],"(ii)":[176],"minimizing":[177],"RMSE":[179],"ensures":[180],"solver-level":[181],"accuracy,":[182],"(iii)":[184],"improve":[187],"The":[190],"proposed":[191],"establishes":[193],"foundation":[195],"fine-grained,":[197],"diagnostic":[198],"LLMs":[201],"in":[202],"modeling.":[204]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-22T00:00:00"}
